Abstract

We present a unified treatment of the diffraction properties of stratified volume holographic optical elements (SVHOE’s). We show that the relative phasing of the diffraction orders as they propagate from layer to layer gives rise to a unique notched diffraction response of the +1 order (for the case of Bragg incidence) as a function of the normalized buffer-layer thickness, the grating spatial frequency, and the readout wavelength. For certain combinations of these parameters Bragg diffraction behavior characteristic of volume holographic optical elements (VHOE’s) is observed, whereas for other combinations pure Raman–Nath behavior periodically recurs. By using these same relative-phasing arguments, the principal features of the periodic angular sensitivity of the +1 and −1 orders can be predicted. In addition to examining the fundamental aspects of SVHOE diffraction behavior, we discuss several possible applications, including optical array generation, spatial frequency filtering, and wavelength notch filtering. With the use of the SVHOE concept, holographic materials with otherwise exemplary characteristics that are currently available only in thin-film form can be used in structures designed either to access unique SVHOE diffraction properties or to emulate conventional VHOE’s.

© 1992 Optical Society of America

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1991 (3)

F. H. Mok, M. C. Tackitt, H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3 crystal,” Opt. Lett. 16, 605–607 (1991).
[CrossRef] [PubMed]

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydik, K. T. Short, R. D. Feldman, R. F. Austin, “High sensitivity optical image processing device based on CdZnTe/ZnTe multiple quantum well structures,” Appl. Phys. Lett. 59, 1832–1834 (1991).
[CrossRef]

M. C. Gupta, “Diffraction of a light beam by doubly periodic structures,” Opt. Lett. 16, 1301–1303 (1991).
[CrossRef] [PubMed]

1990 (4)

1989 (2)

1988 (5)

1987 (4)

N. N. Evtikhiev, D. I. Mirovitskii, N. V. Rostovtseva, O. B. Serov, “Multilayer holographic functional element in an analog-digital converter,” Sov. J. Quantum. Electron. 16, 1180–1184 (1987).
[CrossRef]

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 28, 5061–5074 (1987),
[CrossRef]

D. Z. Anderson, D. M. Lininger, “Dynamic optical interconnects: volume holograms as optical two-port operators,” Appl. Opt. 26, 5031–5038 (1987).
[CrossRef] [PubMed]

V. A. Komotskii, V. F. Nikulin, “Theoretical analysis of diffraction of a Gaussian optical beam by a system of two diffraction gratings,” Opt. Spectrosc. (USSR) 63, 239–242 (1987).

1986 (4)

J. Slaby, T. Szoplik, “Resonant modes in a cascaded system of Fourier holograms,” Opt. Acta 33, 301–313 (1986).
[CrossRef]

A. R. Tanguay, R. V. Johnson, “Stratified volume holographic optical elements,” J. Opt. Soc. Am. A 3 (13), P53 (1986).

R. V. Johnson, A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235–249 (1986).
[CrossRef]

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, B. Y. Zel’dovich, “Bilayer holograms: theory and experiment,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

1985 (1)

V. N. Malysh, O. I. Ovcharenko, A. N. Osovitskii, “Light diffraction by a layered structure with periodically modulated interfaces,” Opt. Spectrosc. (USSR) 58, 513–516 (1985).

1984 (2)

B. Y. Zel’dovich, T. Y. Yakovleva, “Theory of a two-layer hologram,” Sov. J. Quantum. Electron. 14, 323–328 (1984).
[CrossRef]

B. Y. Zel’dovich, D. I. Mirovitskii, N. V. Rostovtseva, O. B. Serov, “Characteristics of two-layer phase holograms,” Sov. J. Quantum. Electron. 14, 364–369 (1984).
[CrossRef]

1983 (1)

J. Slaby, T. Szoplik, K. Chalasinska-Macukow, “Cascaded phase Fourier holograms,” Opt. Acta 30, 529–543 (1983).
[CrossRef]

1982 (3)

D. Yevick, L. Thylen, “Analysis of gratings by the beam-propagation method,” J. Opt. Soc. Am. 72, 1081–1089 (1982).
[CrossRef]

L. Thylen, D. Yevick, “Beam propagation method in anisotropic media,” Appl. Opt. 21, 2751–2754 (1982).
[CrossRef] [PubMed]

S.-W. Lee, G. Zarrillo, C.-L. Law, “Simple formulas for transmission through periodic metal grids or plates,” IEEE Trans. Antennas Propag. AP-30, 904–909 (1982).

