WO2001050177A1

WO2001050177A1 - Optical apparatus which uses a virtually imaged phased array to produce chromatic dispersion

Info

Publication number: WO2001050177A1
Application number: PCT/US2000/033679
Authority: WO
Inventors: Masataka Shirasaki; Simon 'Xiaofan' CAO
Original assignee: Fujitsu Limited; Avanex Corporation
Priority date: 1999-12-14
Filing date: 2000-12-13
Publication date: 2001-07-12
Also published as: AU2727001A; CN100514118C; JP4373046B2; CN1409828A; EP1252544A1; JP2004500600A

Abstract

A VIPA generator (240) produces a light traveling from the VIPA generator (240), and the mirror (254) reflects the light back to the generator (240).

Description

TITLE OF THE INVENTION

OPTICAL APPARATUS WHICH USES A VIRTUALLY IMAGED PHASED

ARRAY TO PRODUCE CHROMATIC DISPERSION

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. application 09/461 ,277, filed December

14, 1999; and U.S. application 09/576,541, filed May 23, 2000, which are

incorporated herein by reference.

This application also claims priority to U.S. application titled "OPTICAL

APPARATUS WHICH USES A VIRTUALLY IMAGED PHASED ARRAY TO

PRODUCE CHROMATIC DISPERSION," inventors Simon Cao and Masataka

Shirasaki, serial number not vet assigned, attorney docket 21.1930cip2, filed

December 4, 2000, and which is incorporated herein by reference.

The subject matter of the present application is related to U.S. application

08/796,842, filed February 7, 1997; U.S. application 08/685,362, filed My 24, 1996;

and U.S. application 08/910,251, filed August 13, 1997; which are incorporated

herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention The present invention relates to an apparatus producing chromatic dispersion,

and which can be used to compensate for chromatic dispersion accumulated in an optical fiber transmission line. More specifically, the present invention relates to an

apparatus which uses a virtually imaged phased array to produce chromatic dispersion.

2. Description of the Related Art

FIG. 1(A) is a diagram illustrating a conventional fiber optic communication

system, for transmitting information via light. Referring now to FIG. 1(A), a

transmitter 30 transmits pulses 32 through an optical fiber 34 to a receiver 36.

Unfortunately, chromatic dispersion, also referred to as "wavelength dispersion", of

optical fiber 34 degrades the signal quality of the system. More specifically,

as a result of chromatic dispersion, the propagating speed of a signal in an optical fiber

depends on the wavelength of the signal. For example, when a pulse with a longer

wavelength (for example, a pulse with wavelengths representing a "red" color pulse)

travels faster than a pulse with a shorter wavelength (for example, a pulse with

wavelengths representing a "blue" color pulse), the dispersion is typically referred to

as "normal" dispersion. By contrast, when a pulse with a shorter wavelength (such as

a blue color pulse) is faster than a pulse with a longer wavelength (such as a red color

pulse), the dispersion is typically referred to as "anomalous" dispersion.

Therefore, if pulse 32 consists of red and blue color pulses when emitted from

transmitter 30, pulse 32 will be split as it travels through optical fiber 34 so that a

separate red color pulse 38 and a blue color pulse 40 are received by receiver 36 at

different times. FIG. 1(A) illustrates a case of "normal" dispersion, where a red color

pulse travels faster than a blue color pulse. As another example of pulse transmission, FIG. 1(B) is a diagram illustrating

a pulse 42 having wavelength components continuously from blue to red, and

transmitted by transmitter 30. FIG. 1(C) is a diagram illustrating pulse 42 when

arrived at receiver 36. Since the red component and the blue component travel at

different speeds, pulse 42 is broadened in optical fiber 34 and, as illustrated by FIG.

1(C), is distorted by chromatic dispersion. Such chromatic dispersion is very common

in fiber optic communication systems, since all pulses include a finite range of

wavelengths.

Therefore, for a fiber optic communication system to provide a high

transmission capacity, the fiber optic communication system must compensate for

chromatic dispersion.

FIG. 2 is a diagram illustrating a fiber optic communication system having an

opposite dispersion component to compensate for chromatic dispersion. Referring now to FIG. 2, generally, an opposite dispersion component 44 adds an "opposite"

dispersion to a pulse to cancel dispersion caused by traveling through optical fiber 34.

There are conventional devices which can be used as opposite dispersion

component 44. For example, FIG. 3 is a diagram illustrating a fiber optic

communication system having a dispersion compensation fiber which has a special

cross-section index profile and thereby acts as an opposite dispersion component, to

compensate for chromatic dispersion. Referring now to FIG. 3, a dispersion

compensation fiber 46 provides an opposite dispersion to cancel dispersion caused by

optical fiber 34. However, a dispersion compensation fiber is expensive to manufacture, and must be relatively long to sufficiently compensate for chromatic

dispersion. For example, if optical fiber 34 is 100 km in length, then dispersion

compensation fiber 46 should be approximately 20 to 30 km in length.

FIG. 4 is a diagram illustrating a chirped grating for use as an opposite

dispersion component, to compensate for chromatic dispersion. Referring now to FIG.

4, light traveling through an optical fiber and experiencing chromatic dispersion is

provided to an input port 48 of an optical circulator 50. Circulator 50 provides the

light to chirped grating 52. Chirped grating 52 reflects the light back towards

circulator 50, with different wavelength components reflected at different distances

along chirped grating 52 so that different wavelength components travel different

distances to thereby compensate for chromatic dispersion. For example, chirped

grating 52 can be designed so that longer wavelength components are reflected at a

farther distance along chirped grating 52, and thereby travel a farther distance than

shorter wavelength components. Circulator 50 then provides the light reflected from

chirped grating 52 to an output port 54. Therefore, chirped grating 52 can add

opposite dispersion to a pulse.

Unfortunately, a chirped grating has a very narrow bandwidth for reflecting

pulses, and therefore cannot provide a wavelength band sufficient to compensate for

light including many wavelengths, such as a wavelength division multiplexed light. A

number of chirped gratings may be cascaded for wavelength multiplexed signals, but

this results in an expensive system. Instead, a chirped grating with a circulator, as in FIG. 4, is more suitable for use when a single channel is transmitted through a fiber

optic communication system.

FIG. 5 is a diagram illustrating a conventional diffraction grating, which can

be used in producing chromatic dispersion. Referring now to FIG. 5, a diffraction

grating 56 has a grating surface 58. Parallel lights 60 having different wavelengths are

incident on grating surface 58. Lights are reflected at each step of grating surface 58

and interfere with each other. As a result, lights 62, 64 and 66 having different

wavelengths are output from diffraction grating 56 at different angles. A diffraction

grating can be used in a spatial grating pair arrangement, as discussed in more detail

below, to compensate for chromatic dispersion.

More specifically, FIG. 6(A) is a diagram illustrating a spatial grating pair arrangement for use as an opposite dispersion component, to compensate for chromatic

dispersion. Referring now to FIG. 6(A), light 67 is diffracted from a first diffraction

grating 68 into a light 69 for shorter wavelength and a light 70 for longer wavelength.

These lights 69 and 70 are then diffracted by a second diffraction grating 71 into lights

propagating in the same direction. As can be seen from FIG. 6(A), wavelength

components having different wavelengths travel different distances, to add opposite

dispersion and thereby compensate for chromatic dispersion. Since longer wavelengths

(such as lights 70) travel longer distance than shorter wavelengths (such as lights 69),

a spatial grating pair arrangement as illustrated in FIG. 6(A) has anomalous dispersion.

FIG. 6(B) is a diagram illustrating an additional spatial grating pair arrangement

for use as an opposite dispersion component, to compensate for chromatic dispersion. As illustrated in FIG. 6(B), lenses 72 and 74 are positioned between first and second

diffraction gratings 68 and 71 so that they share one of the focal points. Since longer

wavelengths (such as lights 70) travel shorter distance than shorter wavelengths (such

as lights 69), a spatial grating pair arrangement as illustrated in FIG. 6(B) has normal

dispersion.

A spatial grating pair arrangement as illustrated in FIGS. 6(A) and 6(B) is

typically used to control dispersion in a laser resonator. However, a practical spatial

grating pair arrangement cannot provide a large enough dispersion to compensate for

the relatively large amount of chromatic dispersion occurring in a fiber optic

communication system. More specifically, the angular dispersion produced by a

diffraction grating is usually extremely small, and is typically approximately 0.05

degrees/nm. Therefore, to compensate for chromatic dispersion occurring in a fiber

optic communication system, first and second gratings 68 and 71 would have to be

separated by very large distances, thereby making such a spatial grating pair

arrangement impractical.

SUMMARY OF THE INVENTION

Therefore, it is an object ofthe present invention to provide an apparatus which

produces chromatic dispersion, and which is practical for compensating for chromatic

dispersion accumulated in an optical fiber.

Objects of the present invention are achieved by providing an apparatus which

includes a device herein referred to as a "virtually imaged phased array", "VIPA" or "VIPA generator" . The VIPA generator produces a light propagating away from the

VIPA generator. The apparatus also includes a mirror or reflecting surface which

returns the light back to the VIPA generator to undergo multiple reflection inside the

VIPA generator.

Objects of the present invention are achieved by providing an apparatus

comprising a VIPA generator and a reflecting surface. The VIPA generator receives

an input light at a respective wavelength and produces a corresponding collimated

output light traveling from the VIPA generator in a direction determined by the

wavelength of the input light. The reflecting surface reflects the output light back to

the VIPA generator. The reflecting surface has different curvatures at different

positions along a direction perpendicular to an angular dispersion direction of the VIPA generator, or a plane which includes the traveling directions of collimated output

light from the VIPA generator for input light at different wavelengths.

Objects of the present invention are also achieved by providing an apparatus

which includes a VIPA generator, a reflecting surface, and a lens. The VIPA generator

receives an input light at a respective wavelength and produces a corresponding

collimated output light traveling from the VIPA generator in a direction determined by the wavelength ofthe input light, the output light thereby being spatially distinguishable

from an output light produced for an input light at a different wavelength. The

reflecting surface has a cone shape, or a modified cone shape. The lens focuses the

output light traveling from the VIPA generator onto the reflecting surface so that the reflecting surface reflects the output light, the reflected light being directed by the lens back to the VIPA generator. The modified cone shape can be designed so that the

apparatus provides a uniform chromatic dispersion to light in the same channel of a

wavelength division multiplexed light.

Objects of the present invention are achieved by providing an apparatus

comprising an angular dispersive component and a reflecting surface. The angular

dispersive component has a passage area to receive light into, and to output light from,

the angular dispersive component. The angular dispersive component receives, through

the passage area, an input light having a respective wavelength within a continuous

range of wavelengths, and causes multiple reflection of the input light to produce

self-interference that forms a collimated output light which travels from the angular dispersive component along a direction determined by the wavelength ofthe input light

and is thereby spatially distinguishable from an output light formed for an input light

having any other wavelength within the continuous range of wavelengths. The

reflecting surface reflects the output light back to the angular dispersive component to

undergo multiple reflection in the angular dispersive component and then be output

from the passage area. The reflecting surface has different curvatures at different

positions along a direction which is perpendicular to a plane which includes the travel

direction of collimated output light from the angular dispersive component for input

light at different wavelengths.

Moreover, objects of the present invention are achieved by providing an

apparatus which includes an angular dispersive component and a reflecting surface.

The angular dispersive component has a passage area to receive light into, and to output light from, the angular dispersive component. The angular dispersive

component receives, through the passage area, a line focused input light and causes

multiple reflection ofthe input light to produce self-interference that forms a collimated

output light which travels from the angular dispersive component along a direction

determined by the wavelength of the input light and is thereby spatially distinguishable

from an output light formed for an input light having a different wavelength. The

light at different wavelengths.

Objects of the present invention are still further achieved by providing an

apparatus comprising first and second reflecting surfaces, and a mirror. The second

reflecting surface has a reflectivity which causes a portion of light incident thereon to

be transmitted therethrough. An input light at a respective wavelength is focused into

a line. The first and second reflecting surfaces are positioned so that the input light

radiates from the line to be reflected a plurality of times between the first and second

reflecting surfaces and thereby cause a plurality of lights to be transmitted through the

second reflecting surface. The plurality of transmitted lights interfere with each other

to produce a collimated output light which travels from the second reflecting surface

along a direction determined by the wavelength of the input light, and is thereby specially distinguishable from an output light formed for an input light having a

different wavelength. The mirror surface reflects output the light back to the second reflecting surface to pass through the second reflecting surface and undergo multiple

reflection between the first and second reflecting surfaces. The mirror surface has

different curvatures at different positions along a direction which is perpendicular to

a plane which includes the travel direction of collimated output light from the second

reflecting surface for input light at different wavelengths.

Objects of the present invention are also achieved by providing an apparatus

which includes a VIPA generator, a lens, first and second mirrors, and a wavelength

filter. The VIPA generator receives a line focused wavelength division multiplexed

(WDM) light including light at first and second wavelengths, and produces collimated first and second output lights corresponding, respectively, to the first and second

wavelengths. The first and second output lights travel from the VIPA generator in first

and second directions, respectively, determined by the first and second wavelengths,

respectively. The lens focuses the first and second output lights traveling from the

VIPA generator. The first and second mirrors each having a cone shape or a modified cone shape for producing a uniform chromatic dispersion. The wavelength filter filters

light focused by the lens so that light at the first wavelength is focused to the first

mirror and reflected by the first mirror, and light at the second wavelength is focused

to the second mirror and reflected by the second mirror . The reflected first and second

lights are directed by the wavelength filter and the lens back to the VIPA generator. Moreover, objects of the present invention are achieved by causing the input

light to have a double-hump shaped far field distribution. For example, a phase mask

can be provided on an input fiber, or on a surface of the VIPA generator, to cause the

input light to have a double-hump shaped far field distribution.

Objects of the present invention are achieved by providing an apparatus which

includes a device herein referred to as a "virtually imaged phased array", "VIPA" or

"VIPA generator" . The VIPA generator produces a light propagating away from the

VIPA generator.

Objects of the present invention are achieved by providing an apparatus

output light traveling from the VIPA generator in a direction determined by the

positions along a direction perpendicular to an angular dispersion direction of the

VIPA generator, or a plane which includes the traveling directions of collimated output

light from the VIPA generator for input light at different wavelengths.

Objects of the present invention are also achieved by providing an apparatus

which includes a VIPA generator , a reflecting surface , and a lens . The VIPA generator

receives an input light at a respective wavelength and produces a corresponding collimated output light traveling from the VIPA generator in a direction determined by

the wavelength ofthe input light, the output light thereby being spatially distinguishable

from an output light produced for an input light at a different wavelength. The

output light traveling from the VIPA generator onto the reflecting surface so that the

reflecting surface reflects the output light, the reflected light being directed by the lens

back to the VIPA generator. The modified cone shape can be designed so that the

wavelength division multiplexed light.

Objects of the present invention are achieved by providing an apparatus

the angular dispersive component. The angular dispersive component receives , through the passage area, an input light having a respective wavelength within a continuous

self-interference that forms a collimated output light which travels from the angular

dispersive component along a direction determined by the wavelength ofthe input light

and is thereby spatially distinguishable from an output light formed for an input light having any other wavelength within the continuous range of wavelengths. The

from the passage area. The reflecting surface has different curvatures at different positions along a direction which is perpendicular to a plane which includes the travel

light at different wavelengths.

Moreover, objects of the present invention are achieved by providing an

The angular dispersive component has a passage area to receive light into, and to

output light from, the angular dispersive component. The angular dispersive

determined by the wavelength ofthe input light and is thereby spatially distinguishable

light at different wavelengths.

Objects of the present invention are still further achieved by providing an

apparatus comprising first and second reflecting surfaces, and a mirror. The second reflecting surface has a reflectivity which causes a portion of light incident thereon to

be transmitted therethrough. An input light at a respective wavelength is focused into a line. The first and second reflecting surfaces are positioned so that the input light

along a direction determined by the wavelength of the input light, and is thereby

specially distinguishable from an output light formed for an input light having a

different wavelength. The mirror surface reflects output the light back to the second

reflecting surface to pass through the second reflecting surface and undergo multiple

reflecting surface for input light at different wavelengths.

Objects of the present invention are also achieved by providing an apparatus

(WDM) light including light at first and second wavelengths, and produces collimated

first and second output lights corresponding, respectively, to the first and second

to the second mirror and reflected by the second mirror. The reflected first and second

lights are directed by the wavelength filter and the lens back to the VIPA generator.

Moreover, objects of the present invention are achieved by causing the input

input light to have a double-hump shaped far field distribution.

Objects ofthe present invention are achieved by providing an apparatus which

includes (a) a variable curvature mirror positioned to reflect light produced by a

virtually imaged phased array (VIPA) generator back to the VIPA generator; and (b)

a rotation axis around which the mirror is rotated to change the curvature ofthe mirror

where the output light is reflected.

Objects of the present invention are also achieved by providing an apparatus

which includes (a) a virtually imaged phased array (VIPA) generator producing a light

traveling from the VIPA generator; (b) a variable curvature mirror positioned to reflect

the light back to the VIPA generator; and (c) a rotation axis around which the mirror

is rotated to change the curvature of the mirror where the output light is reflected.

Objects of the present invention are further achieved by providing an apparatus

which includes (a) a virtually imaged phased array (VIPA) generator receiving an input

light at a respective wavelength and producing a corresponding output light traveling from the VIPA generator in a direction determined by the wavelength ofthe input light;

(b) a variable curvature mirror positioned to reflect the output light back to the VIPA

generator so that the reflected output light travels through the VIPA generator, to

thereby provide dispersion compensation to the input light; and (c) a rotation axis

around which the mirror is rotated to change the curvature of the mirror where the

output light is reflected, to thereby vary an amount of dispersion compensation

provided to the input light.

Moreover, objects of the present invention are achieved by providing an

apparatus which includes (a) a radiation window; (b) first and second reflecting

surfaces in parallel with each other, the first reflecting surface allowing substantially

no light to be transmitted therethrough and being in the same plane as the radiation

window, the second reflecting surface having a reflectivity which causes a portion of

light incident thereon to be transmitted therethrough, where an input light at a

respective wavelength travels through the radiation window and is focused into a line,

and the first and second reflecting surfaces are positioned so that the input light radiates

from the line to be reflected a plurality of times between the first and second reflecting

surfaces and thereby cause a plurality of lights to be transmitted through the second reflecting surface, the plurality of transmitted lights interfering with each other to

produce a collimated output light which travels from the second reflecting surface along

a direction determined by the wavelength of the input light, and is thereby specially

distinguishable from an output light formed for an input light having a different wavelength; (c) a variable curvature mirror reflecting the output light back to the second reflecting surface to pass through the second reflecting surface and undergo

multiple reflection between the first and second reflecting surfaces; and (d) a rotation

axis around which the mirror is rotated to change the curvature ofthe mirror where the

output light is reflected.

Objects of the present invention are achieved by providing an apparatus which

includes (a) a plurality of mirrors having different surface curvatures to reflect light;

and (b) a holder having a rotation axis and holding the plurality of mirrors equidistantly

from the rotation axis, the holder being rotatable around the rotation axis to bring a

different, respective mirror of the plurality of mirrors in position to reflect light

produced by a virtually imaged phased array (VIPA) generator back to the VIPA

generator.

Objects of the present invention are achieved by providing an apparatus which

includes (a) a virtually imaged phased array (VIPA) generator producing light; (b) a

plurality of mirrors having different surface curvatures; and (c) a holder having a

rotation axis and holding the plurality of mirrors equidistantly from the rotation axis,

the holder being rotatable around the rotation axis to bring a different, respective

mirror of the plurality of mirrors in position to reflect the light produced by a VIPA

generator back to the VIPA generator.

In addition, objects of the present invention are achieved by providing an

apparatus which includes (a) a virtually imaged phased array (VIPA) generator

receiving an input light at a respective wavelength and producing a corresponding

output light traveling from the VIPA generator in a direction determined by the wavelength of the input light; (b) a plurality of mirrors having different surface

curvatures; and (c) a holder having a rotation axis and holding the plurality of mirrors

equidistantly from the rotation axis, the holder being rotatable around the rotation axis

to bring a different, respective mirror of the plurality of mirrors in position to reflect

the output light back to the VIPA generator, to thereby provide dispersion

compensation to the input light.

Objects of the present invention are also achieved by providing an apparatus

which includes (a) a radiation window; (b) first and second reflecting surfaces in

parallel with each other, the first reflecting surface allowing substantially no light to

be transmitted therethrough and being in the same plane as the radiation window, the

second reflecting surface having a reflectivity which causes a portion of light incident

thereon to be transmitted therethrough, where an input light at a respective wavelength

travels through the radiation window and is focused into a line, and the first and second

reflecting surfaces are positioned so that the input light radiates from the line to be

reflected a plurality of times between the first and second reflecting surfaces and

thereby cause a plurality of lights to be transmitted through the second reflecting

surface, the plurality of transmitted lights interfering with each other to produce a

collimated output light which travels from the second reflecting surface along a

direction determined by the wavelength of the input light, and is thereby specially

distinguishable from an output light formed for an input light having a different

wavelength; (c) a plurality of mirrors having different surface curvatures; and (d) a

holder having a rotation axis and holding the plurality of mirrors equidistantly from the rotation axis, the holder being rotatable around the rotation axis to bring a different,

respective mirror of the plurality of mirrors in position to reflect the output light back

to the second reflecting surface to pass through the second reflecting surface and

undergo multiple reflection between the first and second surfaces.

Moreover, objects of the present invention are achieved by providing an

apparatus which includes (a) a plurality of fixed mirrors having different surface

curvatures to reflect light; and (b) a rotating mirror rotatable about a rotation axis to

reflect light produced by a virtually imaged phased array (VIPA) generator to a

respective fixed mirror of the plurality of fixed mirrors, and to reflect the light

reflected by the respective fixed mirror back to the VIPA generator.

