Abstract

Surface-relief diffractive optical elements made interferometrically typically are recorded with the off-axis technique, for which the fringe maxima lie on planes that are predominantly perpendicular to the recording surface and with an intensity variation that is sinusoidal. Such a structure can be readily replicated by mechanical means. Volume diffractive elements, on the other hand, which result from beams propagating in opposite directions, have fringe planes that are predominantly parallel to the surface and, as such, cannot be mechanically replicated. A new type of surface-relief diffractive structure called Aztec is discussed here; it combines features of both off-axis and volume recording geometries, with the result being a phase-quantized, or terraced, surface-relief pattern. The groove profile, instead of being sinusoidal, resembles a stepped pyramid. This structure has been replicated by metal mastering and molding into plastic in the same manner as conventional embossed surface-relief elements, but the diffraction characteristics are typical of volume phase reflective structures. Light of a given wavelength is resonantly diffracted from steps that are a half-wavelength apart and with a bandwidth that is inversely proportional to the number of steps. Color control has been achieved by overcoating the step structure with a clear dielectric that shifts the resonant wavelength to a new value, depending on the index of refraction of the dielectric. Information content is less for the single-layered, but stepped, Aztec structure than for the usual multilayered volume diffractive element. Deep Aztec stepped gratings have also been fabricated by optical lithography, using multiple-mask techniques.