1981 (1)

V. A. Komatskii, T. D. Black, “Analysis and application of stationary reference grating method for optical detection of surface acoustic waves,” J. Appl. Phys. 51, 129–136 (1981).
[CrossRef]

1980 (3)

A. P. Yakimovich, “Multilayer three-dimensional holographic gratings,” Opt. Spectrosc. (USSR) 49, 85–88 (1980).

K. Chalasinska-Macukow, T. Szoplik, “Reconstruction of two stacked Fourier holograms—experiments and results,” Opt. Commun. 33, 245–250 (1980).
[CrossRef]

A. F. Bessonov, L. N. Deryugin, V. A. Komotskii, “Phenomena of optical wave diffraction by traveling spatial phase modulation on stationary phase gratings,” Opt. Spectrosc. (USSR) 49, 81–84 (1980).

1978 (2)

K. Chalasinska-Macukow, B. Karczewski, T. Szoplik, “Reconstruction of two stacked Fourier holograms,” Opt. Commun. 27, 311–316 (1978).
[CrossRef]

M. D. Feit, J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978).
[CrossRef] [PubMed]

1977 (1)

F. Calligaris, P. Ciuti, I. Gabrielli, “Temporal light modulation in thick-screen diffraction by ultrasound beam plus amplitude grating,” J. Acoust. Soc. Am. 61, 959–964 (1977).
[CrossRef]

1976 (1)

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

1975 (2)

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped lithium niobate,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

K. Kodate, T. Kamiya, H. Takenaka, H. Yanai, “Double diffraction of phase gratings in the Fresnel region,” Jpn. J. Appl. Phys. 14, 1323–1334 (1975).
[CrossRef]

1974 (2)

1972 (1)

H. Blok, G. Mur, “Diffraction by a double grating,” Appl. Sci. Res. 26, 389–397 (1972).
[CrossRef]

1971 (1)

K. Kodate, T. Kamiya, M. Kamiyama, “Double diffraction in the Fresnel region,” Jpn. J. Appl. Phys. 10, 1040–1045 (1971).
[CrossRef]

1970 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

1962 (1)

L. E. Hargrove, E. A. Hiedemann, R. Mertens, “Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency,” Z. Phys. 167, 326–336 (1962).
[CrossRef]

1960 (1)

L. E. Hargrove, “Diffraction of light passing through two adjacent ultrasonic progressive waves of different frequency,” J. Acoust. Soc. Am. 32, 940 (1960).
[CrossRef]

Amodei, J. J.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped lithium niobate,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Anderson, D. Z.

Asthana, P.

P. Asthana, G. Nordin, S. Piazzolla, A. R. Tanguay, B. K. Jenkins, “Analysis of interchannel crosstalk and throughput efficiency in highly multiplexed fan-out/fan-in holographic interconnections,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 242.

Austin, R. F.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydik, K. T. Short, R. D. Feldman, R. F. Austin, “High sensitivity optical image processing device based on CdZnTe/ZnTe multiple quantum well structures,” Appl. Phys. Lett. 59, 1832–1834 (1991).
[CrossRef]

Bessonov, A. F.

A. F. Bessonov, L. N. Deryugin, V. A. Komotskii, “Phenomena of optical wave diffraction by traveling spatial phase modulation on stationary phase gratings,” Opt. Spectrosc. (USSR) 49, 81–84 (1980).

Black, T. D.

D. A. Larson, T. D. Black, M. Green, R. G. Torti, Y. J. Wang, R. Magnusson, “Optical modulation by a traveling surface acoustic wave and a holographic reference grating,” J. Opt. Soc. Am. A 7, 1745–1750 (1990).
[CrossRef]

V. A. Komatskii, T. D. Black, “Analysis and application of stationary reference grating method for optical detection of surface acoustic waves,” J. Appl. Phys. 51, 129–136 (1981).
[CrossRef]

Blok, H.

H. Blok, G. Mur, “Diffraction by a double grating,” Appl. Sci. Res. 26, 389–397 (1972).
[CrossRef]

Brady, D.

D. Psaltis, D. Brady, X.-G. Gu, K. Hsu, “Optical implementation of neural computers,” in Optical Processing and Computing, H. Arsenault, ed. (Academic, San Diego, Calif., 1988).

Brady, D. J.

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Burke, W. J.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped lithium niobate,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Calligaris, F.

F. Calligaris, P. Ciuti, I. Gabrielli, “Temporal light modulation in thick-screen diffraction by ultrasound beam plus amplitude grating,” J. Acoust. Soc. Am. 61, 959–964 (1977).
[CrossRef]

Campbell, S.

Caulfield, H. J.