In addition, objects of the present invention are achieved by providing an

apparatus which includes (a) a virtually imaged phased array (VIPA) generator

producing light; (b) a plurality of fixed mirrors having different surface curvatures to

reflect light; and (c) a rotating mirror rotatable about a rotation axis to reflect light

produced by the VIPA generator to a respective fixed mirror of the plurality of fixed

mirrors, and to reflect the light reflected by the respective fixed mirror back to the

VIPA generator.

Further, objects ofthe present invention are achieved by providing an apparatus

light at a respective wavelength and producing a corresponding output light traveling

from the VIPA generator in a direction determined by the wavelength ofthe input light; (b) a plurality of fixed mirrors having different surface curvatures to reflect light; and (c) a rotating mirror rotatable about a rotation axis to reflect the output light traveling

from the VIPA generator to a respective fixed mirror of the plurality of fixed mirrors,

and to reflect the light reflected by the respective fixed mirror back to the VIPA

generator, to thereby provide dispersion compensation to the input light.

Also, objects of the present invention are achieved by providing an apparatus

wavelength; (c) a plurality of fixed mirrors having different surface curvatures to

reflect light; and (d) a rotating mirror rotatable about a rotation axis to reflect the output light traveling from the second reflecting surface to a respective fixed mirror

of the plurality of fixed mirrors , and to reflect the light reflected by the respective fixed mirror back to the second reflecting surface to pass through the second reflecting

surface and undergo multiple reflection between the first and second reflecting

surfaces.

Objects of the present invention are achieved by providing an apparatus which

includes (a) a plurality of fixed mirrors having different surface curvatures to reflect

light; and (b) an off-axis parabolic mirror rotatable about a rotation axis to reflect light

produced by a virtually imaged phased array (VIPA) generator to a respective fixed

mirror of the plurality of fixed mirrors, and to reflect the light reflected by the

respective fixed mirror back to the VIPA generator.

Further, objects ofthe present invention are achieved by providing an apparatus

which includes (a) a virtually imaged phased array (VIPA) generator producing light;

(b) a plurality of fixed mirrors having different surface curvatures to reflect light; and

(c) an off-axis parabolic mirror rotatable about a rotation axis to reflect light produced

by the VIPA generator to a respective fixed mirror of the plurality of fixed mirrors,

generator.

In addition, objects of the present invention are achieved by providing an

apparatus which includes (a) a virtually imaged phased array (VIPA) generator

output light traveling from the VIPA generator in a direction determined by the

wavelength of the input light; (b) a plurality of fixed mirrors having different surface

curvatures to reflect light; and (c) an off-axis parabolic mirror rotatable about a rotation axis to reflect the output light traveling from the VIPA generator to a respective fixed

respective fixed mirror back to the VIPA generator, to thereby provide dispersion

compensation to the input light.

Moreover, objects of the present invention are achieved by providing an

and the first and second reflecting surfaces are positioned so that the input light radiates from the line to be reflected a plurality of times between the first and second reflecting

surfaces and thereby cause a plurality of lights to be transmitted through the second

reflecting surface, the plurality of transmitted lights interfering with each other to

produce a collimated output light which travels from the second reflecting surface along a direction determined by the wavelength of the input light, and is thereby specially

reflect light; and (d) an off-axis parabolic mirror rotatable about a rotation axis to reflect the output light traveling from the second reflecting surface to a respective fixed mirror of the plurality of fixed mirrors, and to reflect the light reflected by the respective fixed mirror back to the second reflecting surface to pass through the second

reflecting surface and undergo multiple reflection between the first and second

reflecting surfaces.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects and advantages of the invention will become apparent

and more readily appreciated from the following description of the preferred

embodiments, taken in conjunction with the accompanying drawings of which:

FIG. 1(A) (prior art) is a diagram illustrating a conventional fiber optic

communication system.

FIG. 1(B) is a diagram illustrating a pulse before transmission through a fiber

in a conventional fiber optic communication system.

FIG. 1(C) is a diagram illustrating a pulse after being transmitted through a fiber in a conventional fiber optic communication system.

FIG. 2 (prior art) is a diagram illustrating a fiber optic communication system

having an opposite dispersion component to compensate for chromatic dispersion.

FIG. 3 (prior art) is a diagram illustrating a fiber optic communication system

having a dispersion compensation fiber as an opposite dispersion component.

FIG. 4 (prior art) is a diagram illustrating a chirped grating for use as an

opposite dispersion component, to compensate for chromatic dispersion.

FIG. 5 (prior art) is a diagram illustrating a conventional diffraction grating. FIG. 6(A) (prior art) is a diagram illustrating a spatial grating pair arrangement

for production of anomalous dispersion.

FIG. 6(B) (prior art) is a diagram illustrating a spatial grating pair arrangement

for production of normal dispersion.

FIG. 7 is a diagram illustrating a VIPA.

FIG. 8 is a detailed diagram illustrating the VIPA of FIG. 7.

FIG. 9 is a diagram illustrating a cross-section along lines IX—IX of the VIPA

illustrated in FIG. 7.

FIG. 10 is a diagram illustrating interference between reflections produced by

a VIPA.

FIG. 11 is a diagram illustrating a cross-section along lines IX-IX of the VIPA

illustrated in FIG. 7, for determining the tilt angle of input light.

FIGS. 12(A), 12(B), 12(C) and 12(D) are diagrams illustrating a method for

producing a VIPA.

FIG. 13 is a diagram illustrating an apparatus which uses a VIPA as an angular

dispersion component to produce chromatic dispersion.

FIG. 14 is a more detailed diagram illustrating the operation of the apparatus

in FIG. 13.

FIG. 15 is a diagram illustrating various orders of interference of a VIPA. FIG. 16 is a graph illustrating the chromatic dispersion for several channels of

a wavelength division multiplexed light. FIG. 17 is a diagram illustrating different channels of a wavelength division

multiplexed light being focused at different points on a mirror by a VIPA.

FIG. 18 is a diagram illustrating a side view of an apparatus which uses a VIPA

to provide variable chromatic dispersion to light.

FIG. 19 is a diagram illustrating a side view of an apparatus which uses a VIPA

to provide variable chromatic dispersion to light.

FIGS. 20(A) and 20(B) are diagrams illustrating side views of an apparatus

which uses a VIPA to provide chromatic dispersion to light.

FIG. 21 is a graph illustrating the output angle of a luminous flux from a VIPA

versus wavelength of the luminous flux.

FIG. 22 is a graph illustrating the angular dispersion of a VIPA versus the

wavelength of a luminous flux.

FIG. 23 is a graph illustrating the effect of different mirror types in an

apparatus using a VIPA.

FIG. 24 is a diagram illustrating chromatic dispersion versus wavelength in an

apparatus using a VIPA, for different types of mirrors used in the apparatus.

FIG. 25 is a graph illustrating the effect of a mirror in an apparatus which uses

a VIPA.

FIG. 26 is a graph illustrating constant chromatic dispersion of an apparatus

using a VIPA.

FIG. 27 is a graph illustrating characteristics of different mirror designs for an apparatus using a VIPA. FIGS. 28(A), 28(B), 28(C), 28(D), 28(E) and 28(F) are diagrams illustrating

examples of mirrors of an apparatus using a VIPA.

FIG. 29 is a diagram illustrating a cylindrical mirror.

FIG. 30(A) is a graph illustrating chromatic dispersion versus wavelength for

one channel of a wavelength division multiplexed light, after undergoing chromatic

dispersion compensation with a VIPA with a cylindrical mirror.

FIG. 30(B) is a graph illustrating chromatic dispersion versus wavelength for

all wavelengths of a wavelength division multiplexed light, after undergoing chromatic dispersion compensation with a VIPA with a cylindrical mirror.

FIG. 31(A) is a graph illustrating chromatic dispersion versus wavelength for

dispersion compensation with a VIPA with a modified cylindrical mirror.

FIG. 31(B) is a graph illustrating chromatic dispersion versus wavelength for

all wavelengths of a wavelength division multiplexed light, after undergoing chromatic dispersion compensation with a VIPA with a modified cylindrical mirror.

FIG. 32 is a diagram illustrating a top view of an apparatus using a VIPA to

provide variable chromatic dispersion to light, according to a further embodiment of

the present invention. FIGS. 33(A) and 33(B) are diagrams illustrating how a mirror can be formed from a section of a cone, according to an embodiment of the

present invention.

FIG. 34(A) is a graph illustrating the amount of chromatic dispersion versus

wavelength within one channel for different radii of curvature of a mirror in an apparatus using a VIPA to provide chromatic dispersion, according to an embodiment

of the present invention.

FIG. 34(B) is a diagram illustrating radii of curvature of FIG. 34(A), according

to an embodiment of the present invention.

FIG. 34(C) is a diagram illustrating modified radii of curvature, according to

an embodiment of the present invention.

FIG. 35 is a graph illustrating the chromatic dispersion versus wavelength for

different radii of curvature in an apparatus using a VIPA to provide chromatic

dispersion, according to an embodiment of the present invention.

FIG. 36 is a diagram illustrating various angles in an apparatus which uses a

VIPA, according to an embodiment of the present invention.

FIG. 37 is an additional diagram illustrating angles in an apparatus which uses

a VIPA, according to an embodiment of the present invention.

FIG. 38 is a diagram illustrating how chromatic dispersion is generated in an

apparatus using a VIPA, according to an embodiment of the present invention.

FIGS. 39(A), 39(B) and 39(C) are graphs illustrating mirror curves, according

to an embodiment of the present invention.

FIG. 40 is a diagram illustrating a cone for forming a mirror, according to an

embodiment of the present invention. FIG. 41 is a diagram illustrating a step shaped mirror surface, according to an

embodiment of the present invention. FIG. 42 is a diagram illustrating a side view of an apparatus using a VIPA to

provide chromatic dispersion slope, according to an additional embodiment of the

present invention.

FIG. 43(A) is a graph illustrating the amount of chromatic dispersion for all

wavelengths with the apparatus in FIG. 42 using a cone shaped mirror, according to

an embodiment of the present invention.

FIG. 43(B) is a graph illustrating the amount of chromatic dispersion for all

wavelengths with the apparatus in FIG. 42 using a modified cone shaped mirror,

according to an embodiment of the present invention.

FIG. 44 is a diagram illustrating the use of a holographic grating between a

VIPA and a lens, according to an embodiment of the present invention.

FIG. 45 is a diagram illustrating the use of a reflection type grating between

a VIPA and a lens, according to an embodiment of the present invention.

FIGS. 46 and 47 are diagrams illustrating the use of quarter wave plate,

according to embodiments of the present invention.

FIG. 48(A) is a diagram illustrating a side or top view of an apparatus which

uses a VIPA to provide different chromatic dispersion for different channels, according

to a still further embodiment of the present invention.

FIG. 48(B) is a graph illustrating chromatic dispersion versus wavelength for

the apparatus in FIG. 48(A), according to an embodiment of the present invention. FIG. 49 is a diagram illustrating a side or top view of an apparatus which uses

a VIPA to provide different chromatic dispersion for different channels, according to

an embodiment of the present invention.

FIG. 50 is a graph illustrating insertion loss in an apparatus which uses a VIPA

to provide chromatic dispersion, according to an embodiment of the present invention.

FIG. 51 is a diagram illustrating different diffraction efficiency at different

wavelengths in an apparatus which uses a VIPA to provide chromatic dispersion,

according to an embodiment of the present invention.

FIG. 52 is a diagram illustrating the light intensity of light traveling out of a

fiber and into a VIPA, according to an embodiment of the present invention.

FIG. 53 is a diagram illustrating a side view of an optical phase mask on an

input fiber to produce a double-humped shape far field distribution, in an apparatus

which uses a VIPA to provide chromatic dispersion, according to an embodiment ofthe

present invention.

FIG. 54 is a diagram illustrating a cross-sectional view along lines 54-54 in

FIG. 53, according to an embodiment of the present invention.

FIG. 55 is a diagram illustrating a side view of phase masks on a VIPA to

provide a double-humped shape far field distribution with respect to light received

inside the VIPA, according to an embodiment of the present invention.

FIG. 56 is a diagram illustrating a side view of phase masks on a VIPA to provide a double-humped shape far field distribution with respect to light received

inside the VIPA, according to an additional embodiment of the present invention. FIGS. 57 and 58 are diagrams illustrating a side view of phase masks on a

VIPA to provide a double-humped shape far field distribution with respect to light

received inside the VIPA, according to an additional embodiment of the present

invention.

FIG. 59 is a diagram illustrating excessive loss added to a loss curve, according

to an embodiment of the present invention.

FIG. 60 is a diagram illustrating the use of an excess loss component to provide

excess loss, according to an embodiment of the present invention.

FIG. 61 is a diagram illustrating a side view of a mirror for use with a VIPA

to provide chromatic dispersion, according to an embodiment of the present invention .

FIG. 62 is a diagram illustrating a front view of a mirror, according to an

embodiment of the present invention.

FIGS. 63(A), 63(B) and 63(C) are diagrams illustrating a way to modulate effective reflectivity in an apparatus using a VIPA, according to an embodiment ofthe

present invention.

FIG. 64 is a diagram illustrating the use of a grating between a VIPA and a

lens, according to an embodiment of the present invention.

FIGS. 65, 66 and 67 are diagrams illustrating the use of a VIPA with a movable

mirror, according to embodiments of the present invention.

FIGS . 68 and 69 are diagrams illustrating a tunable dispersion compensator that

utilizes a rotatable variably curved mirror, according to an embodiment of the present

invention. FIG. 70 is a diagram illustrating an example of a variably curved mirror for

utilization as part of a tunable dispersion compensator, according to an embodiment of

the present invention.

FIG. 71 is a diagram illustrating a tunable dispersion compensator that utilizes

a plurality of curved mirrors or mirror segments, according to an embodiment of the

present invention.

FIG. 72 is a diagram illustrating a tunable dispersion compensator that utilizes

a plurality of curved mirrors or mirror segments and a rotatable flat mirror, according

to an embodiment of the present invention.

FIG. 73 is a diagram illustrating a tunable dispersion compensator that utilizes

a plurality of curved mirrors or mirror segments and a rotatable off-axis parabolic

mirror, according to an embodiment of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Reference will now be made in detail to the present preferred embodiments of

the present invention, examples of which are illustrated in the accompanying drawings,

wherein like reference numerals refer to like elements throughout.

FIG. 7 is a diagram illustrating a virtually imaged phased array (VIPA).

Moreover, hereinafter, the terms "virtually imaged phased array," "VIPA" and "VIPA

generator" may be used interchangeably.

Referring now to FIG. 7, a VIPA 76 is preferably made of a thin plate of glass.

An input light 77 is focused into a line 78 with a lens 80, such as a semi-cylindrical lens, so that input light 77 travels into VIPA 76. Line 78 is hereinafter referred to as

"focal line 78". Input light 77 radially propagates from focal line 78 to be received

inside VIPA 76. VIPA 78 then outputs a luminous flux 82 of collimated light, where

the output angle of luminous flux 82 varies as the wavelength of input light 77 changes.

For example, when input light 77 is at a wavelength λl, VIPA 76 outputs a luminous

flux 82a at wavelength λl in a specific direction. When input light 77 is at a

wavelength λl, VIPA 76 outputs a luminous flux 82b at wavelength λl in a different

direction. Therefore, VIPA 76 produces luminous fluxes 82a and 82b which are

spatially distinguishable from each other.

FIG. 8 is a detailed diagram illustrating VIPA 76. Referring now to FIG. 8,

VIPA 76 includes a plate 120 made of, for example, glass, and having reflecting films

122 and 124 thereon. Reflecting film 122 preferably has a reflectance of approximately

95% or higher, but less than 100% . Reflecting film 124 preferably has a reflectance

of approximately 100% . A radiation window 126 is formed on plate 120 and

preferably has a reflectance of approximately 0% reflectance.

Input light 77 is focused into focal line 78 by lens 80 through radiation window 126, to undergo multiple reflection between reflecting films 122 and 124. Focal line

78 is preferably on the surface of plate 120 to which reflecting film 122 is applied.

Thus, focal line 78 is essentially line focused onto reflecting film 122 through radiation

window 126. The width of focal line 78 can be referred to as the "beam waist" of input

light 77 as focused by lens 80. Thus, the embodiment of the present invention as

illustrated is FIG. 8 focuses the beam waist of input light 77 onto the far surface (that is, the surface having reflecting film 122 thereon) of plate 120. By focusing the beam

waist on the far surface of plate 120, the present embodiment of the present invention

reduces the possibility of overlap between (i) the area of radiation window 126 on the

surface of plate 120 covered by input light 77 as it travels through radiation window

126 (for example, the area "a" illustrated in FIG. 11, discussed in more detail further

below), and (ii) the area on reflecting film 124 covered by input light 77 when input

light 77 is reflected for the first time by reflecting film 124 (for example, the area "b" illustrated in FIG. 11 , discussed in more detail further below) . It is desirable to reduce

such overlap to ensure proper operation of the VIPA.

In FIG. 8, an optical axis 132 of input light 77 has a small tilt angle θ. Upon

the first reflection off of reflecting film 122, 5% of the light passes through reflecting

film 122 and diverges after the beam waist, and 95 % of the light is reflected towards

reflecting film 124. After being reflecting by reflecting film 124 for the first time, the

light again hits reflecting film 122 but is displaced by an amount d. Then, 5 % of the

light passes through reflecting film 122. In a similar manner, as illustrated in FIG. 8,

the light is split into many paths with a constant separation d. The beam shape in each

path forms so that the light diverges from virtual images 134 of the beam waist.

Virtual images 134 are located with constant spacing 2t along a line that is normal to

plate 120, where t is the thickness of plate 120. The positions of the beam waists in

virtual images 134 are self-aligned, and there is no need to adjust individual positions.

The lights diverging from virtual images 134 interfere with each other and form collimated light 136 which propagates in a direction that changes in accordance with

the wavelength of input light 77.

The spacing of light paths is d = 2tSinθ, and the difference in the path lengths

between adjacent beams is 2tCosθ . The angular dispersion is proportional to the ratio

of these two numbers, which is cotθ. As a result, a VIPA produces a significantly

large angular dispersion.

As easily seen from FIG. 8, the term "virtually imaged phased array" arises

from the formation of an array of virtual images 134.

FIG. 9 is a diagram illustrating a cross-section along lines IX--IX of VIPA 76

illustrated in FIG. 7. Referring now to FIG. 9, plate 120 has reflecting surfaces 122

and 124 thereon. Reflecting surfaces 122 and 124 are in parallel with each other and

spaced by the thickness t of plate 120. Reflecting surfaces 122 and 124 are typically

reflecting films deposited on plate 120. As previously described, reflecting surface 124

has a reflectance of approximately 100%, except in radiation window 126, and

reflecting surface 122 has a reflectance of approximately 95% or higher. Therefore,

reflecting surface 122 has a transmittance of approximately 5% or less so that

approximately 5 % of less of light incident on reflecting surface 122 will be transmitted

therethrough and approximately 95% or more of the light will be reflected. The

reflectances of reflecting surfaces 122 and 124 can easily be changed in accordance

with the specific VIPA application. However, generally, reflecting surface 122 should

have a reflectance which is less than 100% so that a portion of incident light can be transmitted therethrough. Reflecting surface 124 has radiation window 126 thereon. Radiation window

126 allows light to pass therethrough, and preferably has no reflectance, or a very low

reflectance. Radiation window 126 receives input light 77 to allow input light 77 to be

received between, and reflected between, reflecting surfaces 122 and 124.

Since FIG. 9 represents a cross-section along lines IX— IX in FIG. 7, focal line

78 in FIG. 7 appears as a "point" in FIG. 9. Input light 77 then propagates radially

from focal line 78. Moreover, as illustrated in FIG. 9, focal line 78 is positioned on

reflecting surface 122. Although it is not required for focal line 78 to be on reflecting

surface 122, a shift in the positioning of focal line 78 may cause small changes in the characteristics of VIPA 76.

As illustrated in FIG. 9, input light 77 enters plate 120 through an area A0 in

radiation window 126, where points P0 indicate peripheral points of area A0.

Due to the reflectivity of reflecting surface 122, approximately 95% or more

of input light 77 is reflected by reflecting surface 122 and is incident on area Al of

reflecting surface 124. Points PI indicate peripheral points of area Al. After

reflecting off area Al on reflecting surface 124, input light 77 travels to reflecting

surface 122 and is partially transmitted through reflecting surface 122 as output light

Outl defined by rays Rl. In this manner, as illustrated in FIG. 9, input light 77

experiences multiple reflections between reflecting surfaces 122 and 124, wherein each

reflection off of reflecting surface 122 also results in a respective output light being

transmitted therethrough. Therefore, for example, each time immediately after input

light 77 reflects off of areas A2, A3 and A4 on reflecting surface 124, input light 77 reflects off of reflecting surface 122 to produce output lights Out2, Out3 and Out4.

Points P2 indicate peripheral points of area A2, points P3 indicate peripheral points of

area A3, and points P4 indicate peripheral points of area A4. Output light Out2 is

defined by rays R2, output light Out3 is defined by rays R3 and output light Out4 is

defined by rays R4. Although FIG. 9 only illustrates output lights OutO, Outl, Out2,

Out3 and Out4, there will actually be many more output lights, depending on the power

on input light 77 and the reflectances of reflecting surfaces 122 and 124. As will be

discussed in more detail further below, the output lights interfere with each other to

produce a luminous flux having a direction which changes in accordance with the

wavelength of input light 77. Therefore, the luminous flux can be described as being a resulting output light formed from the interference of output lights OutO, Outl , Out2,

Out3 and Out4.

FIG. 10 is a diagram illustrating interference between reflections produced by

a VIPA. Referring now to FIG. 10, light traveling from focal line 78 is reflected by

reflecting surface 124. As previously described, reflecting surface 124 has a

reflectance of approximately 100% and, therefore, functions essentially as a mirror.