© 1990 Optical Society of America

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References

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  1. E. N. Leith, J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962).
    [CrossRef]
  2. Yu. N. Denisyuk, “Photographic reconstruction of the optical properties of an object in its own scattered radiation field,” Sov. Phys. Dokl. 7, 543–545 (1962).
  3. N. K. Sheridon, “Production of blazed holograms,” Appl. Phys. Lett. 12, 316–318 (1968).
    [CrossRef]
  4. M. C. Hutley, “Blazed interference diffraction gratings for the ultraviolet,” Opt. Acta 22, 1–13 (1975).
    [CrossRef]
  5. M. T. Gale, K. Knop, “Embossed relief images and their application for color motion pictures,” J. Soc. Motion Pict. Telev. Eng. 87, 6–8 (1978).
  6. R. C. Enger, S. K. Case, “High-frequency holographic transmission gratings in photoresist,” J. Opt. Soc. Am. 73, 1113–1118 (1983).
    [CrossRef]
  7. H. Werlich, G. Sincerbox, B. Yung, “Fabrication of high-efficiency surface-relief holograms,” J. Imaging Technol. 10, 105–108 (1984).
  8. C. J. Kramer, “Hologon laser scanners for nonimpact printing,” in High Speed Read/Write Techniques For Advanced Printing and Data Handling, L. Beiser, ed., Proc. Soc. Photo-Opt. Instrum. Eng.390, 165–173 (1983).
    [CrossRef]
  9. H. Dammann, “Color separation gratings,” Appl. Opt. 17, 2273–2279 (1978).
    [CrossRef] [PubMed]
  10. J. J. Cowan, “Blazed holographic gratings: formation by surface waves and replication by metal electroforming,” in Periodic Structures, Gratings, Moire Patterns, and Diffraction Phenomena I, C. H. Chi, E. G. Loewen, C. L. O’Bryan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.240, 5–12 (1980).
    [CrossRef]
  11. H. F. Nijhout, “The color patterns of butterflies and moths,” Sci. Am. 245, 140–151 (1981).
    [CrossRef]
  12. M. F. Land, “The physics and biology of animal reflectors,” Prog. Biophys. Mol. Biol. 24, 77–106 (1972).
    [CrossRef]
  13. H. Ghiradella, D. Aneshansley, T. Eisner, R. E. Silberglied, “Ultraviolet reflection of a male butterfly: interference color caused by thin-layer elaboration of wing scales,” Science 178, 1214–1217 (1972).
    [CrossRef] [PubMed]
  14. F. H. Dill, “Optical lithography,” IEEE Trans. Electron Devices ED-22, 440–444 (1975).
    [CrossRef]
  15. A. R. Neureuther, P. K. Jain, W. G. Oldham, “Factors affecting linewidth control including multiple wavelength exposure and chromatic aberration,” in Developments in Microlithography VI, J. Dey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.275, 110–116 (1981).
  16. E. J. Walker, “Reduction of photoresist standing-wave effects by post-exposure bake,” IEEE Trans. Electron Devices ED-22, 464–466 (1975).
    [CrossRef]
  17. M. A. Narasimham, “Projection printed photolithographic images in positive photoresists,” IEEE Trans. Electron Devices ED-22, 478–482 (1975).
    [CrossRef]
  18. L. F. Johnson, G. W. Kammlott, K. A. Ingersoll, “Generation of periodic surface corregations,” Appl. Opt. 17, 1165–1181 (1978).
    [CrossRef] [PubMed]
  19. C. A. Mack, “Analytical expression for the standing wave intensity in photoresist,” Appl. Opt. 25, 1958–1961 (1985).
    [CrossRef]
  20. J. J. Cowan, “The Aztec grating: a surface-relief volume diffractive structure,” in Digest of the Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), p. 109.
  21. J. J. Cowan, “Embossed volume holograms: the Aztec structure,” in Second International Conference on Holographic Systems, Components and Appliations, Publ. No. 311 (Institution of Electrical Engineers, London, 1989), pp. 38–44.
  22. J. J. Cowan, “Method of replicating volume phase reflection holograms,” U.S. patent4,839,250 (June13, 1989).
  23. J. J. Cowan, “Method of forming volume phase reflection holograms,” U.S. patent4,874,213 (October17, 1989).
  24. J. J. Cowan, “Volume phase reflection holograms and methods for fabricating them,” U.S. patent4,888,260 (December19, 1989).
  25. H. Dammann, “Spectral characteristics of stepped-phase gratings,” Optik 53, 409–417 (1979).
  26. M. T. Gale, K. Knop, Surface-Relief Images for Color Reproduction (Focal, New York, 1980).
  27. This theory was described by S. A. Gaither (Integrated Systems, Inc., 2500 Mission College Boulevard, Santa Clara, California 95054) in an unpublished paper, “Vector coupled-wave analysis of crossed surface-relief diffraction gratings.” The research was conducted for the Binary Optics Group of MIT Lincoln Laboratories in 1988.
  28. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  29. J. J. Cowan, “The recording and large scale replication of crossed holographic grating arrays using multiple beam interferometry,” in International Conference on the Application, Theory, and Fabrication of Periodic Structures, Diffraction Gratings, and Moire Phenomena II, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.503, 120–129 (1984).
  30. J. J. Cowan, “Holographic honeycomb microlens,” Opt. Eng. 24, 796–802 (1985).
    [CrossRef]
  31. J. J. Cowan, W. D. Slafer, “The recording and replication of holographic micropatterns for the ordering of photographic emulsion grains in film systems,” J. Imaging Sci. 31, 100–107 (1987).
  32. J. J. Cowan, W. D. Slafer, “Holographic embossing at Polaroid: the Polaform process,” in Progress in Holographic Applications, J. Ebbeni, ed., Proc. Soc. Photo-Opt. Instrum. Eng.600, 49–56 (1985).
    [CrossRef]
  33. N. K. Sheridon, “Blazed hologram fabrication,” U.S. patent3,623,798 (November30, 1971).
  34. J. Leger, M. Holz, G. Swanson, W. Veldkamp, “Coherent laser beam addition: an application of binary optics technology,” Lincoln Lab. J. 1, 225–246 (1988).
  35. J. Guerra, “Photon tunneling microscopy,” in Surface Measurement and Characterization, J. M. Bennet, ed., Proc. Soc. Photo-Opt. Eng.1009, 254–263 (1989).
    [CrossRef]
  36. J. J. Cowan, “Spectral characteristics of computer-generated phase-quantized diffractive lenses,” in Digest of the Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 81.

1988 (1)

J. Leger, M. Holz, G. Swanson, W. Veldkamp, “Coherent laser beam addition: an application of binary optics technology,” Lincoln Lab. J. 1, 225–246 (1988).

1987 (1)

J. J. Cowan, W. D. Slafer, “The recording and replication of holographic micropatterns for the ordering of photographic emulsion grains in film systems,” J. Imaging Sci. 31, 100–107 (1987).

1985 (2)

1984 (1)

H. Werlich, G. Sincerbox, B. Yung, “Fabrication of high-efficiency surface-relief holograms,” J. Imaging Technol. 10, 105–108 (1984).