H. J. Caulfield, D. H. McMahon, R. A. Soref, “Stacked hologram apparatus,” U.S. patent3,635,538 (January18, 1972).

H. J. Caulfield, “Stacked page oriented holographic memory,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 203–206 (1988).
[CrossRef]

Chalasinska-Macukow, K.

J. Slaby, T. Szoplik, K. Chalasinska-Macukow, “Cascaded phase Fourier holograms,” Opt. Acta 30, 529–543 (1983).
[CrossRef]

K. Chalasinska-Macukow, T. Szoplik, “Reconstruction of two stacked Fourier holograms—experiments and results,” Opt. Commun. 33, 245–250 (1980).
[CrossRef]

K. Chalasinska-Macukow, B. Karczewski, T. Szoplik, “Reconstruction of two stacked Fourier holograms,” Opt. Commun. 27, 311–316 (1978).
[CrossRef]

Chemla, D. S.

Ciuti, P.

F. Calligaris, P. Ciuti, I. Gabrielli, “Temporal light modulation in thick-screen diffraction by ultrasound beam plus amplitude grating,” J. Acoust. Soc. Am. 61, 959–964 (1977).
[CrossRef]

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

De Bitetto, D. J.

Deryugin, L. N.

A. F. Bessonov, L. N. Deryugin, V. A. Komotskii, “Phenomena of optical wave diffraction by traveling spatial phase modulation on stationary phase gratings,” Opt. Spectrosc. (USSR) 49, 81–84 (1980).

Domash, L.

L. Domash, J. Schwartz, A. Nelson, P. Levin, “Active holographic interconnects for interfacing volume storage,” in Image Storage and Retrieval Systems, A. Jamberdino, W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1662, 211–218 (1991).
[CrossRef]

Doran, G. E.

Evtikhiev, N. N.

N. N. Evtikhiev, D. I. Mirovitskii, N. V. Rostovtseva, O. B. Serov, “Multilayer holographic functional element in an analog-digital converter,” Sov. J. Quantum. Electron. 16, 1180–1184 (1987).
[CrossRef]

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, B. Y. Zel’dovich, “Bilayer holograms: theory and experiment,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

Feit, M. D.

M. D. Feit, J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978).
[CrossRef] [PubMed]

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Feldman, R. D.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydik, K. T. Short, R. D. Feldman, R. F. Austin, “High sensitivity optical image processing device based on CdZnTe/ZnTe multiple quantum well structures,” Appl. Phys. Lett. 59, 1832–1834 (1991).
[CrossRef]

Fleck, J. A.

M. D. Feit, J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978).
[CrossRef] [PubMed]

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Gabrielli, I.

F. Calligaris, P. Ciuti, I. Gabrielli, “Temporal light modulation in thick-screen diffraction by ultrasound beam plus amplitude grating,” J. Acoust. Soc. Am. 61, 959–964 (1977).
[CrossRef]

Glass, A. M.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydik, K. T. Short, R. D. Feldman, R. F. Austin, “High sensitivity optical image processing device based on CdZnTe/ZnTe multiple quantum well structures,” Appl. Phys. Lett. 59, 1832–1834 (1991).
[CrossRef]

A. M. Glass, D. D. Nolte, D. H. Olson, G. E. Doran, D. S. Chemla, W H. Knox, “Resonant photodiffractive four-wave mixing in semi-insulating GaAs/AlGaAs quantum wells,” Opt. Lett. 15, 264–266 (1990).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

Green, M.

Gu, X.-G.

D. Psaltis, D. Brady, X.-G. Gu, K. Hsu, “Optical implementation of neural computers,” in Optical Processing and Computing, H. Arsenault, ed. (Academic, San Diego, Calif., 1988).

Gupta, M. C.

Hargrove, L. E.

L. E. Hargrove, E. A. Hiedemann, R. Mertens, “Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency,” Z. Phys. 167, 326–336 (1962).
[CrossRef]

L. E. Hargrove, “Diffraction of light passing through two adjacent ultrasonic progressive waves of different frequency,” J. Acoust. Soc. Am. 32, 940 (1960).
[CrossRef]

Hiedemann, E. A.

L. E. Hargrove, E. A. Hiedemann, R. Mertens, “Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency,” Z. Phys. 167, 326–336 (1962).
[CrossRef]

Hong, J. H.

Hsu, K.

D. Psaltis, D. Brady, X.-G. Gu, K. Hsu, “Optical implementation of neural computers,” in Optical Processing and Computing, H. Arsenault, ed. (Academic, San Diego, Calif., 1988).

Jenkins, B. K.