As a result, output light Outl can be optically analyzed as if reflecting surfaces 122 and

124 did not exist and, instead, output light Outl was emitted from a focal line I

Similarly, output lights Out2, Out3 and Out4 can be optically analyzed as if they were

emitted from focal lines I_l5 1₂, 1₃ and I₄, respectively. The focal lines I₂, 1₃ and I₄ are

virtual images of a focal line Ϊ_Q. Therefore, as illustrated in FIG. 10, focal line I_j is a distance 2t from focal line I₀, where t equals the distance between reflecting surfaces 122 and 124. Similarly,

each subsequent focal line is a distance 2t from the immediately preceding focal line.

Thus, focal line I₂ is a distance 2t from focal line I_lt Moreover, each subsequent

multiple reflection between reflecting surfaces 122 and 124 produces an output light

which is weaker in intensity than the previous output light. Therefore, output light

Out2 is weaker in intensity than output light Outl.

As illustrated in FIG. 10, output lights from the focal lines overlap and interfere

with each other. More specifically, since focal lines I_l5 I₂, I₃ and I₄ are the virtual

images of focal line I₀, output lights OutO, Outl, Out2, Out3 and Out4 have the same

optical phase at the positions of focal lines I_l5 I₂, I₃ and I₄. Therefore, interference

produces a luminous flux which travels in a specific direction depending on the

wavelength of input light 77.

A VIPA according to the above embodiments of the present invention has

strengthening conditions which are characteristics of the design of the VIPA. The

strengthening conditions increase the interference ofthe output lights so that a luminous

flux is formed. The strengthening conditions of the VIPA are represented by the

following Equation (1):

2t x cosφ = mλ where φ indicates the propagation direction of the resulting luminous flux as

measured from a line perpendicular to the surface of reflecting surfaces 122 and 124, λ indicates the wavelength of the input light, t indicates the distance between the

reflecting surfaces 122 and 124, and m indicates an integer.

Therefore, if t is constant and m is assigned a specific value, then the

propagation direction φ ofthe luminous flux formed for input light having wavelength

λ can be determined.

More specifically, input light 77 is radially dispersed from focal line 78 through

a specific angle. Therefore, input light having the same wavelength will be traveling

in many different direction from focal line 78, to be reflected between reflecting

surfaces 122 and 124. The strengthening conditions of the VIPA cause light traveling

in a specific direction to be strengthened through interference of the output lights to

form a luminous flux having a direction corresponding to the wavelength of the input

light. Light traveling in different direction than the specific direction required by the

strengthening condition will be weakened by the interference of the output lights.

FIG. 11 is a diagram illustrating a cross-section along lines IX-IX ofthe VIPA

illustrated in FIG. 7, showing characteristics of a VIPA for determining the angle of

incidence, or tilt angle, of input light.

Referring now to FIG. 11, input light 77 is collected by a cylindrical lens (not

illustrated) and focused at focal line 78. As illustrated in FIG. 11 , input light 77 covers

an area having a width equal to "a" on radiation window 126. After input light 77 is reflected one time from reflecting surface 122, input light 77 is incident on reflecting surface 124 and covers an area having a width equal to "b" on reflecting surface 124.

Moreover, as illustrated in FIG. 11, input light 77 travels along optical axis 132 which

is at a tilt angle θl with respect to the normal to reflecting surface 122.

The tilt angle θl should be set to prevent input light 77 from traveling out of

the plate through radiation window 126 after being reflected the first time by reflecting

surface 122. In other words, the tilt angle θl should be set so that input light 77

remains "trapped" between reflecting surfaces 122 and 124 and does not escape through

radiation window 126. Therefore, to prevent input light 77 from traveling out of the

plate through radiation window 126, the tilt angle θl should be set in accordance with

the following Equation (2):

tilt of optical axis θl ≥ (a + b) / 4t

Therefore, as illustrated by FIGS. 7-11, a VIPA receives an input light having

a respective wavelength within a continuous range of wavelengths. The VIPA causes

multiple reflection of the input light to produce self-interference and thereby form an

output light. The output light is spatially distinguishable from an output light formed for an input light having any other wavelength within the continuous range of

wavelengths. For example, FIG. 9 illustrates an input light 77 which experiences

multiple reflection between reflecting surfaces 122 and 124. This multiple reflection

produces a plurality of output lights OutO, Outl , Out2, Out3 and Out 4 which interfere with each other to produce a spatially distinguishable luminous flux for each

wavelength of input light 77.

"Self-interference" is a term indicating that interference occurs between a

plurality of lights or beams which all originate from the same source. Therefore, the

interference of output lights OutO, Outl, Out2, Out3 and Out4 is referred to as self-

interference of input light 77, since output lights OutO, Outl, Out2, Out3 and Out4 all

originate from the same source (that is, input light 77).

An input light can be at any wavelength within a continuous range of

wavelengths. Thus, the input light is not limited to being a wavelength which is a

value chosen from a range of discrete values. In addition, the output light produced

for an input light at a specific wavelength within a continuous range of wavelengths is

spatially distinguishable from an output light which would have been produced if the

input light was at a different wavelength within the continuous range of wavelengths.

Therefore, as illustrated, for example, in FIG. 7, the traveling direction (that is, a

"spatial characteristic") of the luminous flux 82 is different when input light 77 is at

different wavelengths within a continuous range of wavelengths.

FIGS. 12(A), 12(B), 12(C) and 12(D) are diagram illustrating a method for producing a VIPA.

Referring now to FIG. 12(A), a parallel plate 164 is preferably made of glass

and exhibits excellent parallelism. Reflecting films 166 and 168 are formed on both

sides of the parallel plate 164 by vacuum deposition, ion spattering or other such

methods. One of reflecting films 166 and 168 has a reflectance of nearly 100%, and the other reflecting film has a reflectance of lower than 100%, and preferably higher

than 80%.

Referring now to FIG. 12(B), one of reflecting films 166 and 168 is partially

shaved off to form a radiation window 170. In FIG. 12(B), reflecting film 166 is

shown as being shaved off so that radiation window 170 can be formed on the same

surface of parallel plate 164 as reflecting film 166. However, instead, reflecting film

168 can be partially shaved off so that a radiation window is formed on the same

surface of parallel plate 164 as reflecting film 168. As illustrated by the various

embodiment of the present invention, a radiation window can be on either side of parallel plate 164.

Shaving off a reflecting film can be performed by an etching process, but a

mechanical shaving process can also be used and is less expensive. However, if a

reflecting film is mechanically shaved, parallel plate 164 should be carefully processed

to minimize damage to parallel plate 164. For example, if the portion of parallel plate

164 forming the radiation window is severely damaged, parallel plate 164 will generate

excess loss caused by scattering of received input light.

Instead of first forming a reflecting film and then shaving it off, a radiation

window can be produced by preliminarily masking a portion of parallel plate 164

corresponding to a radiation window, and then protecting this portion from being covered with reflecting film.

Referring now to FIG. 12(C), a transparent adhesive 172 is applied onto

reflecting film 166 and the portion of parallel plate 164 from which reflecting film 166 has been removed. Transparent adhesive 172 should generate the smallest possible

optical loss since it is also applied to the portion of parallel plate 164 forming a

radiation window.

Referring now to FIG. 12(D), a transparent protector plate 174 is applied onto

transparent adhesive 172 to protect reflecting film 166 and parallel plate 164. Since

transparent adhesive 172 is applied to fill the concave portion generated by removing

reflecting film 166, transparent protector plate 174 can be provided in parallel with the

top surface of parallel plate 164.

Similarly, to protect reflecting film 168, an adhesive (not illustrated) can be

applied to the top surface of reflecting film 168 and should be provided with a protector

plate (not illustrated). If reflecting film 168 has a reflectance of about 100% , and there

is no radiation window on the same surface of parallel plate 164, then an adhesive and

protector plate do not necessarily have to be transparent.

Furthermore, an anti-reflection film 176 can be applied on transparent protector

plate 174. For example, transparent protector plate 174 and radiation window 170 can

be covered with anti-reflection film 176.

A focal line can be on the surface of a radiation window or on the opposite

surface of a parallel plate from which input light enters. Moreover, the focal line can

be in the parallel plate, or before the radiation window.

In accordance with the above, two reflecting films reflect light therebetween, with the reflectance of one reflecting film being approximately 100% . However, a

similar effect can be obtained with two reflecting films each having a reflectance of less than 100% . For example, both reflecting films can have a reflectance of 95 % . In this

case, each reflecting film has light traveling therethrough and causing interference. As

a result, a luminous flux traveling in the direction depending on the wavelength is

formed on both sides of the parallel plate on which the reflecting films are formed.

Thus , the various reflectances of the various embodiments of the present invention can

easily be changed in accordance with required characteristics of a VIPA.

In accordance with the above, a waveguide device is formed by a parallel plate,

or by two reflecting surfaces in parallel with each other. However, the plate or

reflecting surfaces do not necessarily have to be parallel.

In accordance with the above, a VIPA uses multiple-reflection and maintains a

constant phase difference between interfering lights. As a result, the characteristics of

the VIPA are stable, thereby reducing optical characteristic changes causes by

polarization. By contrast, the optical characteristics of a conventional diffraction

grating experience undesirable changes in dependance on the polarization of the input

light.

In accordance with the above, a VIPA provides luminous fluxes which are

"spatially distinguishable" from each other. "Spatially distinguishable" refers to the

luminous fluxes being distinguishable in space. For example, various luminous fluxes

are spatially distinguishable if they are collimated and travel in different directions, or

are focused in different locations . However, the invention is not intended to be limited

to these precise examples, and there are many other ways in which luminous fluxes can

be spatially distinguished from each other. FIG. 13 is a diagram illustrating an apparatus which uses a VIPA as an angular

dispersive component, instead of using diffraction gratings, to produce chromatic

dispersion. Referring now to FIG. 13, a VIPA 240 has a first surface 242 with a

reflectivity of, for example, approximately 100%, and a second surface 244 with a

reflectivity of, for example, approximately 98% . VIPA 240 also includes a radiation

window 247. However, VIPA 240 is not limited to this specific configuration.

Instead, VIPA 240 can have many different configurations as described herein.

As illustrated in FIG. 13, a light is output from a fiber 246, collimated by a

collimating lens 248 and line-focused into VIPA 240 through radiation window 247 by

a cylindrical lens 250. VIPA 240 then produces a collimated light 251 which is

focused by a focusing lens 252 onto a mirror 254. Mirror 254 can be a mirror portion

256 formed on a substrate 258.

Mirror 254 reflects the light back through focusing lens 252 into VIPA 240. The light then undergoes multiple reflections in VIPA 240 and is output from radiation

window 247. The light output from radiation window 247 travels through cylindrical

lens 250 and collimating lens 248 and is received by fiber 246.

Therefore, light is output from VIPA 240 and reflected by mirror 254 back into

VIPA 240. The light reflected by mirror 254 travels through the path which is exactly opposite in direction to the path through which it originally traveled. As will be seen

in more detail below, different wavelength components in the light are focused onto

different positions on mirror 254, and are reflected back to VIPA 240. As a result, different wavelength components travel different distances, to thereby produce

chromatic dispersion.

FIG. 14 is a more detailed diagram illustrating the operation of the VIPA in

FIG. 13. Assume a light having various wavelength components is received by VIPA

240. As illustrated in FIG. 14, VIPA 240 will cause the formation of virtual images

260 of beam waist 262, where each virtual image 260 emits light.

As illustrated in FIG. 14, focusing lens 252 focuses the different wavelength

components in a collimated light from VIPA 240 at different points on mirror 254.

More specifically, a longer wavelength 264 focuses at point 272, a center wavelength

266 focuses at point 270, and a shorter wavelength 268 focuses at point 274. Then,

longer wavelength 264 returns to a virtual image 260 which is closer to beam waist

262, as compared to center wavelength 266. Shorter wavelength 268 returns to a

virtual image 260 which is farther from beam waist 262, as compared to center

wavelength 266. Thus, the arrangement provides for normal dispersion.

Mirror 254 is designed to reflect only light in a specific interference order, and

light in any other interference order should be focused out of mirror 254. More

specifically, as previously described, a VIPA will output a collimated light. This

collimated light will travel in a direction in which the path from each virtual image has

a difference of mλ, where m is an integer. The mth order of interference is defined as an output light corresponding to m.

For example, FIG. 15 is a diagram illustrating various orders of interference

of a VIPA. Referring now to FIG. 15, a VIPA, such as VIPA 240, emits collimated lights 276, 278 and 280. Each collimated light 276, 278 and 280 corresponds to a

different interference order. Therefore, for example, collimated light 276 is collimated

light corresponding to an (n+2)th interference order, collimated light 278 is collimated

light corresponding to an (n+l)th interference order, and collimated light 280 is

collimated light corresponding to an nth interference order, wherein n is an integer.

Collimated light 276 is illustrated as having several wavelength components 276a, 276b

and 276c. Similarly, collimated light 278 is illustrated as having wavelength

components 278a, 278b and 278c, and collimated light 280 is illustrated as having

wavelength components 280a, 280b and 280c. Here, wavelength components 276a,

278a and 280a have the same wavelength. Wavelength components 276b, 278b and

280b have the same wavelength (but different from the wavelength of wavelength

components 276a, 278a and 280a). Wavelength components 276c, 278c and 280c have

the same wavelength (but different from the wavelength of wavelength components

276a, 278a and 280a, and the wavelength of wavelength components 276b, 278b and

280b). Although FIG. 15 only illustrates collimated light for three different

interference orders, collimated lights will be emitted for many other interference

orders.

Since collimated lights at the same wavelength for different interference orders

travel in different directions and are therefore focused at different positions, mirror 254 can be made to reflect only light from a single interference order back into VIPA 240.

For example, as illustrated in FIG. 15, the length of a reflecting portion of mirror 254

should be made relatively small, so that only light corresponding to a single interference order is reflected. More specifically, in FIG. 15, only collimated light 278

is reflected by mirror 254. In this manner, collimated lights 276 and 278 are focused

out of mirror 254.

A wavelength division multiplexed light usually mcludes many channels.

Referring again to FIG. 13 , if the thickness t between first and second surfaces 242 and

244 of VIPA 240 is set at a specific value, the arrangement will be able to

simultaneously compensate for dispersion in each channel.

More specifically, each channel has a center wavelength. These center

wavelengths are usually spaced apart by a constant frequency spacing. The thickness

t of VIPA 240 between first and second surfaces 242 and 244 should be set so that all

of the wavelength components corresponding to the center wavelengths have the same

output angle from VIPA 240 and thus the same focusing position on mirror 254. This

is possible when the thickness t is set so that, for each channel, the round-trip optical

length through VIPA 240 traveled by the wavelength component corresponding to the

center wavelength is a multiple of the center wavelength of each channel. This amount

of thickness t will hereafter be referred to as the "WDM matching free spectral range

thickness", or "WDM matching FSR thickness".

Moreover, in this case, the round-trip optical length (2ntcosθ) through VIPA

240 is equal to the wavelength corresponding to the center wavelength in each channel

multiplied by an integer for the same θ and different integer, where n is the refractive

index of the material between first and second surfaces 242 and 244, θ indicates a

propagation direction of a luminous flux corresponding to the center wavelength of each channel. More specifically, as previously described, θ indicates the small tilt

angle of the optical axis of input light (see FIG. 8).

Therefore, all of the wavelength components corresponding to the center

wavelengths will have the same output angle from VIPA 240 and thus the same

5. focusing position on mirror 254, if t is set so that, for the wavelength component

corresponding to the center wavelength in each channel, 2ntcosθ is an integer multiple

of the center wavelength of each channel for the same θ and different integer.

For example, a 2 mm physical length in round trip (which is approximately

double a 1 mm thickness of VIPA 240) and a refractive index of 1.5 enable all the

0 wavelengths with a spacing of 100 GHz to satisfy this condition. As a result, VIPA

240 can compensate for dispersion in all the channels of a wavelength division

multiplexed light at the same time.

Therefore, referring to FIG. 14, with the thickness t set to the WDM matching

FSR thickness, VIPA 240 and focusing lens 252 will cause (a) the wavelength

5 component corresponding to the center wavelength of each channel to be focused at

point 270 on mirror 254, (b) the wavelength component corresponding to the longer

wavelength component of each channel to be focused at point 272 on mirror 254, and

(c) the wavelength component corresponding to the shorter wavelength component of

each channel to be focused at point 274 on mirror 254. Therefore, VIPA 240 can be

0 used to compensate for chromatic dispersion in all channels of a wavelength division

multiplexed light. FIG. 16 is a graph illustrating the amount of dispersion of several channels of

a wavelength division multiplexed light, in a case when the thickness t is set to the

WDM matching FSR thickness. As illustrated in FIG. 16, all the channels are

provided with the same dispersion. However, the dispersions are not continuous

between the channels. Moreover, the wavelength range for each channel at which

VIPA 240 will compensate for dispersion can be set by appropriately setting the size

of mirror 254.

If the thickness t is not set to the WDM matching FSR thickness, different

channels of a wavelength division multiplexed light will be focused at different points

on mirror 254. For example, if the thickness t is one-half, one-third or some other

fraction of the round trip optical length thickness, then focusing points of two, three,

four or more channels may be focused on the same mirror, with each channel being

focused at a different focusing point. More specifically, when the thickness t is one-

half the WDM matching FSR thickness, the light from odd channels will focus at the

same points on mirror 254, and the light from even channels will focus at the same

points on mirror 254. However, the lights from the even channels will be focused at

different points from the odd channels.

For example, FIG. 17 is a diagram illustrating different channels being focused

at different points on mirror 254. As illustrated in FIG. 17, wavelength components

of the center wavelength of even channels are focused at one point on mirror 254, and

wavelength components of the center wavelength of odd channels are focused at a different point. As a result, VIPA 240 can adequately compensate for dispersion in all

the channels of a wavelength division multiplexed light at the same time.

There are several different ways to vary the value of the dispersion added by

a VIPA. For example, FIG. 18 is a diagram illustrating a side view of an apparatus

which uses a VIPA to provide variable dispersion to light. Referring now to FIG. 18,

VIPA 240 causes each different interference order to have a different angular

dispersion. Therefore, the amount of dispersion added to an optical signal can be

varied by rotating or moving VIPA 240 so that light corresponding to a different

interference order is focused on mirror 254 and reflected back into VIPA 240.

FIG. 19 is a diagram illustrating a side view of an apparatus which uses a VIPA

to provide variable dispersion. Referring now to FIG. 19, the relative distance between focusing lens 252 and mirror 254 is maintained constant, and focusing lens 252 and

mirror 254 are moved together relative to VIPA 240. This movement of focusing lens

252 and mirror 254 changes the shift of light returning to VIPA 240 from mirror 254,

and thereby varies the dispersion.

FIGS. 20(A) and 20(B) are diagrams illustrating side views of apparatuses which use a VIPA to provide various values of chromatic dispersion to light. FIGS.

20(A) and 20(B) are similar to FIG. 14, in that FIGS. 20(A) and 20(B) illustrate the

travel directions of a longer wavelength 264, a center wavelength 266 and a shorter

wavelength 268 of light emitted by a virtual image 260 of beam waist 262.

Referring now to FIG. 20(A), mirror 254 is a convex mirror. With a convex

mirror, the beam shift is magnified. Therefore, a large chromatic dispersion can be obtained with a short lens focal length and a small amount of space. When mirror 254

is convex, as in FIG. 20(A), the convex shape can typically only be seen from a side

view and cannot be seen when viewed from the top.

Referring now to FIG. 20(B), mirror 254 is a concave mirror. With a concave

mirror, the sign of the dispersion is inverted. Therefore, anomalous dispersion can be

obtained with a short lens focal length and a small space. When mirror 254 is concave,

as in FIG. 20(B), the concave shape can typically only be seen from a side view and

cannot be seen when viewed from the top.

Therefore, typically, mirror 254 would appear flat in the top view. However,

it is possible for mirror 254 to also be a concave or a convex mirror when viewed by

the top, thereby indicating that the mirror is a "one-dimensional" mirror.

In FIGS. 20(A) and 20(B), mirror 254 is located at or near the focal point of

focusing lens 252.

Therefore, as described above, mirror 254 can be convex or concave in the side

view, as illustrated, for example, in FIGS. 20(A) and 20(B), respectively. A convex

mirror can enhance the chromatic dispersion and a concave mirror can reduce or even

invert the chromatic dispersion from negative (normal) to positive (anomalous). More

specifically, a convex mirror generates larger dispersion in the negative direction and

a concave mirror generates smaller dispersion in the negative direction or dispersion

inverted to positive. This is possible because the magnitude of chromatic dispersion

is a function of the curvature of the mirror in the side view. FIG. 21 is a graph illustrating the output angle of a luminous flux from VIPA

240 versus wavelength of the luminous flux. As can be seen from FIG. 21, a curve

282 of the wavelength versus the output angle is not linear.

Since the relationship between the wavelength and the output angle of a

luminous flux produced by a VIPA is not linear, the chromatic dispersion is not

constant in a wavelength band as long as a flat mirror, a normal convex mirror or a

normal concave mirror is used as mirror 254. This nonlinearity in chromatic

dispersion is referred to as the higher order dispersion.

Generally, referring to the apparatuses in FIGS. 20(A) and 20(B), the

nonlinearity in chromatic dispersion can be understood by referring to the following

Equation (3):

(angular dispersion)-(l-f-(l/R)) « chromatic dispersion, where f is the focal length of lens 252 and R is the radius of curvature of mirror

254.

FIG. 22 is a graph illustrating the angular dispersion of VIPA 240 versus the

wavelength of a luminous flux. Generally, the curve 284 in FIG. 22 represents the

slope of curve 282 in FIG. 21. As can be seen from FIG. 22, the angular dispersion

is not constant. Instead, the angular dispersion changes as the wavelength changes.