1983 (1)

1982 (1)

1981 (1)

H. F. Nijhout, “The color patterns of butterflies and moths,” Sci. Am. 245, 140–151 (1981).
[CrossRef]

1979 (1)

H. Dammann, “Spectral characteristics of stepped-phase gratings,” Optik 53, 409–417 (1979).

1978 (3)

1975 (4)

M. C. Hutley, “Blazed interference diffraction gratings for the ultraviolet,” Opt. Acta 22, 1–13 (1975).
[CrossRef]

F. H. Dill, “Optical lithography,” IEEE Trans. Electron Devices ED-22, 440–444 (1975).
[CrossRef]

E. J. Walker, “Reduction of photoresist standing-wave effects by post-exposure bake,” IEEE Trans. Electron Devices ED-22, 464–466 (1975).
[CrossRef]

M. A. Narasimham, “Projection printed photolithographic images in positive photoresists,” IEEE Trans. Electron Devices ED-22, 478–482 (1975).
[CrossRef]

1972 (2)

M. F. Land, “The physics and biology of animal reflectors,” Prog. Biophys. Mol. Biol. 24, 77–106 (1972).
[CrossRef]

H. Ghiradella, D. Aneshansley, T. Eisner, R. E. Silberglied, “Ultraviolet reflection of a male butterfly: interference color caused by thin-layer elaboration of wing scales,” Science 178, 1214–1217 (1972).
[CrossRef] [PubMed]

1968 (1)

N. K. Sheridon, “Production of blazed holograms,” Appl. Phys. Lett. 12, 316–318 (1968).
[CrossRef]

1962 (2)

E. N. Leith, J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962).
[CrossRef]

Yu. N. Denisyuk, “Photographic reconstruction of the optical properties of an object in its own scattered radiation field,” Sov. Phys. Dokl. 7, 543–545 (1962).

Aneshansley, D.

H. Ghiradella, D. Aneshansley, T. Eisner, R. E. Silberglied, “Ultraviolet reflection of a male butterfly: interference color caused by thin-layer elaboration of wing scales,” Science 178, 1214–1217 (1972).
[CrossRef] [PubMed]

Case, S. K.

Cowan, J. J.

J. J. Cowan, W. D. Slafer, “The recording and replication of holographic micropatterns for the ordering of photographic emulsion grains in film systems,” J. Imaging Sci. 31, 100–107 (1987).

J. J. Cowan, “Holographic honeycomb microlens,” Opt. Eng. 24, 796–802 (1985).
[CrossRef]

J. J. Cowan, “The recording and large scale replication of crossed holographic grating arrays using multiple beam interferometry,” in International Conference on the Application, Theory, and Fabrication of Periodic Structures, Diffraction Gratings, and Moire Phenomena II, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.503, 120–129 (1984).

J. J. Cowan, “The Aztec grating: a surface-relief volume diffractive structure,” in Digest of the Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), p. 109.

J. J. Cowan, “Embossed volume holograms: the Aztec structure,” in Second International Conference on Holographic Systems, Components and Appliations, Publ. No. 311 (Institution of Electrical Engineers, London, 1989), pp. 38–44.

J. J. Cowan, “Method of replicating volume phase reflection holograms,” U.S. patent4,839,250 (June13, 1989).

J. J. Cowan, “Method of forming volume phase reflection holograms,” U.S. patent4,874,213 (October17, 1989).

J. J. Cowan, “Volume phase reflection holograms and methods for fabricating them,” U.S. patent4,888,260 (December19, 1989).

J. J. Cowan, “Blazed holographic gratings: formation by surface waves and replication by metal electroforming,” in Periodic Structures, Gratings, Moire Patterns, and Diffraction Phenomena I, C. H. Chi, E. G. Loewen, C. L. O’Bryan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.240, 5–12 (1980).
[CrossRef]

J. J. Cowan, W. D. Slafer, “Holographic embossing at Polaroid: the Polaform process,” in Progress in Holographic Applications, J. Ebbeni, ed., Proc. Soc. Photo-Opt. Instrum. Eng.600, 49–56 (1985).
[CrossRef]

J. J. Cowan, “Spectral characteristics of computer-generated phase-quantized diffractive lenses,” in Digest of the Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 81.

Dammann, H.

H. Dammann, “Spectral characteristics of stepped-phase gratings,” Optik 53, 409–417 (1979).

H. Dammann, “Color separation gratings,” Appl. Opt. 17, 2273–2279 (1978).
[CrossRef] [PubMed]

Denisyuk, Yu. N.

Yu. N. Denisyuk, “Photographic reconstruction of the optical properties of an object in its own scattered radiation field,” Sov. Phys. Dokl. 7, 543–545 (1962).