P. Asthana, G. Nordin, S. Piazzolla, A. R. Tanguay, B. K. Jenkins, “Analysis of interchannel crosstalk and throughput efficiency in highly multiplexed fan-out/fan-in holographic interconnections,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 242.

Johnson, R. V.

R. V. Johnson, A. R. Tanguay, “Stratified volume holographic optical elements,” Opt. News 14 (12), 30–31 (1988).
[CrossRef]

R. V. Johnson, A. R. Tanguay, “Stratified volume holographic optical elements,” Opt. Lett. 13, 189–191 (1988).
[CrossRef] [PubMed]

A. R. Tanguay, R. V. Johnson, “Stratified volume holographic optical elements,” J. Opt. Soc. Am. A 3 (13), P53 (1986).

R. V. Johnson, A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235–249 (1986).
[CrossRef]

G. P. Nordin, R. V. Johnson, A. R. Tanguay, “Physical characterization of stratified volume holographic optical elements,” in Annual Meeting, Vol. 11 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 106.

Kamiya, T.

K. Kodate, T. Kamiya, H. Takenaka, H. Yanai, “Double diffraction of phase gratings in the Fresnel region,” Jpn. J. Appl. Phys. 14, 1323–1334 (1975).
[CrossRef]

K. Kodate, T. Kamiya, M. Kamiyama, “Double diffraction in the Fresnel region,” Jpn. J. Appl. Phys. 10, 1040–1045 (1971).
[CrossRef]

Kamiyama, M.

K. Kodate, T. Kamiya, M. Kamiyama, “Double diffraction in the Fresnel region,” Jpn. J. Appl. Phys. 10, 1040–1045 (1971).
[CrossRef]

Karczewski, B.

K. Chalasinska-Macukow, B. Karczewski, T. Szoplik, “Reconstruction of two stacked Fourier holograms,” Opt. Commun. 27, 311–316 (1978).
[CrossRef]

Kestigian, M.

Knox, W H.

Kodate, K.

K. Kodate, T. Kamiya, H. Takenaka, H. Yanai, “Double diffraction of phase gratings in the Fresnel region,” Jpn. J. Appl. Phys. 14, 1323–1334 (1975).
[CrossRef]

K. Kodate, T. Kamiya, M. Kamiyama, “Double diffraction in the Fresnel region,” Jpn. J. Appl. Phys. 10, 1040–1045 (1971).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Komatskii, V. A.

V. A. Komatskii, T. D. Black, “Analysis and application of stationary reference grating method for optical detection of surface acoustic waves,” J. Appl. Phys. 51, 129–136 (1981).
[CrossRef]

Komotskii, V. A.

V. A. Komotskii, V. F. Nikulin, “Theoretical analysis of diffraction of a Gaussian optical beam by a system of two diffraction gratings,” Opt. Spectrosc. (USSR) 63, 239–242 (1987).

A. F. Bessonov, L. N. Deryugin, V. A. Komotskii, “Phenomena of optical wave diffraction by traveling spatial phase modulation on stationary phase gratings,” Opt. Spectrosc. (USSR) 49, 81–84 (1980).

Kujawinska, M.

Kwiek, P.

P. Kwiek, “Light diffraction by two spatially separated ultrasonic waves,” J. Acoust. Soc. Am. 86, 2261–2272 (1989).
[CrossRef]

Larson, D. A.

Law, C.-L.

S.-W. Lee, G. Zarrillo, C.-L. Law, “Simple formulas for transmission through periodic metal grids or plates,” IEEE Trans. Antennas Propag. AP-30, 904–909 (1982).

Lee, S.-W.

S.-W. Lee, G. Zarrillo, C.-L. Law, “Simple formulas for transmission through periodic metal grids or plates,” IEEE Trans. Antennas Propag. AP-30, 904–909 (1982).

Levin, P.

L. Domash, J. Schwartz, A. Nelson, P. Levin, “Active holographic interconnects for interfacing volume storage,” in Image Storage and Retrieval Systems, A. Jamberdino, W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1662, 211–218 (1991).
[CrossRef]

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Lininger, D. M.

Magnusson, R.

Malysh, V. N.

V. N. Malysh, O. I. Ovcharenko, A. N. Osovitskii, “Light diffraction by a layered structure with periodically modulated interfaces,” Opt. Spectrosc. (USSR) 58, 513–516 (1985).

McMahon, D. H.

H. J. Caulfield, D. H. McMahon, R. A. Soref, “Stacked hologram apparatus,” U.S. patent3,635,538 (January18, 1972).

Mertens, R.

