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

• US 20020044364A1
• Filed: 10/30/2001
• Published: 04/18/2002
• Est. Priority Date: 12/14/1999
• Status: Active Grant

• Current Assignee: II-VI Incorporated
• Original Assignee: Fujitsu Limited
• Inventors: Shirasaki, Masataka, Cao, Simon
• Granted Patent: US 6,478,433 B2
• Time in Patent Office: Days
• US Class Current: 359/868
• CPC Class Codes: G02B 27/0087 Phased arrays
• CPC Class Codes: G02B 27/1006 for splitting or combining different wavelengths G02B27/1086, G02B27/141 take precedence
• CPC Class Codes: G02B 27/106 for splitting or combining a plurality of identical beams or images, e.g. image replication
• CPC Class Codes: G02B 27/1073 characterized by manufacturing or alignment methods
• CPC Class Codes: G02B 27/1086 operating by diffraction only
• CPC Class Codes: G02B 27/126 The splitting element being a prism or prismatic array, including systems based on total internal reflection
• CPC Class Codes: G02B 27/144 using partially transparent surfaces without spectral selectivity G02B27/147 takes precedence
• CPC Class Codes: G02B 27/145 having sequential partially reflecting surfaces
• CPC Class Codes: G02B 27/148 including stacked surfaces having at least one double-pass partially reflecting surface
• CPC Class Codes: G02B 5/10 with curved faces
• CPC Class Codes: G02B 6/2931 Diffractive element operating in reflection
• CPC Class Codes: G02B 6/29311 Diffractive element operating in transmission
• CPC Class Codes: G02B 6/29358 Multiple beam interferometer external to a light guide, e.g. Fabry-Pérot, etalon, VIPA plate, OTDL plate, continuous interferometer, parallel plate resonator G02B6/29347, G02B6/29349, G02B6/2935, G02B6/29361 take precedence; resonator evanescently coupled to light guide G02B6/29335
• CPC Class Codes: G02B 6/29361 Interference filters, e.g. multilayer coatings, thin film filters, dichroic splitters or mirrors based on multilayers, WDM filters
• CPC Class Codes: G02B 6/29392 Controlling dispersion G02B6/02214 takes precedence; modal dispersion control G02B6/268
• CPC Class Codes: G02B 6/29394 Compensating wavelength dispersion G02B6/29376 takes precedence; dispersion compensated optical transmission systems H04B10/2507
• CPC Class Codes: G02B 6/29395 configurable, e.g. tunable or reconfigurable switching G02B6/35
• CPC Class Codes: H04B 10/25133 including a lumped electrical or optical dispersion compensator H04B10/2519, H04B10/2525 takes precedence

Abstract

An optical apparatus for producing chromatic dispersion. The apparatus includes a virtually imaged phased array (VIPA) generator, a mirror 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 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 mirror has a cone shape, or a modified cone shape. The lens focuses the output light traveling from the VIPA generator onto the mirror so that the mirror reflects the output light. The reflected light is directed by the lens back to the VIPA generator. In this manner, the apparatus provides chromatic dispersion to the input light. The modified cone shape of the mirror can be designed so that the apparatus provides a uniform chromatic dispersion to light in the same channel of a wavelength division multiplexed light.

Claims

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 of the 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, curvature c(y) of the reflecting surface being as follows;

$c<br><br>\left(y\right)=\frac{K}{8<br><br>f^4}<br><br>y^4+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\Theta <br><br>}}{2<br><br>f^3}<br><br>y^3+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Theta <br><br>}}^2-\left(f-a\right)}{2<br><br>f^2}<br><br>y^2.$

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 6, 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 grating.

10. An apparatus as in claim 9, further comprising:

a quarter wave plate canceling polarization dependence of the grating.

11. An apparatus as in claim 9, wherein the reflecting surface is movable to change a dispersion amount.

12. An apparatus as in claim 1, wherein the input light received by the VIPA generator has a double-hump shaped far field distribution.

13. 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.

14. 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.

15. 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.

16. 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.

17. An apparatus as in claim 1, 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.

18. An apparatus as in claim 17, wherein:

the first surface has substantially 100% reflectivity, and

the radiation window has substantially 100% transmissivity.