Dill, F. H.

F. H. Dill, “Optical lithography,” IEEE Trans. Electron Devices ED-22, 440–444 (1975).
[CrossRef]

Eisner, T.

H. Ghiradella, D. Aneshansley, T. Eisner, R. E. Silberglied, “Ultraviolet reflection of a male butterfly: interference color caused by thin-layer elaboration of wing scales,” Science 178, 1214–1217 (1972).
[CrossRef] [PubMed]

Enger, R. C.

Gaither, S. A.

This theory was described by S. A. Gaither (Integrated Systems, Inc., 2500 Mission College Boulevard, Santa Clara, California 95054) in an unpublished paper, “Vector coupled-wave analysis of crossed surface-relief diffraction gratings.” The research was conducted for the Binary Optics Group of MIT Lincoln Laboratories in 1988.

Gale, M. T.

M. T. Gale, K. Knop, “Embossed relief images and their application for color motion pictures,” J. Soc. Motion Pict. Telev. Eng. 87, 6–8 (1978).

M. T. Gale, K. Knop, Surface-Relief Images for Color Reproduction (Focal, New York, 1980).

Gaylord, T. K.

Ghiradella, H.

H. Ghiradella, D. Aneshansley, T. Eisner, R. E. Silberglied, “Ultraviolet reflection of a male butterfly: interference color caused by thin-layer elaboration of wing scales,” Science 178, 1214–1217 (1972).
[CrossRef] [PubMed]

Guerra, J.

J. Guerra, “Photon tunneling microscopy,” in Surface Measurement and Characterization, J. M. Bennet, ed., Proc. Soc. Photo-Opt. Eng.1009, 254–263 (1989).
[CrossRef]

Holz, M.

J. Leger, M. Holz, G. Swanson, W. Veldkamp, “Coherent laser beam addition: an application of binary optics technology,” Lincoln Lab. J. 1, 225–246 (1988).

Hutley, M. C.

M. C. Hutley, “Blazed interference diffraction gratings for the ultraviolet,” Opt. Acta 22, 1–13 (1975).
[CrossRef]

Ingersoll, K. A.

Jain, P. K.

A. R. Neureuther, P. K. Jain, W. G. Oldham, “Factors affecting linewidth control including multiple wavelength exposure and chromatic aberration,” in Developments in Microlithography VI, J. Dey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.275, 110–116 (1981).

Johnson, L. F.

Kammlott, G. W.

Knop, K.

M. T. Gale, K. Knop, “Embossed relief images and their application for color motion pictures,” J. Soc. Motion Pict. Telev. Eng. 87, 6–8 (1978).

M. T. Gale, K. Knop, Surface-Relief Images for Color Reproduction (Focal, New York, 1980).

Kramer, C. J.

C. J. Kramer, “Hologon laser scanners for nonimpact printing,” in High Speed Read/Write Techniques For Advanced Printing and Data Handling, L. Beiser, ed., Proc. Soc. Photo-Opt. Instrum. Eng.390, 165–173 (1983).
[CrossRef]

Land, M. F.

M. F. Land, “The physics and biology of animal reflectors,” Prog. Biophys. Mol. Biol. 24, 77–106 (1972).
[CrossRef]

Leger, J.

J. Leger, M. Holz, G. Swanson, W. Veldkamp, “Coherent laser beam addition: an application of binary optics technology,” Lincoln Lab. J. 1, 225–246 (1988).

Leith, E. N.

Mack, C. A.

Moharam, M. G.

Narasimham, M. A.

M. A. Narasimham, “Projection printed photolithographic images in positive photoresists,” IEEE Trans. Electron Devices ED-22, 478–482 (1975).
[CrossRef]

Neureuther, A. R.

A. R. Neureuther, P. K. Jain, W. G. Oldham, “Factors affecting linewidth control including multiple wavelength exposure and chromatic aberration,” in Developments in Microlithography VI, J. Dey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.275, 110–116 (1981).

Nijhout, H. F.

H. F. Nijhout, “The color patterns of butterflies and moths,” Sci. Am. 245, 140–151 (1981).
[CrossRef]

Oldham, W. G.

A. R. Neureuther, P. K. Jain, W. G. Oldham, “Factors affecting linewidth control including multiple wavelength exposure and chromatic aberration,” in Developments in Microlithography VI, J. Dey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.275, 110–116 (1981).