L. E. Hargrove, E. A. Hiedemann, R. Mertens, “Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency,” Z. Phys. 167, 326–336 (1962).
[CrossRef]

Mirovitskii, D. I.

N. N. Evtikhiev, D. I. Mirovitskii, N. V. Rostovtseva, O. B. Serov, “Multilayer holographic functional element in an analog-digital converter,” Sov. J. Quantum. Electron. 16, 1180–1184 (1987).
[CrossRef]

B. Y. Zel’dovich, D. I. Mirovitskii, N. V. Rostovtseva, O. B. Serov, “Characteristics of two-layer phase holograms,” Sov. J. Quantum. Electron. 14, 364–369 (1984).
[CrossRef]

Mirovitskiy, D. I.

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, B. Y. Zel’dovich, “Bilayer holograms: theory and experiment,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

Mok, F. H.

Morris, J. R.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Mur, G.

H. Blok, G. Mur, “Diffraction by a double grating,” Appl. Sci. Res. 26, 389–397 (1972).
[CrossRef]

Nelson, A.

L. Domash, J. Schwartz, A. Nelson, P. Levin, “Active holographic interconnects for interfacing volume storage,” in Image Storage and Retrieval Systems, A. Jamberdino, W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1662, 211–218 (1991).
[CrossRef]

Nikulin, V. F.

V. A. Komotskii, V. F. Nikulin, “Theoretical analysis of diffraction of a Gaussian optical beam by a system of two diffraction gratings,” Opt. Spectrosc. (USSR) 63, 239–242 (1987).

Nolte, D. D.

Nordin, G.

P. Asthana, G. Nordin, S. Piazzolla, A. R. Tanguay, B. K. Jenkins, “Analysis of interchannel crosstalk and throughput efficiency in highly multiplexed fan-out/fan-in holographic interconnections,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 242.

Nordin, G. P.

G. P. Nordin, R. V. Johnson, A. R. Tanguay, “Physical characterization of stratified volume holographic optical elements,” in Annual Meeting, Vol. 11 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 106.

Olson, D. H.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydik, K. T. Short, R. D. Feldman, R. F. Austin, “High sensitivity optical image processing device based on CdZnTe/ZnTe multiple quantum well structures,” Appl. Phys. Lett. 59, 1832–1834 (1991).
[CrossRef]

A. M. Glass, D. D. Nolte, D. H. Olson, G. E. Doran, D. S. Chemla, W H. Knox, “Resonant photodiffractive four-wave mixing in semi-insulating GaAs/AlGaAs quantum wells,” Opt. Lett. 15, 264–266 (1990).
[CrossRef] [PubMed]

Osovitskii, A. N.

V. N. Malysh, O. I. Ovcharenko, A. N. Osovitskii, “Light diffraction by a layered structure with periodically modulated interfaces,” Opt. Spectrosc. (USSR) 58, 513–516 (1985).

Ovcharenko, O. I.

V. N. Malysh, O. I. Ovcharenko, A. N. Osovitskii, “Light diffraction by a layered structure with periodically modulated interfaces,” Opt. Spectrosc. (USSR) 58, 513–516 (1985).

Paek, E. G.

Partovi, A.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydik, K. T. Short, R. D. Feldman, R. F. Austin, “High sensitivity optical image processing device based on CdZnTe/ZnTe multiple quantum well structures,” Appl. Phys. Lett. 59, 1832–1834 (1991).
[CrossRef]

Patel, J. S.

Petit, R.

Phillips, W.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped lithium niobate,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Piazzolla, S.

P. Asthana, G. Nordin, S. Piazzolla, A. R. Tanguay, B. K. Jenkins, “Analysis of interchannel crosstalk and throughput efficiency in highly multiplexed fan-out/fan-in holographic interconnections,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 242.

Pohl, D.

Psaltis, D.

D. Psaltis, D. J. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1758 (1988).
[CrossRef]

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 28, 5061–5074 (1987),
[CrossRef]

D. Psaltis, D. Brady, X.-G. Gu, K. Hsu, “Optical implementation of neural computers,” in Optical Processing and Computing, H. Arsenault, ed. (Academic, San Diego, Calif., 1988).

Rostovtseva, N. V.

N. N. Evtikhiev, D. I. Mirovitskii, N. V. Rostovtseva, O. B. Serov, “Multilayer holographic functional element in an analog-digital converter,” Sov. J. Quantum. Electron. 16, 1180–1184 (1987).
[CrossRef]

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, B. Y. Zel’dovich, “Bilayer holograms: theory and experiment,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

B. Y. Zel’dovich, D. I. Mirovitskii, N. V. Rostovtseva, O. B. Serov, “Characteristics of two-layer phase holograms,” Sov. J. Quantum. Electron. 14, 364–369 (1984).
[CrossRef]

Schwartz, J.