FIG. 23 is a graph illustrating the term (l-f-(l/R)) in Equation 3, above, versus

wavelength. More specifically, line 286 represents a graph of the term (l-f-(l/R))

versus wavelength for a flat mirror (radius of curvature equals "∞" (infinity)). Line 288 represents a graph of the term (l-f-(l/R)) versus wavelength for a concave mirror

(radius of curvature equals " + "). Line 290 represents a graph of the term (l-f-(l/R)) versus wavelength for convex mirror (radius of curvature equals "-"). As illustrated

in FIG. 23, each of the mirrors has a constant radius of curvature.

FIG. 24 is a diagram illustrating the chromatic dispersion versus wavelength of

an apparatus such as in FIGS. 20(A) and 20(B), when mirror 254 is a convex mirror,

a flat mirror and a concave mirror. More specifically, curve 292 is a curve of the

chromatic dispersion versus wavelength when mirror 254 is a convex mirror. Curve

294 is a curve ofthe chromatic dispersion versus wavelength when mirror 254 is a flat

mirror. Curve 296 is a curve of the chromatic dispersion versus wavelength when

mirror 254 is a concave mirror.

In a very general manner, curves 292, 294 and 296 each represent a product of

the angular dispersion illustrated in FIG. 22 with the appropriate line illustrated in FIG.

23, as indicated by Equation 3, above. More specifically, generally, curve 292

represents a product of curve 284 in FIG. 22 and line 290 in FIG. 23. Generally,

curve 294 represents a product of curve 284 in FIG. 22 and line 286 in FIG. 23.

Generally, curve 296 represents a product of curve 284 in FIG. 22 and line 288 in FIG.

23.

As can be seen from FIG. 24, the chromatic dispersion is not constant whether a convex, flat or concave mirror is used as mirror 254.

According to the above, this wavelength dependence of chromatic dispersion

can be reduced or eliminated by chirping the curvature of mirror 254. More specifically, FIG. 25 is a graph illustrating a curve 298 of the term (1-

f-(l/R)) in Equation 3, above, versus wavelength. Generally, curve 298 in FIG. 25 is

inverse to curve 284 in FIG. 22. Therefore, a mirror having the characteristics in FIG.

25 will provide a constant chromatic dispersion, as illustrated by the curve 300 in FIG.

26.

For example, with the apparatus illustrated, for example, in FIG. 14, a longer

wavelength has a larger dispersion in the negative direction than a shorter wavelength.

Therefore, mirror 254 can be designed to have a concave portion where the longer

wavelength reflects, and a convex portion were the shorter wavelength reflects, to

effectively cancel the wavelength dependence of dispersion. Ideally, the curvature of

mirror 254 varies from convex to concave continuously along the focusing point of

light when the wavelength changes from short to long. If this modification is based on a conventional convex mirror, not a flat mirror, the curvature of the mirror can be

made to vary from strong convex to weak convex continuously along the focusing point

of light when the wavelength changes from short to long.

Therefore, there are many different designs for mirror 254, to provide a constant chromatic dispersion. For example, FIG. 27 is a graph illustrating

characteristics many different mirror designs. Curve 302 in FIG. 27 illustrates a

mirror which continuously changes from convex to concave as the wavelength of output

light increases. Curve 304 illustrates a mirror which changes from strongly convex to

slightly convex as the wavelength of output light increases. Curve 306 illustrates a mirror which changes from slightly concave to strongly concave as the wavelength of output light increases. Other mirror designs include, for example, those shown by

curves 308 and 310.

There are a virtually unlimited number of mirror designs which could be used,

and such designs could be graphed in FIG. 27. Moreover, mirror designs are not

limited to those having characteristic curves with the same slopes as those in FIG. 27.

FIGS. 28(A), 28(B), 28(C) and 28(D) illustrate the surface shape of various

mirrors which can be used as mirror 254. For example, FIG. 28(A) illustrates a mirror

which continuously changes from convex to concave, as represented by curve 302 in

FIG. 27. FIG. 28(B) illustrates a mirror which continuously changes from strong

convex to weak convex, as represented by curve 310 in FIG. 27. FIG. 28(C) illustrates

a mirror which continuously changes from weak concave to strong concave, as

represented by curve 306 in FIG. 27.

Moreover, there are a virtually unlimited number of mirror designs which could

be used. For example, FIG. 28(D) illustrates a flat mirror which changes to convex.

FIG. 27(E) illustrates a flat mirror which changes to concave. FIG. 28(F) illustrates

a mirror having a convex portion and a concave portion, but where the mirror does not

continuously change from convex to concave.

Therefore, as indicated above, an apparatus includes a VIPA, a mirror and a

lens . The VIPA receives an input light and produces a corresponding output light (such

as a luminous flux) propagating away from the VIPA . The lens focuses the output light

onto the mirror so that the mirror reflects the output light and the reflected light is directed by the lens back to the VIPA. The mirror has a shape which causes the

apparatus to produce a constant chromatic dispersion.

For example, output light focused by the lens is incident on a different surface

point on the mirror as the wavelength ofthe output light changes. The mirror is shaped

so that the surface points change continuously from convex to concave as the

wavelength of the output light changes from shorter to longer. As another example,

the mirror can be shaped so that the surface points change continuously from stronger

convex to weaker convex as the wavelength of the output light changes from shorter

to longer.

Alternatively, the mirror can be shaped so that the surface points change

continuously from weaker concave to stronger concave as the wavelength ofthe output

light changes from shorter to longer. There are many other examples. For example,

the mirror can have a concave portion and a convex portion so that output light at a

shorter wavelength than a specific wavelength reflects off the convex portion and so

that output light at a longer wavelength than the specific wavelength reflect off the

concave portion.

Moreover, for example, the mirror can have a flat portion which continuously

changes to a concave portion in correspondence with an increase in the wavelength of

the output light above a specific wavelength so that output light at a shorter wavelength than the specific wavelength is incident on the flat portion and output light at a longer

wavelength than the specific wavelength is incident on the concave portion. Or, the

mirror can have a convex portion which continuously changes to a flat portion in corresponding with an increase in the wavelength of the output light above a specific

wavelength so that output light at a shorter wavelength than the specific wavelength is incident on the convex portion and output light at a longer wavelength than the specific

wavelength is incident on the flat portion.

A VIPA, as described above, provides a much larger angular dispersion than

a diffraction grating. Therefore, a VIPA can be used to compensate for much larger

chromatic dispersion than a spatial grating pair arrangement as illustrated in FIGS.

6(A) and 6(B).

A mirror, as described above, to reflect light back to a VIPA to compensate for

chromatic dispersion, can be described as a cylindrical mirror since the mirror shape

is that of the surface of a cylinder. In other words, as shown in FIG. 29, the mirror

has the same radius of curvature along an axis forming the cylinder. Since chromatic dispersion is a function of the radius of the mirror curvature as described above, the

chromatic dispersion will not change when the mirror is moved along the axis forming

the cylinder. As shown in FIG. 30(A), the chromatic dispersion may change within

each channel as previously described (see FIG. 24). However, the chromatic

dispersion will be periodic, as shown in FIG. 30(B), and the chromatic dispersion will

be approximately the same for all the channels.

FIG. 31(A) is a graph illustrating chromatic dispersion versus wavelength for

dispersion compensation with a VIPA with a modified cylindrical mirror as in, for

example, FIGS. 28(A) through 28(F). Referring now to FIG. 31(A), it can be seen that the amount of chromatic dispersion is substantially the same for each wavelength within the same channel.

FIG. 31(B) is a graph illustrating chromatic dispersion versus wavelength for

all wavelengths (and therefore, many channels) of a wavelength division multiplexed

light, after undergoing chromatic dispersion compensation with a VIPA with a modified

cylindrical mirror as in, for example, FIGS. 28(A) through 28(F). Referring now to

FIG. 31(B), it can be seen that the amount of chromatic dispersion is substantially the

same, or uniform, for all wavelengths in all channels.

FIG. 32 is a diagram illustrating a top view of an apparatus using a VIPA to

the present invention. Referring now to FIG. 32, a cone shaped mirror 400 is used to

reflect light back to VIPA 240. Mirror 400 is movable in a direction 401.

As previously indicated, VIPA 240 produces a collimated luminous flux, which

can be referred to as a collimated output light, traveling in a direction determined by

the wavelength of the light. The angular dispersion direction of VIPA 240 is the

direction in which the traveling direction of the collimated output light changes as the

wavelength of the light changes, and is represented, for example, by direction 402 in

FIG. 32. Collimated output lights for different wavelengths will be in the same plane.

Therefore, direction 401 is along the surface of the cone and can be described

as being perpendicular to both the angular dispersion direction of VIPA 240 and the

traveling directions of collimated light from VIPA 240. Alternatively, direction 401 can be described as being perpendicular to a plane which includes the traveling

direction of the collimated output lights for different wavelengths from VIPA 240.

FIGS. 33(A) and 33(B) are diagrams illustrating how mirror 400 can be formed,

for example, from a section of a cone 405, according to an embodiment ofthe present

invention. As can be seen from FIG. 33(A), direction 401 preferably passes along the

surface of, and through the top of, cone 405. Although it is preferable for direction

401 to pass through the top of cone 405, it is not necessary to pass through the top.

In FIG. 33(B), mirror 400 is shown with three different radii of curvature A,

B and C. Radius of curvature A is the largest, radius of curvature C is the smallest,

and radius of curvature B is between A and C in size.

By moving the mirror in direction 401 (corresponding, for example, to

direction 401 in FIG. 32), the position of the light focus moves from A to C on the

surface of the cone shaped mirror in FIG. 33(B). Since the radii are different for A,

B and C, the chromatic dispersion will be different. Thus, the chromatic dispersion

will be varied by moving the cone shaped mirror.

FIG. 34(A) is a graph illustrating the amount of chromatic dispersion versus

wavelength within one channel for radii of curvature A, B and C of a cone shaped

mirror when the mirror is moved in a direction such as direction 401, according to an

embodiment of the present invention. As can be seen from FIG. 34(A), generally,

radius of curvature C produces the greatest amount of chromatic dispersion. Generally ,

radius of curvature A produces the smallest amount of chromatic dispersion. As can be seen from FIG. 34(A), the amount of chromatic dispersion produced by radius of

curvature B is between A and C.

As can be seen from FIG. 34(A) and also described with reference to FIGS. 24

and 30(A), the amount of chromatic dispersion will be different for different

wavelengths within a channel. However, as described with reference to FIGS. 26,

31(A) and 31(B), by modifying the mirror, it is possible to provide a uniform amount

of chromatic dispersion in each channel, and in all the channels.

For example, FIG. 34(B) is a diagram illustrating the radii of curvature A, B

and C when a cone shaped mirror is moved in a direction such as direction 401,

according to an embodiment of the present invention. By contrast, FIG. 34(C) is a

diagram illustrating modified radii of curvature A', B' and C when a modified cone

shaped mirror to provide uniform chromatic dispersion is moved in a direction such as direction 401 , according to an embodiment of the present invention. For example, in

the modified mirror, output light focused by lens 252 is incident on a different surface

point on the mirror as the wavelength of the output light changes . The mirror is shaped

so that the surface points change continuously from convex to concave as the

the mirror can be shaped so that the surface points change continuously from stronger convex to weaker convex as the wavelength of the output light changes from shorter

to longer.

Alternatively, the mirror can be shaped so that the surface points change

continuously from weaker concave to stronger concave as the wavelength ofthe output light changes from shorter to longer. There are many other examples. For example, the mirror can have a concave portion and a convex portion so that output light at a

concave portion.

As a result, the modified mirror will provide a uniform chromatic dispersion

in each channel, and in all the channels.

FIG. 35 is a graph illustrating the chromatic dispersion versus wavelength in

one channel for radii of curvature A', B' and C, according to an embodiment of the

present invention. As can be seen from FIG. 35, each radii of curvature A' , B' and C

produces a uniform but different amount of chromatic dispersion. Therefore, each

channel will have a uniform chromatic dispersion and the amount of the chromatic

dispersion is variable by moving the mirror.

FIG. 36 is a diagram illustrating various angles in an apparatus which uses a

VIPA, according to an embodiment of the present invention. Referring now to FIG.

36, Θ and θ are the average incident angles, and Φ and φ are the output angles with

respect to the normal line to a plate, such as second surface 244, forming VIPA 240.

θ and Φ indicate the angles in air, whereas θ and φ indicate the angles in glass

between surfaces 242 and 244 of VIPA 240. The angles in the air are approximately

n times larger than those in the glass because of the refraction at the glass surface.

Here, n is the index of the glass. FIG. 37 is an additional diagram illustrating angles in an apparatus which uses

a VIPA, according to an embodiment of the present invention. As indicated in FIG.

37, the output angle φ is determined as the direction where the difference in the light

paths originating at two adjacent beam waists is a multiple ofthe light wavelength. The

spacing between the adjacent beam waists is 2t (t is the thickness of the VIPA , as

illustrated, for example, in FIG. 8) and the output angle in the glass is φ. So,

2tcosφ = mλ/n (m is an integer) . From this , the angular dispersion is dΦ/dλ = -n²/λ ,

as shown by the following Equation (4):

Separation of the light paths: d= 2tsmφ λ Difference of the path lengths: m- — = t cos φ mkλ = -2tsm n

, Δλ 1ΔΛ Aφ = -cotφ- — * —7-7-

θ : Input angle in glass φ : Output angle in glass

Θ : Input angle in air Φ : Output angle in air

Θ « nθ

Φ « nφ

ΔΦ « Δ^ n Δ2 n² Δ d n²

ΔΦ « - — — — « - — — — , —— » - — — Equation(4) φ λ Φ λ dλ λΦ ^{1 \ J}

FIG. 38 is a diagram illustrating how chromatic dispersion is generated in an

apparatus using a VIPA, according to an embodiment of the present invention. FIG.

14 also illustrates how chromatic dispersion is generated, but FIG. 38 is a more

quantitative description.

Referring now to FIG. 38, the light travel angle in the air with respect to the

normal line to the VIPA is Φ-Θ. Also, the focal length of lens 252 is f and the depth

of the center beam waist is a. The light focusing position y on the mirror is y = f(Φ-Θ) .

The mirror shape is c(y) as a function of y. The mirror slope h is dc/dy. Then, the

beam shift after the round trip is obtained by the following Equation (5):

dc(y) Mirror shape: c(y), Slope of mirror surface: h(y) = — - — , y « f(Φ - Θ) ay

(Beam shift) « 2(f - a)(Φ - Θ ) + 2f h(y) n n (Beam shift)

(Delay) = —(Distance change) « — • c c φ

In¹ _* — — {(/ - α)(Φ - Θ ) + / h(y)} Equation(S)

The distance change in FIG. 38 is easily obtained from the beam shift, and the

delay is the distance change divided by the speed of light in the glass. The chromatic

dispersion is calculated as the delay change with the wavelength change and is shown

by the following Equation (6):

d(Delay)

(Dispersion) = dλ

2n⁴ dh(y)

^< (f - a)Θ + f²Φ - cλΦ ^: dy β(y) Equation (6)

For a cylindrical mirror of radius r:

I f Equation (7)

the mirror

is a cylindrical mirror and has a circular shape along with angular dispersion direction, dh/dy is simply 1/r and the following Equation (7) is obtained: From Equation (7), it can be seen that chromatic dispersion is not uniform in

a WDM channel and, instead, the chromatic dispersion changes approximately in

proportion to 1/Φ³.

As indicated in Equation (6), chromatic dispersion is a function of Φ. To make

this dispersion uniform in a WDM channel, this formula needs to be constant as Φ

changes. Therefore, the value in the large parenthesis of Equation (6) should be

proportional to Φ³ (small change of λ is ignored). Assuming the proportional constant

is K (this means the chromatic dispersion is -2n⁴K/cλ) and that n, c, λ, f and a are

constant or almost constant for the small change of wavelength, we get the following

Equation (8).

(f - α)Θ + f²Φ -^~^ - flι(y) =KΦ³. Equation (8) dy

Here, y«f(Φ-®).So,Φ = +Θ

The condition for a uniform dispersion in a WDM channel is

The mirror slope h should be zero at the center y =0. Equation (8) is solved to get the following Equation (9):

3KΘ KΘ²-(f-a) y) = T 2TfTT⁴ ^■r/ ++ eery² +

2 a + f Ti y Equation (9) The mirror curve is obtained after integration and is shown by the following

Equation (10):

Equation (10)

Equation (10) determines the ideal curves for different K, which were described, for

example, in FIG. 28.

The mirror shape is determined by the value K, which gives the chromatic

dispersion. To get the shape along the curve A, B, and C in FIG. 33(B), a small K,

a medium K, and a large K can be used, respectively, for Equation (10). The curves

are illustrated in FIGS. 39(A), 39(B) and 39(C). However, for easy manufacturing,

the shapes could be approximately a part of an ellipse, or a parabola, or a hyperbola.

In these cases, the mirror can be made as a part of a cone.

FIG. 40 is a diagram illustrating an example of a cone for forming a mirror,

according to an embodiment ofthe present invention. Referring now to FIG. 40, cone

405 has a base 406. If base 406 is a circle, cone 405 is a normal cone. However,

cone 405 may be stretched, for example, in a side direction. In such case, base 406 will be ellipse, as shown in FIG. 40. In the case of ellipse, base 406 has a longer axis r, and a shorter axis r₂. Direction 401 is determined by the line passing along the cone

surface from the top of the cone to the bottom where the cone surface hits the longer

or shorter axis in base 406. However, this line does not necessarily have to hit one of

the axes. As shown in FIG. 40, cone 406 is cut by a plane 407 which is perpendicular

to direction 401. A cut curve 408 for the mirror is an ellipse, parabola or hyperbola,

depending on the top angle of cone 405. Therefore, cut curve 408 in the mirror area

is a part of one of these three curves. A modified cone shaped mirror is defined so that

cut curve 408 is determined by Equation (10), rather than the three shapes.

Light for different WDM channels will be focused at different positions displaced in the direction 401. Therefore, the different WDM channels will see

different curves and generate different chromatic dispersion. Therefore, the cone shape

can be further modified so that the cut curves for different WDM channels are

determined by Equation (10) with desirable value Ks. This indicates that the dispersion

change is not limited to a linear change with wavelength or WDM channels and it could

change in any way.

FIG. 41 is a diagram illustrating a step shaped mirror surface, according to an

embodiment of the present invention. This mirror can provide different shapes for

different WDM channels without causing an excess tilt ofthe mirror with respect to the incident light.

Referring again to FIG. 32, mirror 400 is movable in direction 401. Mirror

400 can also be described as movable in or around a focal plane of lens 252. Mirror 400 has a cone shape, or modified cone shape, as described above, so mirror 400 will

have different curvatures along the surface. Since the curvature changes along

direction 401 , and mirror 400 is movable in this direction, the chromatic dispersion can

be varied by moving mirror 400 by a relatively small distance. In this design, the

moving distance of mirror 400 would typically be less than 1 cm, which is much

smaller than the moving distance of mirror 254 in FIG. 19.

Further, in FIG. 19, the position of lens 252 is movable, whereas in FIG. 32,

the position of lens 252 would typically be fixed. Therefore, in FIG. 19, a large space

will be required between VIPA 240 and lens 252, so that the lens 252 and mirror 254

can be moved together for a relatively large distance to provide the required amount

of chromatic dispersion. This large space between VIPA 240 and lens 252 is

undesirable, and greatly increases the overall size of the apparatus. By comparison,

in FIG. 32, a relatively small space is required between VIPA 240 and lens 252, and mirror 400 only has to move a relatively small distance to provide the required amount

of chromatic dispersion, thereby allowing the overall apparatus to be much smaller than

that in FIG. 19.

FIG. 42 is a diagram illustrating a side view of an apparatus using a VIPA to

present invention. Referring now to FIG. 42, an angular dispersive component 500

is positioned between VIPA 240 and lens 252. Angular dispersive component 500

could be, for example, a transmission type diffraction grating, a reflection type diffraction grating or a holographic grating. Angular dispersive component 500 has an angular dispersion direction which

is perpendicular to the angular dispersion direction of VIPA 240.

Preferably, the amount of angular dispersion provided by angular dispersive

component 500 should be large enough to distinguish the different wavelengths for

different WDM channels. Therefore, preferably, the angular dispersion provided by

angular dispersive component 500 should be larger than approximately 0.1 degrees/nm.

This number is readily achievable by using a diffraction grating as angular dispersive

component 500. However, the present invention is not limited to any particular amount

of angular dispersion.

In FIG. 42, the position of mirror 400 is preferably fixed. This is different than in FIG. 32, where the position of mirror 400 is movable. However, in FIG. 42, mirror

400 is not limited to being fixed, and can be movable to add variable dispersion.

By using angular dispersive component 500 between VIPA 240 and lens 252,

the light in different channels will be focused by lens 252 at positions which are

displaced along direction 401 (not shown in FIG. 42) on the surface of mirror 400

because of the angular dispersion of angular dispersive component 500, and will see

a different curvature of mirror 400. As a result, different channels will have different

chromatic dispersions. This channel dependent chromatic dispersion is called high

order dispersion or dispersion slope, and is required for compensation of a fiber dispersion since different WDM channels traveling in a fiber will see different

chromatic dispersion in the fiber. FIG. 43(A) is a graph illustrating the amount of chromatic dispersion for all

wavelengths (many channels) with a cone shaped mirror used as mirror 400 in FIG. 42, according to an embodiment of the present invention. For example, this cone shaped

mirror would typically be as illustrated in FIGS. 33(A) and 33(B). As illustrated in

FIG. 43(A), the amount of chromatic dispersion is not uniform in each channel and

differs for different channels.

FIG. 43(B) is a graph illustrating the amount of chromatic dispersion for all

wavelengths (many channels) with a modified cone shaped mirror used as mirror 400

in FIG. 42, according to an embodiment of the present invention. For example, this

modified cone shaped mirror would typically have radii of curvature A' , B' and C as

in FIG. 34(C), according to an embodiment ofthe present invention. As illustrated in

FIG. 43(B), the amount of chromatic dispersion is uniform in each channel and

different for different channels.