Sheridon, N. K.

N. K. Sheridon, “Production of blazed holograms,” Appl. Phys. Lett. 12, 316–318 (1968).
[CrossRef]

N. K. Sheridon, “Blazed hologram fabrication,” U.S. patent3,623,798 (November30, 1971).

Silberglied, R. E.

H. Ghiradella, D. Aneshansley, T. Eisner, R. E. Silberglied, “Ultraviolet reflection of a male butterfly: interference color caused by thin-layer elaboration of wing scales,” Science 178, 1214–1217 (1972).
[CrossRef] [PubMed]

Sincerbox, G.

H. Werlich, G. Sincerbox, B. Yung, “Fabrication of high-efficiency surface-relief holograms,” J. Imaging Technol. 10, 105–108 (1984).

Slafer, W. D.

J. J. Cowan, W. D. Slafer, “The recording and replication of holographic micropatterns for the ordering of photographic emulsion grains in film systems,” J. Imaging Sci. 31, 100–107 (1987).

J. J. Cowan, W. D. Slafer, “Holographic embossing at Polaroid: the Polaform process,” in Progress in Holographic Applications, J. Ebbeni, ed., Proc. Soc. Photo-Opt. Instrum. Eng.600, 49–56 (1985).
[CrossRef]

Swanson, G.

J. Leger, M. Holz, G. Swanson, W. Veldkamp, “Coherent laser beam addition: an application of binary optics technology,” Lincoln Lab. J. 1, 225–246 (1988).

Upatnieks, J.

Veldkamp, W.

J. Leger, M. Holz, G. Swanson, W. Veldkamp, “Coherent laser beam addition: an application of binary optics technology,” Lincoln Lab. J. 1, 225–246 (1988).

Walker, E. J.

E. J. Walker, “Reduction of photoresist standing-wave effects by post-exposure bake,” IEEE Trans. Electron Devices ED-22, 464–466 (1975).
[CrossRef]

Werlich, H.

H. Werlich, G. Sincerbox, B. Yung, “Fabrication of high-efficiency surface-relief holograms,” J. Imaging Technol. 10, 105–108 (1984).

Yung, B.

H. Werlich, G. Sincerbox, B. Yung, “Fabrication of high-efficiency surface-relief holograms,” J. Imaging Technol. 10, 105–108 (1984).

Appl. Opt. (3)

Appl. Phys. Lett. (1)

N. K. Sheridon, “Production of blazed holograms,” Appl. Phys. Lett. 12, 316–318 (1968).
[CrossRef]

IEEE Trans. Electron Devices (3)

F. H. Dill, “Optical lithography,” IEEE Trans. Electron Devices ED-22, 440–444 (1975).
[CrossRef]

E. J. Walker, “Reduction of photoresist standing-wave effects by post-exposure bake,” IEEE Trans. Electron Devices ED-22, 464–466 (1975).
[CrossRef]

M. A. Narasimham, “Projection printed photolithographic images in positive photoresists,” IEEE Trans. Electron Devices ED-22, 478–482 (1975).
[CrossRef]

J. Imaging Sci. (1)

J. J. Cowan, W. D. Slafer, “The recording and replication of holographic micropatterns for the ordering of photographic emulsion grains in film systems,” J. Imaging Sci. 31, 100–107 (1987).

J. Imaging Technol. (1)

H. Werlich, G. Sincerbox, B. Yung, “Fabrication of high-efficiency surface-relief holograms,” J. Imaging Technol. 10, 105–108 (1984).

J. Opt. Soc. Am. (3)

J. Soc. Motion Pict. Telev. Eng. (1)

M. T. Gale, K. Knop, “Embossed relief images and their application for color motion pictures,” J. Soc. Motion Pict. Telev. Eng. 87, 6–8 (1978).

Lincoln Lab. J. (1)

J. Leger, M. Holz, G. Swanson, W. Veldkamp, “Coherent laser beam addition: an application of binary optics technology,” Lincoln Lab. J. 1, 225–246 (1988).