20. An apparatus as in claim 19, wherein the cone or modified cone shape of the reflecting surface corrects for non-uniform chromatic dispersion.

21. An apparatus as in claim 19, 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.

22. An apparatus as in claim 19, 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.

23. An apparatus as in claim 19, wherein the reflecting surface is movable in or near a focal plane of said lens or mirror.

24. An apparatus as in claim 19, further comprising:

an angular dispersive element between the VIPA generator and the lens.

25. An apparatus as in claim 24, wherein the angular dispersive element has an angular dispersion direction which is perpendicular to an angular dispersion direction of the VIPA generator.

26. An apparatus as in claim 24, wherein the angular dispersive element is a grating.

27. An apparatus as in claim 26, further comprising:

a quarter wave plate canceling polarization dependence of the grating.

28. An apparatus as in claim 26, wherein the reflecting surface is movable to change a dispersion amount.

29. An apparatus as in claim 19, wherein the input light received by the VIPA generator has a double-hump shaped far field distribution.

30. An apparatus as in claim 19, 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.

31. An apparatus as in claim 19, 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.

32. An apparatus as in claim 19, 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.

33. An apparatus as in claim 19, 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 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.

34. An apparatus as in claim 19, 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.

35. An apparatus as in claim 34, wherein:

the first surface has substantially 100% reflectivity, and

the radiation window has substantially 100% transmissivity.

37. An apparatus as in claim 36, 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.

38. An apparatus as in claim 36, wherein the reflecting surface has a cone or modified cone shape.

39. An apparatus as in claim 37, wherein the reflecting surface has a cone or modified cone shape.

40. An apparatus as in claim 37, wherein the reflecting surface is movable in a direction perpendicular to said plane.

41. An apparatus as in claim 39, wherein the reflecting surface is movable in a direction perpendicular to said plane.

42. An apparatus as in claim 37, wherein the angular dispersive component is a first angular dispersive component, the apparatus further comprising:

a second angular dispersive component be tween 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.

43. An apparatus as in claim 42, wherein the second angular dispersive component is a grating.

44. An apparatus as in claim 43, further comprising:

a quarter wave plate canceling polarization dependence of the grating.

45. An apparatus as in claim 36, 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.

46. An apparatus as in claim 36, 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.

47. An apparatus as in claim 36, 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.

48. An apparatus as in claim 36, 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.

49. An apparatus as in claim 48, wherein:

the first surface has substantially 100% reflectivity, and

the passage area has substantially 100% transmissivity.

19. 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 of the 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, curvature c(y) of the reflecting surface being as follows;

$c<br><br>\left(y\right)=\frac{K}{8<br><br>f^4}<br><br>y^4+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\Theta <br><br>}}{2<br><br>f^3}<br><br>y^3+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Theta <br><br>}}^2-\left(f-a\right)}{2<br><br>f^2}<br><br>y^2.$

36. 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, curvature c(y) of the reflecting surface being as follows;

$c<br><br>\left(y\right)=\frac{K}{8<br><br>f^4}<br><br>y^4+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\Theta <br><br>}}{2<br><br>f^3}<br><br>y^3+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Theta <br><br>}}^2-\left(f-a\right)}{2<br><br>f^2}<br><br>y^2.$

50. 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, a line focused input light 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 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, curvature c(y) of the reflecting surface being as follows;

$c<br><br>\left(y\right)=\frac{K}{8<br><br>f^4}<br><br>y^4+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\Theta <br><br>}}{2<br><br>f^3}<br><br>y^3+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Theta <br><br>}}^2-\left(f-a\right)}{2<br><br>f^2}<br><br>y^2.$

51. An apparatus as in claim 50, 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.

52. An apparatus as in claim 50, wherein the reflecting surface has a cone or modified cone shape.

53. An apparatus as in claim 51, wherein the reflecting surface has a cone or modified cone shape.

54. An apparatus as in claim 50, wherein the reflecting surface is movable in a direction perpendicular to said plane.

55. An apparatus as in claim 51, 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.

56. An apparatus as in claim 55, wherein the second angular dispersive component is a grating.

57. An apparatus as in claim 56, further comprising:

a quarter wave plate canceling polarization dependence of the grating.