In FIGS. 43(A) and 43(B), the dispersion is shown as increasing with increasing

wavelength. However, in some embodiments of the present invention, the dispersion

could decrease with increasing wavelength by inverting angular dispersive component

500 or by inverting the direction of the cone shaped mirror.

Therefore, parameters (such as the mirror shape, lens focal length, etc.) are

preferably designed so that the chromatic dispersion for each WDM channel, such as

those shown, for example, in FIGS. 43(A) or 43(B), is the same amount but opposite sign to the chromatic dispersion of the transmission line at the corresponding wavelength for the purpose of the simultaneous dispersion compensation of all WDM channels. Namely, although different WDM channels may experience different

chromatic dispersion amounts through the transmission line, a VIPA can be used, as

described herein, to compensate for the dispersion ofthe WDM channels with different

dispersion amounts.

FIG. 44 is a diagram illustrating the use of a holographic grating 510 as an

angular dispersive component between VIPA 240 and lens 252, according to an

embodiment of the present invention.

Moreover, FIG. 45 is a diagram illustrating the use of a reflection type grating

520 as an angular dispersive component between VIPA 240 and lens 252, according

to an embodiment of the present invention.

When a diffraction grating is used as an angular dispersive component (see FIG.

42), one problem is its polarization dependence. Therefore, a quarter wave plate can

be used to cancel the polarization dependence of the diffraction grating.

For example, FIG. 46 is a diagram illustrating the use of a quarter wave plate 530 inserted between the diffraction grating and lens 252.

FIG. 47 is a diagram illustrating the use of quarter wave plate 530 inserted

between lens 252 and the cone shape mirror 400. As an example, quarter wave plate

530 is positioned with the axes at 45° with respect to the plane of s or p polarization

of the diffraction grating.

With configurations as in FIGS. 46 and 47, light passed through the diffraction

grating with p-polarization will return to the diffraction grating with s-polarization, and

light passed through the diffraction grating with s-polarization will return to the diffraction grating with p-polarization. Therefore, the polarization dependence of the

diffraction grating is canceled.

FIG. 48(A) is a diagram illustrating a side or top view of an apparatus which

uses a VIPA to provide two different chromatic dispersions for different channels,

according to a still further embodiment of the present invention. Referring now to

FIG . 48 ( A) , a wavelength filter 510 is positioned between lens 252 and mirrors M 1 and

M2. Wavelength filter 510 filters the light from lens 252 so that light at wavelength

λl is directed to mirror Ml, and light at wavelength λ2 is directed to mirror M2.

Mirror Ml has a different curvature than mirror M2 and therefore, l and λ2 will

have different chromatic dispersion. Thus, each of mirrors Ml and M2 can be, for

example, a cylindrical mirror or a modified cylindrical mirror, as described herein.

For example, mirrors Ml and M2 can be modified cylindrical mirrors to provide

uniform but different amount of chromatic dispersion in channels corresponding to λl

and λ2.

FIG. 48(B) is a graph illustrating chromatic dispersion versus wavelength for

the apparatus in FIG. 48(A), where mirrors Ml and M2 are modified cylindrical

mirrors to provide uniform chromatic dispersion within each channel, according to an

embodiment of the present invention. While FIG. 48(A) shows an apparatus

configured for two wavelengths, there is generally no limit in the number of

wavelength filters and mirrors which can be used to separate additional wavelengths

or channels. For example, FIG. 49 is a diagram illustrating a side or top view of an

apparatus which uses a VIPA to provide three different chromatic dispersion for

different channels, according to an embodiment of the present invention. Referring

now to FIG. 49, wavelength filters 520 and 530 are used to direct light at wavelengths

λl, λ2 and λ3 to mirrors Ml, M2 and M3, respectively.

According to the above embodiments of the present mvention, an apparatus

which uses a VIPA in combination with a mirror, such as a cone or modified cone

shaped mirror, to generate dispersion slope or higher order dispersion. The cone or

modified cone shape of the mirror is designed so that the dispersion slope or higher

order dispersion of the apparatus compensates for dispersion slope or higher order

dispersion of a transmission line (fiber).

In an optical communication system in which a transmitter transmits an optical

signal through a transmission line to a receiver, the apparatus of the present invention

can be inserted in the transmitter, the transmission line, the receiver, or in any

combination of the transmitter, transmission line and receiver. For example, in FIG.

1 , the apparatus of the present invention can be inserted in transmitter 30, optical fiber

34 (for example, a transmission line) or receiver 36, or in any combination of

transmitter 30, optical fiber 34 and receiver 36. Further, two or more of the

apparatuses of the present invention can be cascaded together, or only one apparatus

can be used in transmitter 30, optical fiber 34 and/or receiver 36. Thus, the present

invention is not limited to the number of apparatuses which can be used together to provide the required affect. One problem with an apparatus which use a VIPA to provide chromatic

dispersion, as in the above-described embodiments ofthe present invention, is that the

apparatus has a relatively narrow band in the transmission spectrum. Generally, the

band is narrow due to insertion loss from fiber-to-fiber. For example, in FIG. 13,

insertion loss occurs from the light traveling out of fiber 246 to when the light is again received by fiber 246 after traveling through VIPA 240 and being reflected by mirror

254.

For example, FIG. 50 is a graph illustrating the insertion loss in an apparatus

present invention. Referring now to FIG. 50, curve 550 illustrates the actual insertion

loss which might typically occur for one channel. By contrast, curve 560 illustrates a

more desirable insertion loss for the channel.

The insertion loss is due to several different factors, one major factor is a loss

due to different diffraction efficiency at different wavelengths.

For example, FIG. 51 is a diagram illustrating different diffraction efficiency

at different wavelengths. Referring now to FIG. 51, light output from VIPA 240 is

focused by lens 252 on a mirror 570. Light at the shortest wavelength is focused at

point 580, light at the center wavelength is focused at point 590, and light at the longest

wavelength is focused at point 600. However, due to the characteristics of VIPA 240,

and especially to the physics underlying the multiple reflection incurring inside VIPA

240, the light at the center wavelength at point 590 will be the strongest, whereas the light at the shortest wavelength and the longest wavelength at points 580 and 600,

respectively, will be weaker.

For example, FIG. 52 is a diagram illustrating the light intensity of light

traveling out of a fiber and into a VIPA in the above embodiments of the present

invention. FIG. 52 includes fiber 246 and lenses 248 and 250 as in FIG. 13, but the

VIPA is removed and the light is allowed to travel to a screen 610. A dotted box 240

shows where the VIPA would be positioned.

As indicated in FIG. 52, the light has a light intensity shown by curve 620 at

screen 610. As a result, the insertion loss can be made closer to the desired insertion

loss 560 in FIG. 50 if the far field distribution of the input light provided to the VIPA

is a double-humped shape. In this manner, the transmission spectrum ofthe apparatus

will be much flatter.

FIG. 53 is a diagram illustrating a side view of an optical phase mask on an

which uses a VIPA to provide chromatic dispersion, according to an embodiment of the

present invention. Referring now to FIG. 53, an input fiber 246 (corresponding, for

example, to input fiber 246 in FIG. 13) has a core 650. Optical phase masks 660 and

670 cover a portion of the top and bottom, respectively, of core 650. As a result, a

double-humped shape far field distribution will be provided at the input to the VIPA

(not illustrated in FIG. 53), and the insertion loss of the apparatus will have a more

desirable insertion loss. FIG. 54 is a diagram illustrating a cross-sectional view along lines 54—54 in

FIG. 53, according to an embodiment of the present invention. As can be seen from

FIGS. 53 and 54, phase masks 660 and 670 cover the top and bottom, respectively.

The phase masks should not be on the side portions of the core. It is not necessary for the phase masks to be on the input fiber. Instead, for

example, the phase masks could be on the VIPA.

For example, FIG. 55 is a diagram illustrating a side view of phase masks on

a VIPA to provide a double-humped shape far field distribution with respect to light

received inside the VIPA, according to an embodiment of the present invention.

Elements in FIG. 55 are similar to that in FIG. 11.

Referring now to FIG. 55, optical phase masks 690 and 695 are positioned on

the light incident window surface 124, to provide a double-humped shape far field

distribution of light received into the VIPA.

FIG. 56 is a diagram illustrating a side view of phase masks on a VIPA to

inside the VIPA, according to an additional embodiment ofthe present invention. FIG.

56 is different than FIG. 55 in that phase masks 690 and 695 are provided on reflecting

surface 122. Therefore, phase masks can be on either reflecting surface or on the light

incident window of the VIPA.

Further, a double-humped shape far field distribution can be obtained by

positioning phase masks in the center of the input light. For example, FIGS. 57 and 58 are diagrams illustrating a side view of phase

masks on a VIPA to provide a double-humped shape far field distribution with respect

to light received inside the VIPA, according to an additional embodiment ofthe present

invention. In FIGS. 57 and 58, a phase mask 700 is positioned in the center of the

input light. In this case, the optical phase at the center of the far field distribution may

be π, and may be 0 at the ends. This is the opposite of the far field distribution in

FIGS. 53-56.

As indicated above, phase masks can be used to provide a double-humped shape

far field distribution. The phase mask preferably has a thickness corresponding to the

addition of π to the optical phase. However, a preferable range of optical phase added

by the phase mask is 2/3 π to 4/3 π.

Any transparent material that provides the proper additional phase can be used

for the phase mask. For example, SiO₂ would be a typical material for use as a phase

mask.

As indicated above, a phase mask is used to provide a double-hump shaped far

field distribution. Here, a "double-humped shape" is defined as having two almost

identical peaks with a valley between the peaks. The depth ofthe valley should be less

than or equal to 50% of the top peak value, and preferably less than 20% of the top

peak value. Preferably, the peaks are identical, but it is satisfactory for the peaks to

have an amplitude of within 10% of each other. Further, instead of using a phase mask, there are other ways to produce a

double-hump shaped far field distribution, and the present invention is not limited to

using a phase mask for this purpose.

The above described embodiments using a phase mask to produce a double-

hump shaped far field distribution are applicable to embodiments of the present

invention that use a VIPA to produce chromatic dispersion. However, these

embodiments are also applicable to the use of a VIPA as a demultiplexer. For

example, the above-described embodiments ofthe present invention relating to the use

of a phase mask to produce a double-hump shaped far field distribution can be applied

to the VIPA in FIGS . 7 and 8.

As described above, an apparatus using a VIPA to compensate for chromatic

dispersion would typically have a loss curve in each WDM channel as shown in FIG.

50. As described above, this loss curve can be flattened by using an optical phase

mask. However, there are other ways to flatten the loss curve, such as by adding

excess loss.

For example, FIG. 59 is a diagram illustrating excessive loss added to the loss curve, according to an embodiment of the present invention. Referring now to FIG.

59, by adding excess loss 705, loss curve 550 will be flattened to become curve 710.

excess loss, and thereby flatten the loss curve, according to an embodiment of the

present invention. Referring now to FIG. 60, a VIPA dispersion compensator 720 represents an apparatus which uses a VIPA to produce chromatic dispersion, as described herein. An excess loss component 730 is cascaded with VIPA dispersion

component 720. Excess loss component 730 could be either upstream or downstream

of VIPA dispersion component 720 and there might be some optical components

between VIPA dispersion component 720 and excess loss component 730. Thus, the

present invention is not limited to any specific placement of VIPA dispersion

component 720 with respect to excess loss component 730.

Excess loss component 730 can be, for example, an optical interferometer or

a wavelength filter. However, a Mach-Zehnder interferometer or a Fabry-Perot

interferometer would be suitable, because they have a periodic transmission curve and

the period can be adjusted to the WDM channel spacing by choosing appropriate

parameters of the interferometer. Therefore, the overall transmission curve will be

flattened for all the WDM channels simultaneously.

The above described embodiments using an excess loss component are

applicable to embodiments of the present invention that use a VIPA to produce

chromatic dispersion. However, these embodiments are also applicable to the use of a

VIPA as a demultiplexer. For example, the above-described embodiments of the

present invention relating to the use of an excess loss component can be applied with

the VIPA in FIGS. 7 and 8.

Instead of using an excessive loss component, there are other ways to flatten the loss curve.

For example, FIG. 61 is a diagram illustrating a side view of a mirror for use

with a VIPA to provide chromatic dispersion, and which will flatten the loss curve, according to an embodiment of the present invention. Referring now to FIG. 61, a

mirror 704 could be a cone shaped mirror, a modified cone shaped mirror, a flat

mirror, or any other shape mirror. FIG. 61 shows positions P, Q and R in the side

view. Positions P, Q and R corresponds, respectively to points 274, 270 and 272,

respectively, in FIG. 14. Light at a shorter wavelength is focused at point 274 or P,

and light at a longer wavelength is focused at point 272 or R.

The reflectivity on mirror 740 is modulated along the angular dispersion

direction of the VIPA. That is, the reflectivity at the position Q is lowest, to thereby

provide a higher loss, and the reflectivity at the position P and R is higher, to thereby

provide a lower loss. Therefore, the power of the reflected light is reduced near the

center of the WDM channel, and thus the loss curve is flattened. To modify the

reflectivity, a layer of light absorbing material may be coated near position Q or, in the

case of a multi-layer mirror, the thickness of one or more layer may be modulated.

This modulation ofthe reflectivity can be effectively achieved by patterning the

mirror instead of actually modulating the reflectivity , if the VIPA is used with a mirror

which is not a cone or modified cone shape, that is, if the VIPA is used with a mirror

such as, for example, mirror 254 in FIGS. 14, 20(A), 20(B), or the mirror shapes in

FIGS. 28(A) through 28(F).

For example, FIG. 62 is a diagram illustrating a front view of a mirror 750,

according to an embodiment of the present invention. Referring now to FIG. 62,

mirror 750 is patterned as illustrated in the figure, to change the reflectivity of mirror

750. Here, the width of mirror 750 is smaller than the focused beam size 760 near the position Q, and therefore, the light power reflected from near position Q is reduced.

FIGS. 63(A), 63(B) and 63(C) are diagrams illustrating another way to

modulate the effective reflectivity in the case of a VIPA used with a mirror 770 which

is not a cone or modified cone shape, according to an embodiment of the present invention. More specifically, FIGS. 63(A), 63(B) and 63(C) illustrate a top view of

incident beam 780 on mirror 770 at positions P, Q and R, respectively. As illustrated

in FIGS. 63(A), 63(B) and 63(C), instead of modulating the reflectivity, the mirror

angle in the top view is changed. In previously described embodiments of the present invention, such as that in FIG. 14, the mirror is preferably perpendicular to the average

light incident angle in the top view. However, if the mirror is tilted in the top view,

as in FIGS. 63(A), 63(B) and 63(C), the reflected light is deflected and the coupling

efficiency to the output fiber is reduced. At positions P and R, incident light 780 is

perpendicular to mirror 770 and the light is fully returned to the output fiber. On the

other hand, at position Q, mirror 770 is tilted in the top view and the reflected light is

slightly diverged from the output fiber direction. This causes an excess loss and

flattening of the loss curve. By changing this tilting angle of mirror 770 in the top

view gradually along the angular dispersion direction of the VIPA, the excess loss to

flatten the loss curve can be effectively produced. The changing ofthe mirror angle as in FIGS. 63(A), 63(B) and 63(C), and the

patterning of the mirror as in FIG .62 , could be used in the above-described apparatuses

which use a VIPA in combination with a mirror which is not cone or modified cone shaped. This is because, in the case of a cone or modified cone shaped mirror, the

light at a wavelength may be focused effectively at different positions on the mirror in

the top view, and therefore, the mirror should not be patterned or tilted in the top view.

FIG. 64 is a diagram illustrating the use of a grating between a VIPA and a

lens , according to an embodiment of the present invention. FIG. 64 is similar to FIGS .

44 and 45. However, whereas the embodiments in FIGS. 44 and 45 use a holographic

grating and a reflection type grating, respectively, the embodiment in FIG. 64 uses a

grating 800. Grating 800 is, for example, a type of transmission grating, but the output

light from grating 800 has a large angle which is in a range of greater than or equal to

30 degrees and less than or equal to 150 degrees from the input light to grating 800.

For example, in the specific example of FIG. 64, the output light from grating 800 is

approximately 90 degrees from the input light to grating 800. Grating 800 may be

made, for example, holographically. The configuration in FIG. 64 is highly practical,

since the angular dispersion of grating 800 is relatively large within a small space.

Moreover, the embodiments in FIGS. 46 and 47 can be applied to the

embodiment in FIG. 64. More specifically, quarter wave plate 530, as shown in FIGS. 46 and 47, can be applied to the embodiment in FIG. 64, to cancel the polarization

dependence of grating 800.

In FIGS.44, 45 and 64, mirror 400 could be movable to change the dispersion

amount.

For example, FIGS. 65, 66 and 67 correspond, respectively, to FIGS. 44, 45

and 64, but show mirror 400 as being movable to change the dispersion amount. For example, in FIGS. 65, 66 and 67, mirror 400 is movable in a direction 810 along the

surface of mirror 400 and perpendicular to the angular dispersion direction 402 of

VIPA 240.

As should be understood from the above, in various embodiments ofthe present

invention, the amount of chromatic dispersion can be changed. Therefore, the VIPA

operates in conjunction with other elements (such as a mirror, lens, etc) to provide a

tunable chromatic dispersion compensator.

FIGS. 68 and 69 illustrate a tunable dispersion compensator, according to

another embodiment ofthe present invention. Referring now to FIGS. 68 and 69, the

tunable dispersion compensator comprises a variable-curvature mirror 455 whose

curvature changes along a dimension parallel to the angular dispersion direction of a

VIPA 340. As illustrated in FIG. 70, the variable-curvature mirror 455 comprises, for

example, a flat portion 455a and a convex portion 455b, although an unlimited number

of other configurations are possible.

As illustrated in FIGS . 68 and 69, the tunable dispersion compensator comprises

a mechanism for rotating the variable-curvature mirror 455 about an axis 456 that is

perpendicular to the angular dispersion direction of VIPA 340. Alternatively, axis 456

can be described as being perpendicular to a plane which includes the traveling

directions of the collimated output lights for different wavelengths from VIPA 340.

The rotation around axis 456 allows differently curved portions of mirror 455 to be

brought into the focal plane of a focusing lens 352. FIGS. 68 and 69 both illustrate the pathways of light comprising a longer wavelength 464 of a channel and of the light comprising a shorter wavelength 468 of

a channel through the tunable dispersion compensator. However, the light comprising

any optical channel comprises light of a continuum of wavelengths. In FIG. 68,

variable-curvature mirror 455 is disposed so that convex portion 455b intercepts and

reflects the longer wavelength light 464 and the shorter wavelength light 468, whereas,

in FIG. 69, the mirror is disposed such that flat portion 455a intercepts and reflects

these lights. As previously described, the convex and flat portions 455a-455b reflect

lights 464 and 468 back through lens 352 and back into VIPA 340 such that a greater

magnitude of chromatic dispersion is produced when the convex portion is disposed in

the light paths.

Because variable-curvature mirror 455 comprises a plate with axis of rotation

456 disposed on or within the plate, then, in general, the axis of rotation does not

coincide with the center of curvature of any particular portion of variable-curvature

mirror 455. Therefore, rotation of variable-curvature mirror 455 about axis 456 will generally not bring the differently curved portions of variable-curvature mirror 455 into

the correct position at or near the focus of lens 352. Therefore, the movement of the

mirror between its various positions comprises both a rotation of variable-curvature

mirror 455 about axis 456 as well as a translation of axis 456 along a pre-defined path.

In FIGS. 68 and 69, axis 456 comprises a rod or pin which is caused to move along a

slot or track 458 during rotation from the position illustrated in FIG. 68 to that illustrated in FIG. 69, and vice versa. Alternatively, the translation of the axis might be realized by many other mechanisms. The rotation of mirror 455 and translation of

axis 456 are simultaneously controlled in the apparatus so as to bring mirror portions

comprising different magnitudes and types of curvature (convex, concave, and planar)

into the path of the light paths as desired. In this fashion, this apparatus in FIGS. 68

and 69 functions as a tunable chromatic dispersion compensator.

FIG. 71 illustrates a tunable dispersion compensator, according to another

embodiment of the present invention. The compensator in FIG. 71 comprises similar

components to the compensator in FIGS. 68 and 69 except that a mirror assembly 558

of the compensator replaces the single variable-curvature mirror 455 in FIGS. 68 and

69. Mirror assembly 558 comprises a plurality of mirrors 555a, 555b, 555c, etc. all

rigidly disposed approximately equidistantly from a rotational axis 556. Here, a

"plurality" of mirrors indicates two or more mirrors or mirror segments. These mirror

or mirror segments generally comprise surfaces with a variety of magnitudes and types

of curvature (convex, concave, and planar). The mirrors or mirror segments 555a,

555b, 555c, etc. are attached to a mirror holder 557 centered upon the rotational axis

556. Through rotation of mirror holder 557 about axis 556, different respective

individual mirrors of the plurality of mirrors 555a, 555b, 555c, etc. may be brought

into position so as to intercept and reflect lights 464 and 468.

In FIG. 71, mirror holder 557 comprises a cylinder centered upon rotational

axis 556. However, any geometric shape or construction may be utilized for mirror

holder 557 provided that the distance from the center of lens 352 to the surface of the

mirror from which lights 464 and 468 are reflected is maintained approximately equal to the focal distance of lens 352. Although the mirrors or mirror segments 555a, 555b,

555c, etc. are illustrated as separate non-contiguous mirror segments in FIG. 71, these

mirrors may also comprise portions of a single mirror surface of continuously varying

curvature.