Opt. Acta (1)

M. C. Hutley, “Blazed interference diffraction gratings for the ultraviolet,” Opt. Acta 22, 1–13 (1975).
[CrossRef]

Opt. Eng. (1)

J. J. Cowan, “Holographic honeycomb microlens,” Opt. Eng. 24, 796–802 (1985).
[CrossRef]

Optik (1)

H. Dammann, “Spectral characteristics of stepped-phase gratings,” Optik 53, 409–417 (1979).

Prog. Biophys. Mol. Biol. (1)

M. F. Land, “The physics and biology of animal reflectors,” Prog. Biophys. Mol. Biol. 24, 77–106 (1972).
[CrossRef]

Sci. Am. (1)

H. F. Nijhout, “The color patterns of butterflies and moths,” Sci. Am. 245, 140–151 (1981).
[CrossRef]

Science (1)

H. Ghiradella, D. Aneshansley, T. Eisner, R. E. Silberglied, “Ultraviolet reflection of a male butterfly: interference color caused by thin-layer elaboration of wing scales,” Science 178, 1214–1217 (1972).
[CrossRef] [PubMed]

Sov. Phys. Dokl. (1)

Yu. N. Denisyuk, “Photographic reconstruction of the optical properties of an object in its own scattered radiation field,” Sov. Phys. Dokl. 7, 543–545 (1962).

Other (15)

C. J. Kramer, “Hologon laser scanners for nonimpact printing,” in High Speed Read/Write Techniques For Advanced Printing and Data Handling, L. Beiser, ed., Proc. Soc. Photo-Opt. Instrum. Eng.390, 165–173 (1983).
[CrossRef]

J. J. Cowan, “Blazed holographic gratings: formation by surface waves and replication by metal electroforming,” in Periodic Structures, Gratings, Moire Patterns, and Diffraction Phenomena I, C. H. Chi, E. G. Loewen, C. L. O’Bryan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.240, 5–12 (1980).
[CrossRef]

A. R. Neureuther, P. K. Jain, W. G. Oldham, “Factors affecting linewidth control including multiple wavelength exposure and chromatic aberration,” in Developments in Microlithography VI, J. Dey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.275, 110–116 (1981).

J. J. Cowan, W. D. Slafer, “Holographic embossing at Polaroid: the Polaform process,” in Progress in Holographic Applications, J. Ebbeni, ed., Proc. Soc. Photo-Opt. Instrum. Eng.600, 49–56 (1985).
[CrossRef]

N. K. Sheridon, “Blazed hologram fabrication,” U.S. patent3,623,798 (November30, 1971).

J. Guerra, “Photon tunneling microscopy,” in Surface Measurement and Characterization, J. M. Bennet, ed., Proc. Soc. Photo-Opt. Eng.1009, 254–263 (1989).
[CrossRef]

J. J. Cowan, “Spectral characteristics of computer-generated phase-quantized diffractive lenses,” in Digest of the Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 81.

M. T. Gale, K. Knop, Surface-Relief Images for Color Reproduction (Focal, New York, 1980).

This theory was described by S. A. Gaither (Integrated Systems, Inc., 2500 Mission College Boulevard, Santa Clara, California 95054) in an unpublished paper, “Vector coupled-wave analysis of crossed surface-relief diffraction gratings.” The research was conducted for the Binary Optics Group of MIT Lincoln Laboratories in 1988.

J. J. Cowan, “The recording and large scale replication of crossed holographic grating arrays using multiple beam interferometry,” in International Conference on the Application, Theory, and Fabrication of Periodic Structures, Diffraction Gratings, and Moire Phenomena II, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.503, 120–129 (1984).

J. J. Cowan, “The Aztec grating: a surface-relief volume diffractive structure,” in Digest of the Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), p. 109.

J. J. Cowan, “Embossed volume holograms: the Aztec structure,” in Second International Conference on Holographic Systems, Components and Appliations, Publ. No. 311 (Institution of Electrical Engineers, London, 1989), pp. 38–44.

J. J. Cowan, “Method of replicating volume phase reflection holograms,” U.S. patent4,839,250 (June13, 1989).

J. J. Cowan, “Method of forming volume phase reflection holograms,” U.S. patent4,874,213 (October17, 1989).

J. J. Cowan, “Volume phase reflection holograms and methods for fabricating them,” U.S. patent4,888,260 (December19, 1989).

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Figures (40)

Fig. 1
Fig. 1

(a) Morpho rhetenor butterfly wing surface, 1260×; (b) 14,000×; (c) Morpho menelaus, 14,140×. The white bar in (a) measures 10 μm to scale; those in (b) and (c), 1 μm to scale.

Fig. 2
Fig. 2

Aztec structure recording geometry.

Fig. 3
Fig. 3

Aztec structure in developed photoresist layer.