L. Domash, J. Schwartz, A. Nelson, P. Levin, “Active holographic interconnects for interfacing volume storage,” in Image Storage and Retrieval Systems, A. Jamberdino, W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1662, 211–218 (1991).
[CrossRef]

Serov, O. B.

N. N. Evtikhiev, D. I. Mirovitskii, N. V. Rostovtseva, O. B. Serov, “Multilayer holographic functional element in an analog-digital converter,” Sov. J. Quantum. Electron. 16, 1180–1184 (1987).
[CrossRef]

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, B. Y. Zel’dovich, “Bilayer holograms: theory and experiment,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

B. Y. Zel’dovich, D. I. Mirovitskii, N. V. Rostovtseva, O. B. Serov, “Characteristics of two-layer phase holograms,” Sov. J. Quantum. Electron. 14, 364–369 (1984).
[CrossRef]

Short, K. T.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydik, K. T. Short, R. D. Feldman, R. F. Austin, “High sensitivity optical image processing device based on CdZnTe/ZnTe multiple quantum well structures,” Appl. Phys. Lett. 59, 1832–1834 (1991).
[CrossRef]

Slaby, J.

J. Slaby, T. Szoplik, “Resonant modes in a cascaded system of Fourier holograms,” Opt. Acta 33, 301–313 (1986).
[CrossRef]

J. Slaby, T. Szoplik, K. Chalasinska-Macukow, “Cascaded phase Fourier holograms,” Opt. Acta 30, 529–543 (1983).
[CrossRef]

Soref, R. A.

H. J. Caulfield, D. H. McMahon, R. A. Soref, “Stacked hologram apparatus,” U.S. patent3,635,538 (January18, 1972).

Staebler, D. L.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped lithium niobate,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Stoll, H. M.

Szoplik, T.

J. Slaby, T. Szoplik, “Resonant modes in a cascaded system of Fourier holograms,” Opt. Acta 33, 301–313 (1986).
[CrossRef]

J. Slaby, T. Szoplik, K. Chalasinska-Macukow, “Cascaded phase Fourier holograms,” Opt. Acta 30, 529–543 (1983).
[CrossRef]

K. Chalasinska-Macukow, T. Szoplik, “Reconstruction of two stacked Fourier holograms—experiments and results,” Opt. Commun. 33, 245–250 (1980).
[CrossRef]

K. Chalasinska-Macukow, B. Karczewski, T. Szoplik, “Reconstruction of two stacked Fourier holograms,” Opt. Commun. 27, 311–316 (1978).
[CrossRef]

Tackitt, M. C.

Takenaka, H.

K. Kodate, T. Kamiya, H. Takenaka, H. Yanai, “Double diffraction of phase gratings in the Fresnel region,” Jpn. J. Appl. Phys. 14, 1323–1334 (1975).
[CrossRef]

Tanguay, A. R.

R. V. Johnson, A. R. Tanguay, “Stratified volume holographic optical elements,” Opt. News 14 (12), 30–31 (1988).
[CrossRef]

R. V. Johnson, A. R. Tanguay, “Stratified volume holographic optical elements,” Opt. Lett. 13, 189–191 (1988).
[CrossRef] [PubMed]

A. R. Tanguay, R. V. Johnson, “Stratified volume holographic optical elements,” J. Opt. Soc. Am. A 3 (13), P53 (1986).

R. V. Johnson, A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235–249 (1986).
[CrossRef]

G. P. Nordin, R. V. Johnson, A. R. Tanguay, “Physical characterization of stratified volume holographic optical elements,” in Annual Meeting, Vol. 11 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 106.

P. Asthana, G. Nordin, S. Piazzolla, A. R. Tanguay, B. K. Jenkins, “Analysis of interchannel crosstalk and throughput efficiency in highly multiplexed fan-out/fan-in holographic interconnections,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 242.

Tayeb, G.

Thaxter, J. B.

Thylen, L.

L. Thylen, D. Yevick, “Beam propagation method in anisotropic media,” Appl. Opt. 21, 2751–2754 (1982).
[CrossRef] [PubMed]

D. Yevick, L. Thylen, “Analysis of gratings by the beam-propagation method,” J. Opt. Soc. Am. 72, 1081–1089 (1982).
[CrossRef]

Torti, R. G.

Wagner, K.

D. Psaltis, D. J. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1758 (1988).
[CrossRef]

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 28, 5061–5074 (1987),
[CrossRef]

Wang, Y. J.