FIG. 72 is a diagram illustrating a tunable dispersion compensator, according

to another embodiment of the present invention. The tunable dispersion compensator

in FIG. 72 comprises the same VIPA 340 and focusing lens 352 components that also

comprise the tunable dispersion compensator in FIGS. 68 and 69, and the tunable

dispersion compensator in FIG. 71. However, in contrast to the tunable dispersion

compensator in FIGS. 68 and 69, and the tunable dispersion compensator in FIG. 71,

there is no curved mirror disposed along the focal line of lens 352. Instead, the

compensator in FIG. 72 comprises a plurality of mirrors or mirror segments 655a,

655b, 655c, etc. disposed off said focal line and a rotating flat mirror 602. The mirror

or mirror segments 655a, 655b, 655c, etc. generally comprise surfaces with a variety

of magnitudes and types of curvature (convex, concave, and planar). Although these

mirrors or mirror segments are illustrated as separate non-contiguous mirror segments

in FIG. 72, these mirrors may also comprise portions of a single mirror surface of

continuously varying curvature.

In FIG. 72, the rotating flat mirror 602 is disposed along the focal line of lens

352 opposite to VIPA 340 and at an angle to this line so as to fold the paths of lights

464 and 468 onto one or more of the mirrors or mirror segments 655a, 655b, 655c,

etc. Flat mirror 602 rotates about an axis 603 that is disposed at the reflective surface flat mirror 602 and along the focal line of lens 352. It is to be kept in mind that axis

603 shown in FIG. 72 is generally not a physical component but only a geometrical

construction. The pathway (not shown) of light of a center wavelength of an optical

channel intercepts mirror 602 at the position of rotational axis 603.

The plurality of mirrors or mirror segments 655a, 655b, 655c, etc. comprising

the tunable dispersion compensator in FIG. 72 are disposed along a circular arc 606

which represents a portion of a circle centered at rotational axis 603. The radius of arc 606 is such that the sum ofthe distance from the center of lens 352 to axis 603 plus the

distance from axis 603 to arc 606 is equal to the focal distance of lens 352. Therefore,

lights 464 and 468 are both focused or approximately focused at points 472 and 474,

respectively, wherein both points 472 and 474 are located at the surface of one of the

mirrors or mirror segments 655a, 655b, 655c, etc. Lights 464 and 468 are reflected

by one of the plurality of mirrors or mirror segments 655a, 655b, 655c, etc. such that

each of lights 464 and 468 returns back to the rotating flat mirror 602, back through

lens 352 and back into VIPA 340.

In the tunable dispersion compensator of FIG. 72, the amount of chromatic

dispersion produced in the optical signal comprising lights 464 and 468 may be varied by rotating flat mirror 602 about its center as shown by the adjustment direction 604.

This rotation of the rotating flat mirror 602 causes controlled movement of the

reflection points 472 and 474 from one to another of the fixed set of mirrors or mirror

segments 655a, 655b, 655c, etc. As previously described, the magnitude and direction of the mirror curvature of the particular mirror or mirror segment of the set 655a, 655b, 655c, etc. from which the signal lights are reflected back to VIPA 340

determines the amount of chromatic dispersion produced by the apparatus. The signal

lights remain focused at the surface of each mirror or mirror segment 655a, 655b,

655c, etc. according to the disposition of these mirrors or mirror segments along arc

606. In this fashion, this apparatus functions as a tunable chromatic dispersion

compensator.

FIG. 73 is a diagram illustrating a tunable dispersion compensator, according

to a further embodiment of the present invention. The tunable dispersion compensator

in FIG. 73 comprises the same VIPA 340 as that within the tunable dispersion

compensators in FIGS. 68, 69, 71 and 72. However, in contrast to these other tunable

dispersion compensators, the tunable dispersion compensator in FIG. 73 does not

comprise a focusing lens at the output side of VIPA 340. Instead, the tunable

dispersion compensator in FIG. 73 comprises an off-axis parabolic mirror 702 that

performs the focusing function. Off-axis parabolic mirror 702 is disposed at the output

side of VIPA 340 so as to intercept and reflect the lights comprising an optical channel

that are output by VIPA 340. The paths of two such lights, a light 464 comprising a

longer wavelength and a light 468 comprising a shorter wavelength, are illustrated in

FIG. 73. Off-axis parabolic mirror 702 is capable of rotation about an axis 703 that

is disposed along the line at which the light of a central wavelength (not shown) of an

optical channel intercepts parabolic mirror 702. It is to be kept in mind that axis 703

shown in FIG. 73 is generally not a physical component but only a geometrical construction. Off-axis parabolic mirror 702 comprises a focus point 705. Through the

focusing power of off-axis parabolic mirror 702, collimated light rays output by VIPA

340 and comprising a central wavelength of an optical channel (not shown) are brought

to a focus at point 705. Light 464 comprising a longer wavelength and light 468

comprising a shorter wavelength of said channel are focused at points 472 and 474,

respectively, as illustrated in FIG. 73. Points 472 and 474 are disposed at opposite sides of focus point 705, as further illustrated in FIG. 73. During rotation of off-axis

parabolic mirror 702 about axis 703, focus point 705 and points 472 and 474 move

along an arc 706 that represents a portion of a circle centered at axis 703. The tunable

dispersion compensator in FIG. 73 further comprises a plurality of mirrors or mirror

segments 755a, 755b, 755c, etc., whose surfaces are tangentially disposed along arc

706. Although the mirrors or mirror segments 755a, 755b, 755c, etc. are illustrated

as separate non-contiguous mirror segments in FIG. 73, these mirrors may also

comprise portions of a single mirror surface of continuously varying curvature.

In the tunable dispersion compensator of FIG. 73, the amount of chromatic

dispersion produced in the optical signal comprising the lights 464 and 468 may be

varied by rotating off-axis parabolic mirror 702 about the axis 703 as shown by the

adjustment direction 704. This rotation of off-axis parabolic mirror 702 causes

controlled movement of the reflection points 472 and 474 from one to another of the set of mirrors or mirror segments 755a, 755b, 755c, etc. The lights comprising a

signal channel are then reflected by one ofthe mirrors or mirror segments 755a, 755b,

755c, etc. back to off-axis parabolic mirror 702. These lights are then re-collimated by off-axis parabolic mirror 702 and reflected back to VIPA 340. As previously

described, the magnitude and type (convex, concave or planar) ofthe mirror curvature

ofthe particular mirror or mirror segment ofthe set 755a, 755b, 755c, etc. from which

the signal lights are reflected back to the VIPA determines the amount of chromatic

dispersion produced by the apparatus in FIG. 73. The signal lights remain focused at

the surface of each mirror or mirror segment 755a, 755b, 755c, etc. according to the

disposition of these mirrors or mirror segments along arc 706. In this fashion, this

apparatus functions as a tunable chromatic dispersion compensator.

As described above, a mirror is used to reflect light back into a VIPA . Thus,

a mirror can be referred to as a "light returning device" which returns light back to the

VIPA. However, the present invention is not limited to the use of a mirror as a light returning device. For example, a prism (instead of a mirror) can be used as a light

returning device to return light back to the VIPA. Moreover, various combinations of

mirrors and/or prisms, or lens apparatuses can be used as a light returning device to

return light back to VIPA.

In various embodiments of the present invention, a lens is used to focus light from a VIPA to a mirror, and to direct the returning light from the mirror back to the

VIPA. See, for example, the operation of lens 252 in FIG. 13. However, the present

invention is not limited to using a lens for this purpose. Instead, other types of light

directing devices can be used in place of the lens. For example, a mirror can be used in place of lens 252 to focus the light from the VIPA, and to direct the returning light

back to the VIPA. In the above embodiments ofthe present invention, a VIPA has reflecting films to reflect light. For example, FIG. 8 illustrates a VIPA 76 having reflecting films 122

and 124 to reflect light. However, it is not intended for a VIPA to be limited to the use

of "film" to provide a reflecting surface. Instead, the VIPA must simply have

appropriate reflecting surfaces , and these reflecting surfaces may or may not be formed

by "film".

Further, in the above embodiments of the present invention, a VIPA includes

a transparent glass plate in which multiple reflection occurs. For example, FIG. 8

illustrates a VIPA 76 having a transparent glass plate 120 with reflecting surfaces

thereon. However, it is not intended for a VIPA to be limited to the use of a glass

material, or any type of "plate", to separate the reflecting surfaces. Instead, the

reflecting surfaces must simply be maintained to be separated from each other by some

type of spacer. For example, the reflecting surfaces of a VIPA can be separated by

"air" , without having a glass plate therebetween. Therefore, the reflecting surfaces can be described as being separated by a transparent material which is , for example, optical

glass or air.

According to the above embodiments ofthe present invention, an apparatus uses

a VIPA to compensate for chromatic dispersion. For this purpose, the embodiments

ofthe present invention are not intended to be limited to a specific VIPA configuration.

Instead, any of the different VIPA configurations discussed herein, or those disclosed

inU.S. application number 08/685,362, which is incorporated herein by reference, can

be used in an apparatus to compensate for chromatic dispersion. For example, the VIPA may or may not have a radiation window, and the reflectances on the various

surfaces of the VIPA are not intended to be limited to any specific examples.

The present invention relates to a VIPA dispersion compensator. The term

"VIPA dispersion compensator" refers to an apparatus which uses a VIPA to produce

chromatic dispersion, such as those described herein. For example, the apparatuses in

FIGS. 13, 19, 32, 42, 44 and 48(A), among others, show a VIPA dispersion

compensator.

The various embodiments of a VIPA described herein can also be referred to

as a virtually imaged phased array (VIPA) generator.

Although a few preferred embodiments of the present invention have been

shown and described, it would be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of

the invention, the scope of which is defined in the claims and their equivalents.

Claims

CLAIMSWhat is claimed is:

1. An apparatus comprising:

a virtually imaged phased array (VIPA) generator receiving an input light at a

respective wavelength and producing a corresponding collimated output light traveling

from the VIPA generator in a direction determined by the wavelength ofthe input light; and

a reflecting surface reflecting the output light back to the VIPA generator, the

reflecting surface having different curvatures at different positions along a direction

perpendicular to a plane which includes the traveling directions of collimated output

light from the VIPA generator for input light at different wavelengths.

2. An apparatus as in claim 1, further comprising:

a lens or mirror focusing the output light traveling from the VIPA generator

onto the reflecting surface so that the reflecting surface reflects the output light, the

reflected light being directed by said lens or mirror back to the VIPA generator.

3. An apparatus as in claim 1, wherein the reflecting surface has a cone or

modified cone shape.

4. An apparatus as in claim 2, wherein the reflecting surface is movable in or

around a focal plane of the lens.

5. An apparatus as in claim 2, wherein the reflecting surface has a cone or

modified cone shape.

6. An apparatus as in claim 2 , wherein the reflecting surface touches a focal plane

of the lens along a line which is in the focal plane and is perpendicular to the light

traveling directions of the collimated output light from the VIPA.

7. An apparatus as in claim 1, wherein the reflecting surface is movable in the

direction of said line.

8. An apparatus as in claim 2, further comprising: an angular dispersive element between the VIPA generator and said lens or

mirror, the angular dispersive element having an angular dispersion direction which is

perpendicular to said plane.

9. An apparatus as in claim 8, wherein the angular dispersive element is a

transmission type diffraction grating, a reflection type diffraction grating or a

holographic grating.

10. An apparatus as in claim 1, wherein the input light received by the VIPA

generator has a double-hump shaped far field distribution.

11. An apparatus as in claim 1, further comprising:

means for causing the input light received by the VIPA generator to have a

double-hump shaped far field distribution.

12. An apparatus as in claim 1, further comprising:

at least one phase mask causing the input light received by the VIPA generator

to have a double-hump shaped far field distribution.

13. An apparatus as in claim 1, further comprising:

a fiber providing the input light to the VIPA generator; and

at least one phase mask on the fiber to cause the input light received by the

VIPA generator to have a double-hump shaped far field distribution.

14. An apparatus as in claim 1, further comprising:

at least one phase mask on a surface of the VIPA generator to cause the input

light received by the VIPA generator to have a double-hump shaped far field

distribution.

15. An apparatus as in claim 1, wherein the input light is a wavelength division multiplexed (WDM) light having a

plurality of channels, each channel having an amount of chromatic dispersion

corresponding to wavelength and due to traveling through a transmission line, and

parameters of the reflecting surface cause the apparatus to provide chromatic

dispersion to each channel in the same amount but opposite sign to that due to traveling

through the transmission line.

16. An apparatus as in claim 1, wherein

the input light has an associated loss curve, and the apparatus further comprises an excess loss component adding loss to the

input light to flatten the loss curve.

17. An apparatus comprising: a virtually imaged phased array (VIPA) generator receiving an input light at a

from the VIPA generator in a direction determined by the wavelength ofthe input light,

the output light thereby being spatially distinguishable from an output light produced

for an input light at a different wavelength;

reflecting surface having a cone or modified cone shape; and

a lens or mirror focusing the output light traveling from the VIPA generator

onto the reflecting surface so that the reflecting surface reflects the output light, the reflected light being directed by the said lens or mirror back to the VIPA generator.

18. An apparatus as in claim 17, wherein the cone or modified cone shape of the

reflecting surface corrects for non-uniform chromatic dispersion.

19. An apparatus as in claim 17, wherein the cone or modified cone shaped reflecting surface is movable in direction which is perpendicular to an angular

dispersion direction of the VIPA generator.

20. An apparatus as in claim 17, wherein the reflecting surface is movable in a

direction perpendicular to a plane which includes the traveling directions of collimated

output light from the VIPA generator for input light at different wavelengths.

21. An apparatus as in claim 17, wherein the reflecting surface is movable in or

near a focal plane of said lens or mirror.

22. An apparatus as in claim 17, further comprising:

an angular dispersive element between the VIPA generator and the lens.

23. An apparatus as in claim 22, wherein the angular dispersive element has an angular dispersion direction which is perpendicular to an angular dispersion direction

of the VIPA generator.

24. An apparatus as in claim 22, wherein the angular dispersive element is a

holographic grating.

25. An apparatus as in claim 17, wherein the input light received by the VIPA

generator has a double-hump shaped far field distribution.

26. An apparatus as in claim 17, further comprising:

means for causing the input light received by the VIPA generator to have a

double-hump shaped far field distribution.

27. An apparatus as in claim 17, further comprising: at least one phase mask causing the input light received by the VIPA generator

to have a double-hump shaped far field distribution.

28. An apparatus as in claim 17, further comprising: a fiber providing the input light to the VIPA generator; and

at least one phase mask on the fiber to cause the input light received by the

VIPA generator to have a double-hump shaped far field distribution.

29. An apparatus as in claim 17, further comprising: at least one phase mask on a surface of the VIPA generator to cause the input

light received by the VIPA generator to have a double-hump shaped far field

distribution.

30. An apparatus as in claim 17, wherein

the input light is a wavelength division multiplexed (WDM) light having a

plurality of channels, each channel having an amount of chromatic dispersion

parameters of at least one of said reflecting surface and said lens or mirror cause

the apparatus to provide chromatic dispersion to each channel in the same amount but

opposite sign to that due to traveling through the transmission line.

31. An apparatus as in claim 17, wherein

the input light has an associated loss curve, and

the apparatus further comprises an excess loss component adding loss to the

input light to flatten the loss curve.

32. An apparatus comprising:

an angular dispersive component having a passage area to receive light into , and

to output light from, the angular dispersive component, the angular dispersive

component receiving, through the passage area, an input light having a respective

wavelength within a continuous range of wavelengths, and causing multiple reflection of the input light to produce self-interference that forms a collimated output light which

travels from the angular dispersive component along a direction determined by the

wavelength of the input light and is thereby spatially distinguishable from an output

light formed for an input light having any other wavelength within the continuous range

of wavelengths; and a reflecting surface reflecting the output light back to the angular dispersive

component to undergo multiple reflection in the angular dispersive component and then

be output from the passage area, the reflecting surface having different curvatures at

different positions along a direction which is perpendicular to a plane which includes

the travel direction of collimated output light from the angular dispersive component

for input light at different wavelengths.

33. An apparatus as in claim 32, further comprising:

a lens or mirror focusing the output light traveling from the angular dispersive component onto the reflecting surface so that the reflecting surface reflects the output

light, the reflected light being directed by said lens or mirror back to the angular

dispersive component.

34. An apparatus as in claim 32, wherein the reflecting surface has a cone or

modified cone shape.

35. An apparatus as in claim 33, wherein the reflecting surface has a cone or

modified cone shape.

36. An apparatus as in claim 32, wherein the reflecting surface is movable in a

direction perpendicular to said plane.

37. An apparatus as in claim 35, wherein the reflecting surface is movable in a

direction perpendicular to said plane.

38. An apparatus as in claim 33 , wherein the angular dispersive component is a first

angular dispersive component, the apparatus further comprising:

a second angular dispersive component between the first angular dispersive

component and said lens or mirror, the first angular dispersive component having an

angular dispersion direction which is perpendicular to said plane.

39. An apparatus as in claim 38 , wherein the second angular dispersive component

is a transmission type diffraction grating, a reflection type diffraction grating or a

holographic grating.

40. An apparatus as in claim 32, wherein the input light received by the angular

dispersive component has a double-hump shaped far field distribution.

41. An apparatus as in claim 32, further comprising:

means for causing the input light received by the angular dispersive component

to have a double-hump shaped far field distribution.

42. An apparatus as in claim 32, further comprising:

at least one phase mask causing the input light received by the angular

dispersive component to have a double-hump shaped far field distribution.

43. An apparatus as in claim 32, further comprising:

a fiber providing the input light to the angular dispersive component; and

at least one phase mask on the fiber to cause the input light received by the

angular dispersive component to have a double-hump shaped far field distribution.

44. An apparatus as in claim 32, further comprising:

at least one phase mask on a surface of the angular dispersive component to

cause the input light received by the angular dispersive component to have a double- hump shaped far field distribution.

45. An apparatus comprising:

to output light from, the angular dispersive component, the angular dispersive component receiving, through the passage area, a line focused input light and causing multiple reflection of the input light to produce self-interference that forms a collimated

from an output light formed for an input light having a different wavelength; and

a reflecting surface reflecting the output light back to the angular dispersive

for input light at different wavelengths.

46. An apparatus as in claim 45, further comprising:

a lens or mirror focusing the output light traveling from the angular dispersive

component onto the reflecting surface so that the reflecting surface reflects the output

dispersive component.

47. An apparatus as in claim 45, wherein the reflecting surface has a cone or

modified cone shape.

48. An apparatus as in claim 46, wherein the reflecting surface has a cone or

modified cone shape.

49. An apparatus as in claim 45, wherein the reflecting surface is movable in a

direction perpendicular to said plane.

50. An apparatus as in claim 46, wherein the reflecting surface is movable in a

direction perpendicular to said plane.

51. An apparatus as in claim 46 , wherein the angular dispersive component is a first

angular dispersive component, the apparatus further comprising:

a second angular dispersive component between the first angular dispersive

component and said lens or mirror, the second angular dispersive component having

an angular dispersion direction which is perpendicular to said plane.

52. An apparatus as in claim 51 , wherein the second angular dispersive component

holographic grating.

53. An apparatus as in claim 45, wherein the input light received by the angular

dispersive component has a double-hump shaped far field distribution.

54. An apparatus as in claim 45, further comprising: means for causing the input light received by the angular dispersive component

to have a double-hump shaped far field distribution.

55. An apparatus as in claim 45, further comprising:

at least one phase mask causing the input light received by the angular

dispersive component to have a double-hump shaped far field distribution.

56. An apparatus as in claim 45, further comprising:

a fiber providing the input light to the angular dispersive component; and

at least one phase mask on the fiber to cause the input light received by the

57. An apparatus as in claim 45, further comprising:

at least one phase mask on a surface of the angular dispersive component to

cause the input light received by the angular dispersive component to have a double-

hump shaped far field distribution.

58. An apparatus comprising:

first and second reflecting surfaces, the second reflecting surface having a

reflectivity which causes a portion of light incident thereon to be transmitted

therethrough, where an input light at a respective wavelength is focused into a line, and the first and second reflecting surfaces are positioned so that the input

light radiates from the line to be reflected a plurality of times between the first and

second reflecting surfaces and thereby cause a plurality of lights to be transmitted

through the second reflecting surface, the plurality of transmitted lights interfering with

each other to produce a collimated output light which travels from the second reflecting

surface along a direction determined by the wavelength of the input light, and is

thereby specially distinguishable from an output light formed for an input light having

a different wavelength; and

a mirror surface reflecting output the light back to the second reflecting surface

to pass through the second reflecting surface and undergo multiple reflection between

the first and second reflecting surfaces, the mirror surface having different curvatures

at different positions along a direction which is perpendicular to a plane which

includes the travel direction of collimated output light from the second reflecting

surface for input light at different wavelengths.

59. An apparatus as in claim 58, further comprising:

a lens or mirror focusing the output light traveling from the second reflecting

surface onto the mirror surface so that the mirror surface reflects the output light, the

reflected light being directed by the said lens or mirror back to the second reflecting

surface.

60. An apparatus as in claim 58 , wherein the mirror surface has a cone or modified

cone shape.

61. An apparatus as in claim 59 , wherein the mirror surface has a cone or modified

cone shape.

62. An apparatus as in claim 59, wherein the mirror surface is movable in a

direction which is perpendicular to said plane.

63. An apparatus as in claim 59, further comprising:

an angular dispersive component between the second reflecting surface and said lens or mirror , the angular dispersive component having an angular dispersion direction

which is perpendicular to said plane.

64. An apparatus as in claim 63, wherein the angular dispersive component is a

holographic grating.

65. An apparatus as in claim 58 , wherein the input light has a double-hump shaped

far field distribution.

66. An apparatus as in claim 58, further comprising: means for causing the input light to have a double-hump shaped far field

distribution.

67. An apparatus as in claim 58, further comprising:

at least one phase mask causing the input light to have a double-hump shaped

far field distribution.

68. An apparatus as in claim 58, further comprising:

a fiber providing the input light to be focused into the line; and

at least one phase mask on the fiber to cause the input light to have a double-

hump shaped far field distribution.

69. An apparatus as in claim 58, further comprising:

at least one phase mask on one of the group consisting of first and second

reflecting surfaces, to cause the input light to have a double-hump shaped far field

distribution.