Fig. 4
Fig. 4

Mathematical model of coarse grating profile.

Fig. 5
Fig. 5

Triangular (coarse) grating efficiency as a function of phase angle.

Fig. 6
Fig. 6

Mathematical model of phase-quantized grating profile.

Fig. 7
Fig. 7

Diffraction efficiency of binary grating as a function of phase angle.

Fig. 8
Fig. 8

Diffraction efficiency as a function of phase angle for tertiary symmetric Aztec gratings.

Fig. 9
Fig. 9

Diffraction efficiency as a function of phase angle for quarternary symmetric Aztec gratings.

Fig. 10
Fig. 10

Diffraction efficiency as a function of phase angle for pentiary symmetric Aztec gratings.

Fig. 11
Fig. 11

Diffraction efficiency as a function of phase angle for deciary symmetric Aztec gratings.

Fig. 12
Fig. 12

Diffraction efficiency as a function of wavelength for binary Aztec gratings with step height h = 250 nm.

Fig. 13
Fig. 13

Diffraction efficiency as a function of wavelength for tertiary Aztec gratings with step height h = 250 nm.

Fig. 14
Fig. 14

Diffraction efficiency as a function of wavelength for quarternary Aztec gratings with step height h = 250 nm.

Fig. 15
Fig. 15

Diffraction efficiency as a function of wavelength for pentiary Aztec gratings with step height h = 250 nm.

Fig. 16
Fig. 16

Diffraction efficiency as a function of wavelength for deciary Aztec gratings with step height h = 250 nm.

Fig. 17
Fig. 17

Diffraction efficiency as a function of phase angle for triangular asymmetric (blazed) gratings.

Fig. 18
Fig. 18

Diffraction efficiency as a function of wavelength for triangular asymmetric (blazed) gratings with step height h = 250 nm.

Fig. 19
Fig. 19

Diffraction efficiency as a function of wavelength for tertiary asymmetric Aztec gratings with step height h = 250 nm.

Fig. 20
Fig. 20

Diffraction efficiency as a function of wavelength for quarternary Aztec gratings with step height h = 250 nm.

Fig. 21
Fig. 21

Diffraction efficiency as a function of wavelength for pentiary Aztec gratings with step height h = 250 nm.

Fig. 22
Fig. 22

Diffraction efficiency as a function of wavelength for deciary Aztec gratings with step height h = 250 nm.

Fig. 23
Fig. 23

Aztec microzone-plate stepped-array grating.

Fig. 24
Fig. 24

Prism-coupling total-reflection recording technique for microzone plate-array grating showing step height and propagation vectors within the resist layer.

Fig. 25
Fig. 25

Microzone plate array gratings recorded in photoresist: (a) 60-deg edge view at 7000×, (b) top view at 3500×. The white bars measure 1 μm to scale.

Fig. 26
Fig. 26

Edge view of typical Aztec linear stepped grating at 14,000×. The white bar measures 1 μm to scale.

Fig. 27
Fig. 27

Comparison of scalar theory and experiment for six-level Aztec grating, with d = 5.0 μm, step height h = 0.265 μm, and a depth of 1.325 μm.

Fig. 28
Fig. 28

Formation of Aztec structure nickel master.

Fig. 29
Fig. 29

Nickel master for Aztec zone plate-array grating at 2730×. The white bar measures 10 μm to scale.

Fig. 30
Fig. 30

Embossing of Aztec structure into plastic.

Fig. 31
Fig. 31

Embossed section of Aztec zone plate-array grating in plastic at 5250×. The white bar measures 1 μm to scale.

Fig. 32
Fig. 32

Metallization of embossed Aztec structure.

Fig. 33
Fig. 33

Resonant wavelength shift by coating Aztec structure with different clear dielectric layers.

Fig. 34
Fig. 34

Aztec diffractive-image recording geometry.

Fig. 35
Fig. 35

Developed photoresist layer for Aztec diffractive image.

Fig. 36
Fig. 36

Aztec diffractive image surface profile in photoresist: edge view at 14,000×. The white bar measures 1 μm to scale.

Fig. 37
Fig. 37

Aztec diffractive image surface profile embossed in plastic and metallized at 14,000×. The white bar measures 1 μm to scale.

Fig. 38
Fig. 38

Embossed Aztec diffractive image: top view at 7000×. The white bar measures 1 μm to scale.