Wullert, J. R.

Yakimovich, A. P.

A. P. Yakimovich, “Multilayer three-dimensional holographic gratings,” Opt. Spectrosc. (USSR) 49, 85–88 (1980).

Yakovleva, T. V.

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, B. Y. Zel’dovich, “Bilayer holograms: theory and experiment,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

Yakovleva, T. Y.

B. Y. Zel’dovich, T. Y. Yakovleva, “Theory of a two-layer hologram,” Sov. J. Quantum. Electron. 14, 323–328 (1984).
[CrossRef]

Yanai, H.

K. Kodate, T. Kamiya, H. Takenaka, H. Yanai, “Double diffraction of phase gratings in the Fresnel region,” Jpn. J. Appl. Phys. 14, 1323–1334 (1975).
[CrossRef]

Yeh, P.

Yevick, D.

D. Yevick, L. Thylen, “Analysis of gratings by the beam-propagation method,” J. Opt. Soc. Am. 72, 1081–1089 (1982).
[CrossRef]

L. Thylen, D. Yevick, “Beam propagation method in anisotropic media,” Appl. Opt. 21, 2751–2754 (1982).
[CrossRef] [PubMed]

Zarrillo, G.

S.-W. Lee, G. Zarrillo, C.-L. Law, “Simple formulas for transmission through periodic metal grids or plates,” IEEE Trans. Antennas Propag. AP-30, 904–909 (1982).

Zel’dovich, B. Y.

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, B. Y. Zel’dovich, “Bilayer holograms: theory and experiment,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

B. Y. Zel’dovich, D. I. Mirovitskii, N. V. Rostovtseva, O. B. Serov, “Characteristics of two-layer phase holograms,” Sov. J. Quantum. Electron. 14, 364–369 (1984).
[CrossRef]

B. Y. Zel’dovich, T. Y. Yakovleva, “Theory of a two-layer hologram,” Sov. J. Quantum. Electron. 14, 323–328 (1984).
[CrossRef]

Zydik, G. J.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydik, K. T. Short, R. D. Feldman, R. F. Austin, “High sensitivity optical image processing device based on CdZnTe/ZnTe multiple quantum well structures,” Appl. Phys. Lett. 59, 1832–1834 (1991).
[CrossRef]

Appl. Opt. (9)

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Appl. Phys. Lett. (2)

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydik, K. T. Short, R. D. Feldman, R. F. Austin, “High sensitivity optical image processing device based on CdZnTe/ZnTe multiple quantum well structures,” Appl. Phys. Lett. 59, 1832–1834 (1991).
[CrossRef]

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped lithium niobate,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Appl. Sci. Res. (1)

H. Blok, G. Mur, “Diffraction by a double grating,” Appl. Sci. Res. 26, 389–397 (1972).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

IEEE Trans. Antennas Propag. (1)

S.-W. Lee, G. Zarrillo, C.-L. Law, “Simple formulas for transmission through periodic metal grids or plates,” IEEE Trans. Antennas Propag. AP-30, 904–909 (1982).

J. Acoust. Soc. Am. (3)

L. E. Hargrove, “Diffraction of light passing through two adjacent ultrasonic progressive waves of different frequency,” J. Acoust. Soc. Am. 32, 940 (1960).
[CrossRef]

P. Kwiek, “Light diffraction by two spatially separated ultrasonic waves,” J. Acoust. Soc. Am. 86, 2261–2272 (1989).
[CrossRef]

F. Calligaris, P. Ciuti, I. Gabrielli, “Temporal light modulation in thick-screen diffraction by ultrasound beam plus amplitude grating,” J. Acoust. Soc. Am. 61, 959–964 (1977).
[CrossRef]

J. Appl. Phys. (1)

V. A. Komatskii, T. D. Black, “Analysis and application of stationary reference grating method for optical detection of surface acoustic waves,” J. Appl. Phys. 51, 129–136 (1981).
[CrossRef]

J. Opt. Soc. Am. (1)

D. Yevick, L. Thylen, “Analysis of gratings by the beam-propagation method,” J. Opt. Soc. Am. 72, 1081–1089 (1982).
[CrossRef]

J. Opt. Soc. Am. A (5)

Jpn. J. Appl. Phys. (2)

K. Kodate, T. Kamiya, M. Kamiyama, “Double diffraction in the Fresnel region,” Jpn. J. Appl. Phys. 10, 1040–1045 (1971).
[CrossRef]

K. Kodate, T. Kamiya, H. Takenaka, H. Yanai, “Double diffraction of phase gratings in the Fresnel region,” Jpn. J. Appl. Phys. 14, 1323–1334 (1975).
[CrossRef]