70. An apparatus comprising:

first and second reflecting surfaces, the second reflecting surface having a

reflectivity which causes a portion of light incident thereon to be transmitted

therethrough; means for causing an input light at a respective wavelength and focused into a

line to radiate from the line to be reflected a plurality of times between the first and

through the second reflecting surface , the plurality of transmitted lights interfering with each other to produce a collimated output light traveling from the second reflecting

surface in a direction determined by the wavelength of the input light, and is thereby

spatially distinguishable from an output light produced for an input light at a different

wavelength;

a mirror surface having a cone or modified cone shape; and

a lens or mirror focusing the output light traveling from the second reflecting

reflected light being directed by said lens or mirror back to the second reflecting

surface.

71. An apparatus comprising:

a virtually imaged phased array (VIPA) generator receiving a line focused

wavelength division multiplexed light including light at first and second wavelengths,

and producing collimated first and second output lights corresponding, respectively,

to the first and second wavelengths, the first and second output lights traveling from

the VIPA generator in first and second directions, respectively, determined by the first

and second wavelengths, respectively; a lens or light directing mirror focusing the first and second output lights

traveling from the VIPA generator;

first and second mirrors each having a cone shape or a modified cone shape for

producing a uniform chromatic dispersion; and

a wavelength filter filtering light focused by said lens or light directing mirror

so that light at the first wavelength is focused to the first mirror and reflected by the

first mirror, and light at the second wavelength is focused to the second mirror and

reflected by the second mirror, the reflected first and second lights being directed by the wavelength filter and said lens or light directing mirror back to the VIPA generator.

72. An apparatus as in claim 71 , wherein the first and second mirrors are movable

to change the amount of chromatic dispersion provided to light at the first and second

wavelengths, respectively.

73. An apparatus comprising:

first and second reflecting surfaces, the second reflecting surface having a

reflectivity which causes a portion of light incident thereon to be transmitted

therethrough, where a wavelength division multiplexed (WDM) light including light at first

and second wavelengths is focused into a line, and

the first and second reflecting surfaces are positioned so that the WDM

light radiates from the line to be reflected a plurality of times between the first and second reflecting surfaces and thereby cause a plurality of lights to be transmitted

through the second reflecting surface , the plurality of transmitted lights interfering with

each other to produce collimated first and second output lights corresponding,

respectively, to the first and second wavelengths, the first and second output lights

traveling from the second reflecting surface in first and second directions , respectively ,

determined by the first and second wavelengths, respectively;

a lens or light directing mirror focusing the first and second output lights

traveling from the second reflecting surface;

first and second mirrors each having a cone shape or a modified cone shape for

producing a uniform chromatic dispersion; and a wavelength filter filtering light focused by said lens or light directing mirror

reflected by the second mirror, the reflected first and second lights being directed by

the wavelength filter and said lens or light directing mirror back to the second

reflection between the first and second surfaces.

74. An apparatus as in claim 73 , wherein the first and second mirrors are movable

wavelengths, respectively.

75. A communication system comprising:

an optical transmission line;

a transmitter transmitting an optical signal through the transmission line;

a receiver receiving optical signal from the transmission line; and

a compensation device operatively connected in one of the group consisting of the transmitter, the receiver and the transmission line, to provide dispersion slope or

higher order dispersion to the optical signal, the compensation device comprising

a virtually imaged phased array (VIPA) generator receiving the optical

signal as a line focused input light and producing a corresponding collimated output

light traveling from the VIPA generator in a direction determined by a wavelength of

the input light,

a mirror having a cone or modified cone shape, and

a light directing device focusing the output light traveling from the VIPA

generator onto the mirror so that the mirror reflects the output light, the reflected light

being directed by the light directing device back to the VIPA generator.

76. A communication system comprising:

an optical transmission line;

a transmitter transmitting an optical signal through the transmission line;

a receiver receiving optical signal from the transmission line; and a compensation device operatively connected in one of the group consisting of

the transmitter, the receiver and the transmission line, to provide dispersion slope or

first and second reflecting surfaces , the second reflecting surface having

a reflectivity which causes a portion of light incident thereon to be transmitted

therethrough, where

the optical signal is focused into a line as a line focused input light to the compensation device, and

the first and second reflecting surfaces are positioned so that the

input light radiates from the line to be reflected a plurality of times between the first

and second reflecting surfaces and thereby cause a plurality of lights to be transmitted

surface along a direction determined by a wavelength of the input light, and is thereby

different wavelength, and

a mirror reflecting output the light back to the second reflecting surface

the first and second reflecting surfaces, the mirror having different curvatures at

different positions along a direction which is perpendicular to a plane which includes the travel direction of collimated output light from the second reflecting surface for

input light at different wavelengths.

77. An apparatus comprising:

a virtually imaged phased array (VIPA) generator receiving an input light at a

respective wavelength and having a double-hump shaped far field distribution, and

producing a corresponding collimated output light traveling from the VIPA generator

in a direction determined by the wavelength of the input light; and a reflecting surface reflecting the output light back to the VIPA generator.

78. An apparatus as in claim 77, further comprising:

a lens or mirror focusing the output light traveling from the VIPA generator

79. An apparatus as in claim 77, further comprising:

means for causing the input light received by the VIPA generator to have a

double-hump shaped far field distribution.

80. An apparatus as in claim 77, further comprising:

at least one phase mask causing the input light received by the VIPA generator

to have a double-hump shaped far field distribution.

81. An apparatus as in claim 77, further comprising: a fiber providing the input light to the VIPA generator; and

at least one phase mask on the fiber to cause the input light received by the

VIPA generator to have a double-hump shaped far field distribution.

82. An apparatus as in claim 77, further comprising:

at least one phase mask on a surface of the VIPA generator to cause the input

light received by the VIPA generator to have a double-hump shaped far field distribution.

83. An apparatus comprising:

a virtually imaged phased array (VIPA) generator receiving an input light at a

in a direction determined by the wavelength of the input light, the output light thereby

being spatially distinguishable from an output light produced for an input light at a

different wavelength;

a reflecting surface; and

a lens or mirror focusing the output light traveling from the VIPA generator

84. An apparatus as in claim 83, further comprising: means for causing the input light received by the VIPA generator to have a

double-hump shaped far field distribution.

85. An apparatus as in claim 83, further comprising:

at least one phase mask causing the input light received by the VIPA generator

to have a double-hump shaped far field distribution.

86. An apparatus as in claim 83, further comprising:

a fiber providing the input light to the VIPA generator; and at least one phase mask on the fiber to cause the input light received by the

VIPA generator to have a double-hump shaped far field distribution.

87. An apparatus as in claim 83, further comprising:

at least one phase mask on a surface of the VIPA generator to cause the input

light received by the VIPA generator to have a double-hump shaped far field

distribution.

88. An apparatus comprising: an angular dispersive component having a passage area to receive light into , and

to output light from, the angular dispersive component, the angular dispersive

wavelength within a continuous range of wavelengths and having a double-hump shaped far field distribution, and causing multiple reflection of the input light to

produce self-interference that forms a collimated output light which travels from the

angular dispersive component along a direction determined by the wavelength of the

input light and is thereby spatially distinguishable from an output light formed for an

input light having any other wavelength within the continuous range of wavelengths;

and

a reflecting surface reflecting the output light back to the angular dispersive

be output from the passage area.

89. An apparatus as in claim 88, further comprising:

dispersive component.

90. An apparatus as in claim 88, further comprising:

means for causing the input light received by the angular dispersive component

to have a double-hump shaped far field distribution.

91. An apparatus as in claim 88, further comprising: at least one phase mask causing the input light received by the angular

dispersive component to have a double-hump shaped far field distribution.

92. An apparatus as in claim 88, further comprising:

a fiber providing the input light to the angular dispersive component; and

at least one phase mask on the fiber to cause the input light received by the

93. An apparatus as in claim 88, further comprising:

at least one phase mask on a surface of the angular dispersive component to

hump shaped far field distribution.

94. An apparatus comprising:

to output light from, the angular dispersive component, the angular dispersive component receiving, through the passage area, a line focused input light having a

double-hump shaped far field distribution and causing multiple reflection of the input

light to produce self-interference that forms a collimated output light which travels

from the angular dispersive component along a direction determined by the wavelength

of the input light and is thereby spatially distinguishable from an output light formed

for an input light having a different wavelength; and a reflecting surface reflecting the output light back to the angular dispersive

be output from the passage area.

95. An apparatus as in claim 94, further comprising:

light, the reflected light being directed by the lens or mirror back to the angular

dispersive component.

96. An apparatus as in claim 94, further comprising:

means for causing the input light received by the angular dispersive component

to have a double-hump shaped far field distribution.

97. An apparatus as in claim 94, further comprising:

at least one phase mask causing the input light received by the angular

dispersive component to have a double-hump shaped far field distribution.

98. An apparatus as in claim 94, further comprising:

a fiber providing the input light to the angular dispersive component; and

at least one phase mask on the fiber to cause the input light received by the

99. An apparatus as in claim 94, further comprising:

at least one phase mask on a surface of the angular dispersive component to

hump shaped far field distribution.

100. An apparatus comprising:

first and second reflecting surfaces, the second reflecting surface having a

reflectivity which causes a portion of light incident thereon to be transmitted

therethrough, where

an input light at a respective wavelength is focused into a line and has

a double-hump shaped far field distribution, and

the first and second reflecting surfaces are positioned so that the input

a different wavelength; and a mirror surface reflecting output the light back to the second reflecting surface

the first and second reflecting surfaces.

101. An apparatus as in claim 100, further comprising:

a lens or light directing mirror focusing the output light traveling from the

second reflecting surface onto the mirror surface so that the mirror surface reflects the output light, the reflected light being directed by said lens or light directing mirror back

to the second reflecting surface.

102. An apparatus as in claim 100, further comprising:

means for causing the input light to have a double-hump shaped far field

distribution.

103. An apparatus as in claim 100, further comprising:

at least one phase mask causing the input light to have a double-hump shaped

far field distribution.

104. An apparatus as in claim 100, further comprising:

a fiber providing the input light to be focused into the line; and

at least one phase mask on the fiber to cause the input light to have a double-

hump shaped far field distribution.

105. An apparatus as in claim 100, further comprising:

at least one phase mask on one of the group consisting of first and second

distribution.

106. An apparatus comprising:

a virtually imaged phased array (VIPA) generator receiving a line focused input

light at a respective wavelength and producing a corresponding collimated output light

traveling from the VIPA generator in a direction determined by the wavelength of the

input light, the output light thereby being spatially distinguishable from an output light

produced for an input light at a different wavelength, the input light having an

associated loss curve; and

an excess loss component adding loss to the input light to flatten the loss curve.

107. An apparatus as in claim 106, wherein the excess loss component is one of the

group consisting of a Mach-Zehnder interferometer, a Fabry-Perot interferometer, an

optical interferometer and a wavelength filter.

108. An apparatus comprising:

a virtually imaged phased array (VIPA) generator receiving a line focused input

light at a respective wavelength and producing a corresponding collimated output light traveling from the VIPA generator in a direction determined by the wavelength of the

input light, the VIPA generator having a corresponding angular dispersion direction;

and

a reflecting surface reflecting the output light back to the VIPA generator to

provide chromatic dispersion or higher order dispersion to the input light, wherein

reflectivity of the reflecting surface is modulated along the angular dispersion direction

of the VIPA generator.

109. An apparatus as in claim 108 , wherein the reflecting surface is one of the group

consisting of a cone shaped mirror, a modified cone shaped mirror and a cylindrical mirror.

110. An apparatus comprising: a virtually imaged phased array (VIPA) generator receiving a line focused input

traveling from the VIPA generator in a direction determined by the wavelength ofthe

input light, the VIPA generator having a corresponding angular dispersion direction

and the input light having an associated loss curve;

a reflecting surface; and a lens or mirror focusing the output light traveling from the VIPA generator

onto the reflecting surface so that the reflecting surface reflects the output light, the reflected light being directed by the said lens or mirror back to the VIPA generator,

wherein the reflecting surface is patterned to flatten the loss curve.

111. An apparatus comprising :

a virtually imaged phased array (VIPA) generator receiving an input light at a

from the VIPA generator in a direction determined by the wavelength of the input light ;

and

light from the VIPA generator for input light at different wavelengths, curvature c(y)

of the reflecting surface being as follows:

112. An apparatus as in claim 111, further comprising:

a lens or mirror focusing the output light traveling from the VIPA generator

113. An apparatus as in claim 111, wherein the reflecting surface has a cone or

modified cone shape.

114. An apparatus as in claim 112, wherein the reflecting surface is movable in or

around a focal plane of the lens.

115. An apparatus as in claim 112, wherein the reflecting surface has a cone or

modified cone shape.

116. An apparatus as in claim 112, wherein the reflecting surface touches a focal

plane of the lens along a line which is in the focal plane and is perpendicular to the

light traveling directions of the collimated output light from the VIPA.

117. An apparatus as in claim 116, wherein the reflecting surface is movable in the

direction of said line.

118. An apparatus as in claim 112, further comprising:

an angular dispersive element between the VIPA generator and said lens or

perpendicular to said plane.

119. An apparatus as in claim 118, wherein the angular dispersive element is a

grating.

120. An apparatus as in claim 119, further comprising:

a quarter wave plate canceling polarization dependence of the grating.

121. An apparatus as in claim 119, wherein the reflecting surface is movable to

change a dispersion amount.

122. An apparatus as in claim 111, wherein the input light received by the VIPA

generator has a double-hump shaped far field distribution.

123. An apparatus as in claim 111, further comprising:

at least one phase mask causing the input light received by the VIPA generator

to have a double-hump shaped far field distribution.

124. An apparatus as in claim 111, further comprising:

VIPA generator to have a double-hump shaped far field distribution.

125. An apparatus as in claim 111, further comprising:

at least one phase mask on a surface of the VIPA generator to cause the input

126. An apparatus as in claim 111, wherein

the input light is a wavelength division multiplexed (WDM) light having a

plurality of channels, each channel having an amount of chromatic dispersion

parameters of the reflecting surface cause the apparatus to provide chromatic

through the transmission line.

127. An apparatus as in claim 111, wherein the VIPA generator comprises:

first and second surfaces, the first surface allowing substantially no light to be

transmitted therethrough; and

a radiation window in the same plane as the first surface, the input light passing through the radiation window to enter the VIPA generator , the first and second surfaces

positioned so that the input light entering the VIPA generator through the radiation

window is reflected a plurality of times between the first and second surfaces to

produce said output light.

128. An apparatus as in claim 127, wherein:

the first surface has substantially 100% reflectivity, and

the radiation window has substantially 100% transmissivity.

129. An apparatus comprising:

a virtually imaged phased array (VIPA) generator receiving an input light at a

from the VIPA generator in a direction determined by the wavelength of the input light ,

for an input light at a different wavelength;

reflecting surface having a cone or modified cone shape; and

a lens or mirror focusing the output light traveling from the VIPA generator

reflected light being directed by the said lens or mirror back to the VIPA generator,

curvature c(y) of the reflecting surface being as follows:

130. An apparatus as in claim 129, wherein the cone or modified cone shape of the

reflecting surface corrects for non-uniform chromatic dispersion.

131. An apparatus as in claim 129, wherein the cone or modified cone shaped

reflecting surface is movable in direction which is perpendicular to an angular

dispersion direction of the VIPA generator.

132. An apparatus as in claim 129, wherein the reflecting surface is movable in a

output light from the VIPA generator for input light at different wavelengths.

133. An apparatus as in claim 129, wherein the reflecting surface is movable in or

near a focal plane of said lens or mirror.

134. An apparatus as in claim 129, further comprising:

an angular dispersive element between the VIPA generator and the lens.

135. An apparatus as in claim 134, wherein the angular dispersive element has an

angular dispersion direction which is perpendicular to an angular dispersion direction

of the VIPA generator.

136. An apparatus as in claim 134, wherein the angular dispersive element is a

grating.

137. An apparatus as in claim 136, further comprising: a quarter wave plate canceling polarization dependence of the grating.

138. An apparatus as in claim 136, wherein the reflecting surface is movable to

change a dispersion amount.

139. An apparatus as in claim 129, wherein the input light received by the VIPA

generator has a double-hump shaped far field distribution.

140. An apparatus as in claim 129, further comprising:

at least one phase mask causing the input light received by the VIPA generator

to have a double-hump shaped far field distribution.

141. An apparatus as in claim 129, further comprising:

a fiber providing the input light to the VIPA generator; and

at least one phase mask on the fiber to cause the input light received by the

VIPA generator to have a double-hump shaped far field distribution.

142. An apparatus as in claim 129, further comprising: at least one phase mask on a surface of the VIPA generator to cause the input

light received by the VIPA generator to have a double-hump shaped far field

distribution.

143. An apparatus as in claim 129, wherein

the input light is a wavelength division multiplexed (WDM) light having a

plurality of channels, each channel having an amount of chromatic dispersion

opposite sign to that due to traveling through the transmission line.

144. An apparatus as in claim 129, wherein the VIPA generator comprises:

transmitted therethrough; and

a radiation window in the same plane as the first surface, the input light passing

through the radiation window to enter the VIPA generator, the first and second surfaces

produce said output light.

145. An apparatus as in claim 144, wherein:

the first surface has substantially 100% reflectivity, and

the radiation window has substantially 100% transmissivity.

146. An apparatus comprising: 2 an angular dispersive component having a passage area to receive light into, and

3 to output light from, the angular dispersive component, the angular dispersive

4 component receiving, through the passage area, an input light having a respective

5 wavelength within a continuous range of wavelengths, and causing multiple reflection

6 of the input light to produce self-interference that forms a collimated output light which

7 travels from the angular dispersive component along a direction determined by the

8 wavelength of the input light and is thereby spatially distinguishable from an output

9 light formed for an input light having any other wavelength within the continuous range

10 of wavelengths; and

11 a reflecting surface reflecting the output light back to the angular dispersive

12 component to undergo multiple reflection in the angular dispersive component and then

13 be output from the passage area, the reflecting surface having different curvatures at

14 different positions along a direction which is perpendicular to a plane which includes

15 the travel direction of collimated output light from the angular dispersive component

16 for input light at different wavelengths, .curvature c(y) of the reflecting surface being

17 as follows:

¹ i ⁸s c t(y Λ = ^K,y * ₊ ^mj,y 3 +, K@ ² —- (f₂ - a) y ₂.

1 147. An apparatus as in claim 146, further comprising:

2 a lens or mirror focusing the output light traveling from the angular dispersive

3 component onto the reflecting surface so that the reflecting surface reflects the output light, the reflected light being directed by said lens or mirror back to the angular

dispersive component.

148. An apparatus as in claim 146, wherein the reflecting surface has a cone or

modified cone shape.

149. An apparatus as in claim 147, wherein the reflecting surface has a cone or

modified cone shape.

150. An apparatus as in claim 147, wherein the reflecting surface is movable in a

direction perpendicular to said plane.

151. An apparatus as in claim 149, wherein the reflecting surface is movable in a

direction perpendicular to said plane.

152. An apparatus as in claim 147, wherein the angular dispersive component is a

first angular dispersive component, the apparatus further comprising:

a second angular dispersive component between the first angular dispersive

angular dispersion direction which is perpendicular to said plane.

153. An apparatus as in claim 152 , wherein the second angular dispersive component

is a grating.

154. An apparatus as in claim 153, further comprising:

a quarter wave plate canceling polarization dependence of the grating.

155. An apparatus as in claim 146, further comprising:

at least one phase mask causing the input light received by the angular

dispersive component to have a double-hump shaped far field distribution.

156. An apparatus as in claim 146, further comprising: a fiber providing the input light to the angular dispersive component; and

at least one phase mask on the fiber to cause the input light received by the

157. An apparatus as in claim 146, further comprising: at least one phase mask on a surface of the angular dispersive component to

hump shaped far field distribution.

158. An apparatus as in claim 146, wherein the angular dispersive component comprises: first and second surfaces, the first surface allowing substantially no light to be

transmitted therethrough, the passage area being in the same plane as the first surface,

the first and second surfaces positioned so that the input light enters the angular

dispersive component through the passage area and is then reflected a plurality of times

between the first and second surfaces to produce said output light.

159. An apparatus as in claim 158, wherein:

the first surface has substantially 100% reflectivity, and

the passage area has substantially 100% transmissivity.

160. An apparatus comprising:

to output light from, the angular dispersive component, the angular dispersive component receiving, through the passage area, a line focused input light and causing

multiple reflection of the input light to produce self-interference that forms a collimated

a reflecting surface reflecting the output light back to the angular dispersive

different positions along a direction which is perpendicular to a plane which includes the travel direction of collimated output light from the angular dispersive component

for input light at different wavelengths, curvature c(y) of the reflecting surface being

as follows:

K ₄ K® KQ ² - (f - a) c(y) = - -/ + -

8 2f ++ If " -

161. An apparatus as in claim 160, further comprising:

dispersive component.

162. An apparatus as in claim 160, wherein the reflecting surface has a cone or

modified cone shape.

163. An apparatus as in claim 161, wherein the reflecting surface has a cone or

modified cone shape.

164. An apparatus as in claim 160, wherein the reflecting surface is movable in a

direction perpendicular to said plane.

165. An apparatus as in claim 161, wherein the angular dispersive component is a

first angular dispersive component, the apparatus further comprising:

a second angular dispersive component between the first angular dispersive

an angular dispersion direction which is perpendicular to said plane.

166. An apparatus as in claim 165, wherein the second angular dispersive component

is a grating.

167. An apparatus as in claim 166, further comprising:

a quarter wave plate canceling polarization dependence of the grating.

168. An apparatus as in claim 160, further comprising:

means for causing the input light received by the angular dispersive component

to have a double-hump shaped far field distribution.

169. An apparatus as in claim 160, further comprising: at least one phase mask causing the input light received by the angular

dispersive component to have a double-hump shaped far field distribution.