Fig. 39
Fig. 39

Groove profile of Aztec zone plate lens formed by optical lithography and ion etched into silicon substrate at 15,400×. The white bar measures 1 μm to scale.

Fig. 40
Fig. 40

Embossed section of groove profile of Aztec zone plate lens. Photograph made with photon tunneling microscope.35

Equations (48)

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η ( λ ) = | 1 d 0 d g ( x ) exp ( 2 π i q x / d ) d x | 2 ,
sin α i + sin α q = q λ / d ,
sin α q = q λ / d .
g ( x ) = exp [ 2 π i s ( x ) ( n 2 n 1 ) / λ ] ,
g ( x ) = exp [ 2 π i s ( x ) ( n 1 ) / λ ] .
g ( x ) = exp [ 4 π i s ( x ) / λ ] .
g ( x ) = exp i Φ ( x ) ,
Φ ( x ) = 4 π s ( x ) / λ
η q ( λ ) = | 1 d 0 d exp { i [ Φ ( x ) 2 π q x / d ] } d x | 2 .
η q ( λ ) = | 0 1 exp { i [ Φ ( x ) 2 π q x ] } d x | 2 .
η q ( λ ) = | 1 / 2 1 / 2 exp { i [ Φ ( x ) 2 π q x ] } d x | 2
s ( x ) = { 2 a x x 0 2 a x x 0 .
η 0 ( λ ) = sin 2 φ 2 ( φ 2 ) 2 ,
φ = 4 π a λ .
η ± 1 ( λ ) = ( 2 φ cos φ 2 φ 2 π 2 ) 2 .
η q ( λ ) = | m = 0 P 1 1 / 2 1 / 2 exp [ i ( Φ m 2 π q x ) ] d x | 2 ,
s ( x ) = m h with m = 0,1 , , ( P 1 ) ,
Φ m = 4 π m h / λ ( reflection ) .
η 0 ( λ ) = sin 2 P ( φ 2 ) P 2 sin 2 ( φ 2 ) ,
φ = 4 π h / λ ( reflection ) .
η q ( λ ) = [ sin π q 2 P π q ] 2 [ cos 2 ( P φ 2 ) sin 4 π q 2 + sin 2 ( P φ 2 ) cos 4 π q 2 ] × [ 1 sin ( φ 2 π q 2 P ) + 1 sin ( φ 2 + π q 2 P ) ] 2 .
η q ( λ ) = [ sin π q P sin φ 2 F ( φ ) π q ( sin 2 φ 2 cos 2 π q 2 P cos 2 φ 2 sin 2 π q 2 P ) ] 2 ,
F ( φ ) = sin P φ 2 ( q even )
F ( φ ) = cos P φ 2 ( q odd ) .
η 0 = cos 2 ( φ / 2 )
η ± 1 = [ 4 / π 2 ] sin 2 ( φ / 2 ) ,
η ± 2 = 0 ,
η ± 1 = ( 2 π sin π 3 sin φ ) 2 ( tertiary ) ,
η ± 1 = [ 2 π sin π 4 ( sin 3 φ 2 + tan π 8 sin φ 2 ) ] 2 ( quaternary ) ,
η ± 1 = [ 2 π sin π 5 ( sin 2 φ + 2 sin π 10 sin φ ) ] 2 ( pentiary ) .
η ± 1 = sin 2 ( φ 2 π ) ( φ 2 π ) 2 ,
η 1 = sin 2 ( φ 2 + π ) ( φ 2 + π ) 2 .
η q ( λ ) = ( sin π q P π q P ) 2 { sin [ P ( φ 2 π q P ) ] P sin ( φ 2 π q P ) } 2 ,
Δ φ = 2 π / P ,
φ + = 2 π + π / P
φ = 2 π π / P ,
Δ λ = 4 π h ( 1 φ 1 φ + ) ,
Δ λ λ 0 = 1 1 1 2 P 1 1 + 1 2 P ,
Δ λ λ 0 = 1 / ( P 1 / 4 P ) ,
Δ λ λ 0 1 / P
y = x 2 .
A = π ( x 2 2 x 1 2 ) = π ( y 2 y 1 ) = π Δ y = π h = constant .
h = π / K ,
h = λ m / 2
λ m = 2 π / K ,
K = | K | cos θ = n K 0 cos θ ,
h = 458 / ( 2 × 1.6 × cos 32.8 ) = 170 nm .
λ = 2 n h = 544 nm .

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