58. An apparatus as in claim 50, further comprising:

means for causing the input light received by the angular dispersive component to have a double-hump shaped far field distribution.

59. An apparatus as in claim 50, 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.

60. An apparatus as in claim 50, 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.

61. An apparatus as in claim 50, 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.

62. An apparatus as in claim 50, 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.

63. An apparatus as in claim 62, wherein:

the first surface has substantially 100% reflectivity, and

the passage area has substantially 100% transmissivity.

64. 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 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 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 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, curvature c(y) of the mirror surface being as follows;

$c<br><br>\left(y\right)=\frac{K}{8<br><br>f^4}<br><br>y^4+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\Theta <br><br>}}{2<br><br>f^3}<br><br>y^3+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Theta <br><br>}}^2-\left(f-a\right)}{2<br><br>f^2}<br><br>y^2.$

65. An apparatus as in claim 64, 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.

66. An apparatus as in claim 64, wherein the mirror surface has a cone or modified cone shape.

67. An apparatus as in claim 65, wherein the mirror surface has a cone or modified cone shape.

68. An apparatus as in claim 65, wherein the mirror surface is movable in a direction which is perpendicular to said plane.

69. An apparatus as in claim 65, 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.

70. An apparatus as in claim 69, wherein the angular dispersive component is a grating.

71. An apparatus as in claim 70, further comprising:

a quarter wave plate canceling polarization dependence of the grating.

72. An apparatus as in claim 70, wherein the mirror surface is movable to change a dispersion amount.

73. An apparatus as in claim 64, wherein the input light has a double-hump shaped far field distribution.

74. An apparatus as in claim 64, further comprising:

means for causing the input light to have a double-hump shaped far field distribution.

75. An apparatus as in claim 64, further comprising:

at least one phase mask causing the input light to have a double-hump shaped far field distribution.

76. An apparatus as in claim 64, 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.

77. An apparatus as in claim 64, wherein

the radiation window has substantially 100% transmissivity, and

the first reflecting surface has substantially 100% reflectivity.

80. An apparatus as in claim 79, 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.

81. An apparatus as in claim 79, 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 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.

82. An apparatus as in claim 81, wherein:

the first surface has substantially 100% reflectivity, and

the radiation window has substantially 100% transmissivity.

78. 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 onto the mirror surface so that the mirror surface reflects the output light, the reflected light being directed by said lens or mirror back to the second reflecting surface, curvature c(y) of the mirror surface being as follows;

$c<br><br>\left(y\right)=\frac{K}{8<br><br>f^4}<br><br>y^4+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\Theta <br><br>}}{2<br><br>f^3}<br><br>y^3+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Theta <br><br>}}^2-\left(f-a\right)}{2<br><br>f^2}<br><br>y^2.$

79. 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, curvature c(y) of each of the first and second mirrors being as follows;

$c<br><br>\left(y\right)=\frac{K}{8<br><br>f^4}<br><br>y^4+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\Theta <br><br>}}{2<br><br>f^3}<br><br>y^3+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Theta <br><br>}}^2-\left(f-a\right)}{2<br><br>f^2}<br><br>y^2.$

83. 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

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 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 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 second reflecting surface to pass through the second reflecting surface and undergo multiple reflection between the first and second surfaces, curvature c(y) of each of the first and second mirrors being as follows;

$c<br><br>\left(y\right)=\frac{K}{8<br><br>f^4}<br><br>y^4+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\Theta <br><br>}}{2<br><br>f^3}<br><br>y^3+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Theta <br><br>}}^2-\left(f-a\right)}{2<br><br>f^2}<br><br>y^2.$

84. An apparatus as in claim 83, 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.

85. 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 radiation window having substantially no reflectivity,

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

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 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 a 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 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 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, curvature c(y) of the mirror being as follows;

$c<br><br>\left(y\right)=\frac{K}{8<br><br>f^4}<br><br>y^4+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\Theta <br><br>}}{2<br><br>f^3}<br><br>y^3+\frac{K<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Theta <br><br>}}^2-\left(f-a\right)}{2<br><br>f^2}<br><br>y^2.$