170. An apparatus as in claim 160, further comprising: a fiber providing the input light to the angular dispersive component; and at least one phase mask on the fiber to cause the input light received by the

171. An apparatus as in claim 160, further comprising:

at least one phase mask on a surface of the angular dispersive component to

hump shaped far field distribution.

172. An apparatus as in claim 160, wherein the angular dispersive component

comprises:

between the first and second surfaces to produce said output light.

173. An apparatus as in claim 172, wherein:

the first surface has substantially 100% reflectivity, and

the passage area has substantially 100% transmissivity.

174. An apparatus comprising:

a radiation window; first and second reflecting surfaces, the first reflecting surface allowing

substantially no light to be transmitted therethrough and being in the same plane as the

radiation window, the second reflecting surface having a reflectivity which causes a

portion of light incident thereon to be transmitted therethrough, where

an input light at a respective wavelength travels through the radiation

window and is focused into a line, and

the first and second reflecting surfaces are positioned so that the input

a different wavelength; and

a mirror surface reflecting the output light back to the second reflecting surface

to pass through the second reflecting surface and undergo multiple reflection between the first and second reflecting surfaces, the mirror surface having different curvatures

surface for input light at different wavelengths, curvature c(y) of the mirror surface

being as follows: m K&² - (f - a) ₂ ^c(y) = 8/iτy" + ^ 2 F ₃ r + if — y ^■

175. An apparatus as in claim 174, further comprising:

a lens or mirror focusing the output light traveling from the second reflecting

surface.

176. An apparatus as in claim 174, wherein the mirror surface has a cone or

modified cone shape.

177. An apparatus as in claim 175, wherein the mirror surface has a cone or

modified cone shape.

178. An apparatus as in claim 175, wherein the mirror surface is movable in a

direction which is perpendicular to said plane.

179. An apparatus as in claim 175, further comprising:

an angular dispersive component between the second reflecting surface and said

lens or mirror , the angular dispersive component having an angular dispersion direction

which is perpendicular to said plane.

180. An apparatus as in claim 179, wherein the angular dispersive component is a

grating.

181. An apparatus as in claim 180, further comprising:

a quarter wave plate canceling polarization dependence of the grating.

182. An apparatus as in claim 180, wherein the mirror surface is movable to change

a dispersion amount.

183. An apparatus as in claim 174 , wherein the input light has a double-hump shaped

far field distribution.

184. An apparatus as in claim 174, further comprising:

means for causing the input light to have a double-hump shaped far field

distribution.

185. An apparatus as in claim 174, further comprising:

at least one phase mask causing the input light to have a double-hump shaped

far field distribution.

186. An apparatus as in claim 174, further comprising: a fiber providing the input light to be focused into the line; and

at least one phase mask on the fiber to cause the input light to have a double-

hump shaped far field distribution.

187. An apparatus as in claim 174, wherein

the radiation window has substantially 100% transmissivity, and

the first reflecting surface has substantially 100% reflectivity.

188. An apparatus comprising:

a radiation window;

first and second reflecting surfaces, the first surface being in the same plane as

the radiation window and allowing substantially no light to be transmitted therethrough,

the second reflecting surface having a reflectivity which causes a portion of light

incident thereon to be transmitted therethrough;

means for causing an input light at a respective wavelength traveling through

the radiation window and then focused into a line to radiate from the line to be reflected

a plurality of times between the first and second reflecting surfaces and thereby cause

a plurality of lights to be transmitted through the second reflecting surface, the plurality

of transmitted lights interfering with each other to produce a collimated output light

traveling from the second reflecting surface in a direction determined by the

wavelength of the input light, and thereby being spatially distinguishable from an

output light produced for an input light at a different wavelength; a mirror surface having a cone or modified cone shape; and

a lens or mirror focusing the output light traveling from the second reflecting

surface, curvature c(y) of the mirror surface being as follows:

c r(y) = ^K^y ^ ₊ ^^KΘ y s +, K& ² —- (f₂ - a) y ₂.

189. An apparatus comprising: a virtually imaged phased array (VIPA) generator receiving a line focused

the VIPA generator in first and second directions , respectively , determined by the first

and second wavelengths, respectively;

a lens or light directing mirror focusing the first and second output lights

traveling from the VIPA generator;

first and second mirrors each having a cone shape or a modified cone shape for

first mirror, and light at the second wavelength is focused to the second mirror and reflected by the second mirror, the reflected first and second lights being directed by

the wavelength filter and said lens or light directing mirror back to the VIPA generator ,

curvature c(y) of each of the first and second mirrors being as follows:

K K@ ₃ K@ ² - (f - a) ₂ c(y) = ^y ₊ ^y ₊ —₃ y .

190. An apparatus as in claim 189, wherein the first and second mirrors are movable

wavelengths, respectively.

191. An apparatus as in claim 189, wherein the VIPA generator comprises:

transmitted therethrough; and

a radiation window in the same plane as the first surface, the first and second

surfaces positioned so that the wavelength division multiplexed light passes through

the radiation window to be received by the VIPA generator and is then reflected a

plurality of times between the first and second surfaces to produce said first and second

output lights.

192. An apparatus as in claim 191, wherein:

the first surface has substantially 100% reflectivity, and

the radiation window has substantially 100% transmissivity.

193. An apparatus comprising:

a radiation window;

first and second reflecting surfaces, the first reflecting surface allowing

portion of light incident thereon to be transmitted therethrough, where

a wavelength division multiplexed (WDM) light including light at first

and second wavelengths travels through the radiation window and is then focused into a line, and

the first and second reflecting surfaces are positioned so that the WDM

each other to produce collimated first and second output lights corresponding,

determined by the first and second wavelengths, respectively; a lens or light directing mirror focusing the first and second output lights

traveling from the second reflecting surface;

first and second mirrors each having a cone shape or a modified cone shape for

reflection between the first and second surfaces, curvature c(y) of each of the first and

second mirrors being as follows:

c(y) = ^K,y ^ + ^^K& y ₃ +, K® ² —- (f₂ - a) y ₂.

194. An apparatus as in claim 193 , wherein the first and second mirrors are movable

wavelengths, respectively.

195. A communication system comprising:

an optical transmission line;

a transmitter transmitting an optical signal through the transmission line;

a receiver receiving optical signal from the transmission line; and

a compensation device operatively connected in one of the group consisting of

higher order dispersion to the optical signal, the compensation device comprising a radiation window having substantially no reflectivity,

first and second reflecting surfaces, the first reflecting surface allowing

portion of light incident thereon to be transmitted therethrough, where

the optical signal travels through the radiation window and is

focused into a line as a line focused input light to the compensation device, and

the first and second reflecting surfaces are positioned so that the

each other to produce a collimated output light which travels from the second reflecting surface along a direction determined by a wavelength of the input light, and is thereby

different wavelength, and

a mirror reflectmg output the light back to the second reflecting surface

the travel direction of collimated output light from the second reflecting surface for

input light at different wavelengths, curvature c(y) of the mirror being as follows:

196. An apparatus comprising:

a variable curvature mirror positioned to reflect light produced by a virtually

imaged phased array (VIPA) generator back to the VIPA generator; and

a rotation axis around which the mirror is rotated to change the curvature of the

mirror where the output light is reflected.

197. An apparatus as in claim 196, wherein the curvature of the mirror changes

along a direction parallel to an angular dispersion direction of the VIPA generator.

198. An apparatus as in claim 196, wherein the rotation axis is perpendicular to an

angular dispersion direction of the VIPA generator.

199. An apparatus as in claim 197, wherein the rotation axis is perpendicular to the

angular dispersion direction of the VIPA generator.

200. An apparatus as in claim 196, wherein the rotation axis is disposed on or within

the mirror.

201. An apparatus as in claim 197, wherein the rotation axis is disposed on or within

the mirror.

202. An apparatus as in claim 198, wherein the rotation axis is disposed on or within the mirror.

203. An apparatus as in claim 196, further comprising a translation path along which

the rotation axis is movable to thereby provide both rotation and translation to change

the curvature of the mirror where the output light is reflected.

204. An apparatus as in claim 197 , further comprising a translation path along which

the curvature of the mirror where the output light is reflected.

205. An apparatus as in claim 198 , further comprising a translation path along which

the curvature of the mirror where the output light is reflected.

206. An apparatus as in claim 196, wherein the curvature of the mirror varies from

a flat portion to a convex portion.

207. An apparatus as in claim 197, wherein the curvature of the mirror varies from

a flat portion to a convex portion.

208. An apparatus as in claim 198, wherein the curvature of the mirror varies from

a flat portion to a convex portion.

209. An apparatus as in claim 200, wherein the curvature of the mirror varies from

a flat portion to a convex portion.

210. An apparatus as in claim 203 , wherein the curvature of the mirror varies from

a flat portion to a convex portion.

211. An apparatus comprising :

a virtually imaged phased array (VIPA) generator producing a light traveling

from the VIPA generator;

a variable curvature mirror positioned to reflect the light back to the VIPA

generator; and

mirror where the output light is reflected.

212. An apparatus as in claim 211, wherein the curvature of the mirror changes

213. An apparatus as in claim 211, wherein the rotation axis is perpendicular to an

angular dispersion direction of the VIPA generator.

214. An apparatus as in claim 212, wherein the rotation axis is perpendicular to the

angular dispersion direction of the VIPA generator.

215. An apparatus as in claim 211 , wherein the rotation axis is disposed on or within

the mirror.

216. An apparatus as in claim 212, wherein the rotation axis is disposed on or within

the mirror.

217. An apparatus as in claim 213, wherein the rotation axis is disposed on or within

the mirror.

218. An apparatus as in claim 211, further comprising a translation path along which

the curvature of the mirror where the output light is reflected.

219. An apparatus as in claim 212, further comprising a translation path along which

the curvature of the mirror where the output light is reflected.

220. An apparatus as in claim 213, further comprising a translation path along which

the curvature of the mirror where the output light is reflected.

221. An apparatus as in claim 211, wherein the curvature of the mirror varies from

a flat portion to a convex portion.

222. An apparatus as in claim 212, wherein the curvature of the mirror varies from

a flat portion to a convex portion.

223. An apparatus as in claim 213 , wherein the curvature of the mirror varies from

a flat portion to a convex portion.

224. An apparatus as in claim 215, wherein the curvature of the mirror varies from

a flat portion to a convex portion.

225. An apparatus as in claim 218, wherein the curvature of the mirror varies from

a flat portion to a convex portion.

226. An apparatus as in claim 211, further comprising: a lens directing the light traveling from the VIPA generator to the mirror so that

the mirror reflects the light, the reflected light being directed by the lens back to the

VIPA generator.

227. An apparatus as in claim 218, further comprising:

a lens directing the light traveling from the VIPA generator to the mirror so that

VIPA generator.

228. An apparatus comprising:

a virtually imaged phased array (VIPA) generator receiving an input light at a

respective wavelength and producing a corresponding output light traveling from the

VIPA generator in a direction determined by the wavelength of the input light; a variable curvature mirror positioned to reflect the output light back to the

VIPA generator so that the reflected output light travels through the VIPA generator,

to thereby provide dispersion compensation to the input light; and

mirror where the output light is reflected, to thereby vary an amount of dispersion

compensation provided to the input light.

229. An apparatus as in claim 228, wherein the curvature of the mirror changes

230. An apparatus as in claim 228, wherein the rotation axis is perpendicular to an

angular dispersion direction of the VIPA generator.

231. An apparatus as in claim 229 , wherein the rotation axis is perpendicular to the

angular dispersion direction of the VIPA generator.

232. An apparatus as in claim 228 , wherein the rotation axis is disposed on or within

the mirror.

233. An apparatus as in claim 228 , further comprising a translation path along which

the curvature of the mirror where the output light is reflected.

234. An apparatus as in claim 230 , further comprising a translation path along which

the curvature of the mirror where the output light is reflected.

235. An apparatus as in claim 228, wherein the curvature of the mirror varies from

a flat portion to a convex portion.

236. An apparatus as in claim 228, further comprising: a lens directing the output light traveling from the VIPA generator to the mirror

so that the mirror reflects the output light, the reflected light being directed by the lens

back to the VIPA generator.

237. An apparatus as in claim 233, further comprising:

a lens directing the output light traveling from the VIPA generator to the mirror

back to the VIPA generator.

238. An apparatus comprising:

a radiation window;

first and second reflecting surfaces in parallel with each other, the first

reflecting surface allowing substantially no light to be transmitted therethrough and

being in the same plane as the radiation window, the second reflecting surface having

therethrough, wherein an input light at a respective wavelength travels through the radiation

window and is focused into a line, and

the first and second reflecting surfaces are positioned so that the input

second reflecting surfaces and thereby cause a plurality of lights to be transmitted through the second reflecting surface , the plurality of transmitted lights interfering with each other to produce a collimated output light which travels from the second reflecting

a different wavelength;

a variable curvature mirror reflecting the output light back to the second

reflection between the first and second reflecting surfaces; and

mirror where the output light is reflected.

239. An apparatus as in claim 238, wherein the curvature of the mirror changes

along a direction parallel to a plane which mcludes the travel direction of collimated

output light from the second reflecting surface for input light at different wavelengths .

240. An apparatus as in claim 238, wherein the rotation axis is perpendicular to a

plane which includes the travel direction of collimated output light from the second

reflecting surface for input light at different wavelengths.

241. An apparatus as in claim 238 , wherein the rotation axis is disposed on or within

the mirror.

242. An apparatus as in claim 238 , further comprising a translation path along which

the curvature of the mirror where the output light is reflected.

243. An apparatus as in claim 238, wherein the curvature of the mirror varies from

a flat portion to a convex portion.

244. An apparatus as in claim 238, further comprising:

a lens directing the output light traveling from the second reflecting surface to

the mirror so that the mirror reflects the output light, the reflected light being directed

by the lens back to the second reflecting surface.

245. An apparatus comprising:

a plurality of mirrors having different surface curvatures to reflect light; and

a holder having a rotation axis and holding the plurality of mirrors equidistantly

produced by a virtually imaged phased array (VIPA) generator back to the VIPA

generator.

246. An apparatus as in claim 245, wherein the plurality of mirrors are separate,

non-contiguous mirrors.

247. An apparatus as in claim 245, wherein the plurality of mirrors are portions of

a single mirror surface of continuously varying curvature.

248. An apparatus comprising:

a virtually imaged phased array (VIPA) generator producing light;

a plurality of mirrors having different surface curvatures; and

different, respective mirror of the plurality of mirrors in position to reflect the light

produced by a VIPA generator back to the VIPA generator.

249. An apparatus as in claim 248, wherein the plurality of mirrors are separate,

non-contiguous mirrors.

250. An apparatus as in claim 248, wherein the plurality of mirrors are portions of

a single mirror surface of continuously varying curvature.

251. An apparatus as in claim 248, further comprising:

a lens focusing the light produced by the VIPA generator to the respective

mirror in position to reflect the light, and directing the reflected light back to the VIPA generator.

252. An apparatus comprising:

a virtually imaged phased array (VIPA) generator receiving an input light at a

VIPA generator in a direction determined by the wavelength of the input light;

a plurality of mirrors having different surface curvatures; and

different, respective mirror of the plurality of mirrors in position to reflect the output

light back to the VIPA generator, to thereby provide dispersion compensation to the

input light.

253. An apparatus as in claim 252, wherein the plurality of mirrors are separate,

non-contiguous mirrors.

254. An apparatus as in claim 252, wherein the plurality of mirrors are portions of

a single πurror surface of continuously varying curvature.

255. An apparatus as in claim 252, further comprising:

a lens focusing the output light traveling from the VIPA generator to the

respective mirror in position to reflect the light, and directing the reflected light back

to the VIPA generator.

256. An apparatus comprising:

a radiation window;

first and second reflecting surfaces in parallel with each other, the first

therethrough, wherein

an input light at a respective wavelength travels through the radiation

window and is focused into a line, and the first and second reflecting surfaces are positioned so that the input

a different wavelength;

a plurality of mirrors having different surface curvatures; and

different, respective mirror of the plurality of mirrors in position to reflect the output light back to the second reflecting surface to pass through the second reflecting surface

and undergo multiple reflection between the first and second surfaces.

257. An apparatus as in claim 256, wherein the plurality of mirrors are separate,

non-contiguous mirrors.

258. An apparatus as in claim 256, wherein the plurality of mirrors are portions of

a single mirror surface of continuously varying curvature.

259. An apparatus as in claim 256, further comprising:

a lens focusing the output light traveling from the second reflecting surface to

the respective mirror in position to reflect the output light, and directing the reflected

light back to the second reflecting surface.

260. An apparatus comprising:

a plurality of fixed mirrors having different surface curvatures to reflect light;

and

a rotating mirror rotatable about a rotation axis to reflect light produced by a

virtually imaged phased array (VIPA) generator to a respective fixed mirror of the

plurality of fixed mirrors, and to reflect the light reflected by the respective fixed

mirror back to the VIPA generator.

261. An apparatus as in claim 260, wherein the plurality of fixed mirrors are separate, non-contiguous mirrors.

262. An apparatus as in claim 260, wherein the plurality of fixed mirrors are

portions of a single mirror surface of continuously varying curvature.

263. An apparatus comprising:

a virtually imaged phased array (VIPA) generator producing light;

and

a rotating mirror rotatable about a rotation axis to reflect light produced by the

VIPA generator to a respective fixed mirror of the plurality of fixed mirrors, and to

reflect the light reflected by the respective fixed mirror back to the VIPA generator.

264. An apparatus as in claim 263, wherein the plurality of fixed mirrors are

separate, non-contiguous mirrors.

265. An apparatus as in claim 263, wherein the plurality of fixed mirrors are

portions of a single mirror surface of continuously varying curvature.

266. An apparatus as in claim 263, further comprising: a lens directing the light produced by the VIPA generator to rotating mirror,

and directing the light from the fixed mirror and reflected by the rotating mirror back

to the VIPA generator.

267. An apparatus comprising:

a virtually imaged phased array (VIPA) generator receiving an input light at a

VIPA generator in a direction determined by the wavelength of the input light;

and

a rotating mirror rotatable about a rotation axis to reflect the output light

traveling from the VIPA generator to a respective fixed mirror of the plurality of fixed

mirrors, and to reflect the light reflected by the respective fixed mirror back to the VIPA generator, to thereby provide dispersion compensation to the input light.

268. An apparatus as in claim 267, wherein the plurality of fixed mirrors are

separate, non-contiguous mirrors.

269. An apparatus as in claim 267, wherein the plurality of fixed mirrors are

portions of a single mirror surface of continuously varying curvature.

270. An apparatus as in claim 267, further comprising: a lens focusing the output light traveling from the VIPA generator to the

rotating mirror, and directing the light from the fixed mirror and reflected by the

rotating mirror back to the VIPA generator.

271. An apparatus comprising:

a radiation window;

first and second reflecting surfaces in parallel with each other, the first

therethrough, wherein

an input light at a respective wavelength travels through the radiation

window and is focused into a line, and

the first and second reflecting surfaces are positioned so that the input

each other to produce a collimated output light which travels from the second reflecting surface along a direction determined by the wavelength of the input light, and is

a different wavelength; a plurality of fixed mirrors having different surface curvatures to reflect light;

and

a rotating πurror rotatable about a rotation axis to reflect the output light

traveling from the second reflecting surface to a respective fixed mirror ofthe plurality

of fixed mirrors, and to reflect the light reflected by the respective fixed mirror back

undergo multiple reflection between the first and second reflecting surfaces.

272. An apparatus as in claim 271, wherein the plurality of fixed mirrors are

separate, non-contiguous mirrors.

273. An apparatus as in claim 271, wherein the plurality of fixed mirrors are

portions of a single mirror surface of continuously varying curvature.

274. An apparatus as in claim 271, further comprising:

the rotating mirror, and directing the light from the fixed mirror and reflected by the

rotating mirror back to the second reflecting surface.

275. An apparatus comprising: a plurality of fixed mirrors having different surface curvatures to reflect light; and an off-axis parabolic mirror rotatable about a rotation axis to reflect light

respective fixed mirror back to the VIPA generator.

276. An apparatus as in claim 275, wherein the plurality of fixed mirrors are

separate, non-contiguous mirrors.

277. An apparatus as in claim 275, wherein the plurality of fixed mirrors are

portions of a single mirror surface of continuously varying curvature.

278. An apparatus comprising: a virtually imaged phased array (VIPA) generator producing light;

and

an off-axis parabolic mirror rotatable about a rotation axis to reflect light

VIPA generator.

279. An apparatus as in claim 278, wherein the plurality of fixed mirrors are

separate, non-contiguous mirrors.

280. An apparatus as in claim 278, wherein the plurality of fixed mirrors are

portions of a single mirror surface of continuously varying curvature.

281. An apparatus comprising:

a virtually imaged phased array (VIPA) generator receiving an input light at a

VIPA generator in a direction determined by the wavelength of the input light;

and

an off-axis parabolic mirror rotatable about a rotation axis to reflect the output

light traveling from the VIPA generator to a respective fixed mirror of the plurality

to the VIPA generator, to thereby provide dispersion compensation to the input light.

282. An apparatus as in claim 281, wherein the plurality of fixed mirrors are

separate, non-contiguous mirrors.

283. An apparatus as in claim 281, wherein the plurality of fixed mirrors are

portions of a single mirror surface of continuously varying curvature.

284. An apparatus comprising: a radiation window;

first and second reflecting surfaces in parallel with each other, the first reflecting surface allowing substantially no light to be transmitted therethrough and

therethrough, wherein

an input light at a respective wavelength travels through the radiation

window and is focused into a line, and

the first and second reflecting surfaces are positioned so that the input

a different wavelength;

and

light traveling from the second reflecting surface to a respective fixed mirror of the

mirror back to the second reflecting surface to pass through the second reflecting surface and undergo multiple reflection between the first and second reflecting

surfaces.

285. An apparatus as in claim 284, wherein the plurality of fixed mirrors are

separate, non-contiguous mirrors.

286. An apparatus as in claim 284, wherein the plurality of fixed mirrors are

portions of a single mirror surface of continuously varying curvature.