Opt. Acta (3)

J. Slaby, T. Szoplik, K. Chalasinska-Macukow, “Cascaded phase Fourier holograms,” Opt. Acta 30, 529–543 (1983).
[CrossRef]

J. Slaby, T. Szoplik, “Resonant modes in a cascaded system of Fourier holograms,” Opt. Acta 33, 301–313 (1986).
[CrossRef]

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, B. Y. Zel’dovich, “Bilayer holograms: theory and experiment,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

Opt. Commun. (2)

K. Chalasinska-Macukow, B. Karczewski, T. Szoplik, “Reconstruction of two stacked Fourier holograms,” Opt. Commun. 27, 311–316 (1978).
[CrossRef]

K. Chalasinska-Macukow, T. Szoplik, “Reconstruction of two stacked Fourier holograms—experiments and results,” Opt. Commun. 33, 245–250 (1980).
[CrossRef]

Opt. Eng. (1)

R. V. Johnson, A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235–249 (1986).
[CrossRef]

Opt. Lett. (5)

Opt. News (1)

R. V. Johnson, A. R. Tanguay, “Stratified volume holographic optical elements,” Opt. News 14 (12), 30–31 (1988).
[CrossRef]

Opt. Spectrosc. (USSR) (4)

V. A. Komotskii, V. F. Nikulin, “Theoretical analysis of diffraction of a Gaussian optical beam by a system of two diffraction gratings,” Opt. Spectrosc. (USSR) 63, 239–242 (1987).

A. F. Bessonov, L. N. Deryugin, V. A. Komotskii, “Phenomena of optical wave diffraction by traveling spatial phase modulation on stationary phase gratings,” Opt. Spectrosc. (USSR) 49, 81–84 (1980).

V. N. Malysh, O. I. Ovcharenko, A. N. Osovitskii, “Light diffraction by a layered structure with periodically modulated interfaces,” Opt. Spectrosc. (USSR) 58, 513–516 (1985).

A. P. Yakimovich, “Multilayer three-dimensional holographic gratings,” Opt. Spectrosc. (USSR) 49, 85–88 (1980).

Sov. J. Quantum. Electron. (3)

N. N. Evtikhiev, D. I. Mirovitskii, N. V. Rostovtseva, O. B. Serov, “Multilayer holographic functional element in an analog-digital converter,” Sov. J. Quantum. Electron. 16, 1180–1184 (1987).
[CrossRef]

B. Y. Zel’dovich, T. Y. Yakovleva, “Theory of a two-layer hologram,” Sov. J. Quantum. Electron. 14, 323–328 (1984).
[CrossRef]

B. Y. Zel’dovich, D. I. Mirovitskii, N. V. Rostovtseva, O. B. Serov, “Characteristics of two-layer phase holograms,” Sov. J. Quantum. Electron. 14, 364–369 (1984).
[CrossRef]

Z. Phys. (1)

L. E. Hargrove, E. A. Hiedemann, R. Mertens, “Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency,” Z. Phys. 167, 326–336 (1962).
[CrossRef]

Other (8)

G. P. Nordin, R. V. Johnson, A. R. Tanguay, “Physical characterization of stratified volume holographic optical elements,” in Annual Meeting, Vol. 11 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 106.

L. Domash, J. Schwartz, A. Nelson, P. Levin, “Active holographic interconnects for interfacing volume storage,” in Image Storage and Retrieval Systems, A. Jamberdino, W. Niblack, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1662, 211–218 (1991).
[CrossRef]

H. J. Caulfield, D. H. McMahon, R. A. Soref, “Stacked hologram apparatus,” U.S. patent3,635,538 (January18, 1972).

H. J. Caulfield, “Stacked page oriented holographic memory,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 203–206 (1988).
[CrossRef]

D. Psaltis, D. Brady, X.-G. Gu, K. Hsu, “Optical implementation of neural computers,” in Optical Processing and Computing, H. Arsenault, ed. (Academic, San Diego, Calif., 1988).

P. Asthana, G. Nordin, S. Piazzolla, A. R. Tanguay, B. K. Jenkins, “Analysis of interchannel crosstalk and throughput efficiency in highly multiplexed fan-out/fan-in holographic interconnections,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 242.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

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Figures (18)

Fig. 1
Fig. 1

Schematic diagram of the SVHOE structure, in which modulation layers composed of a thin holographic recording material are interleaved with optically homogeneous buffer layers.

Fig. 2
Fig. 2

Definition of the readout beam incidence angle θ0 relative to the SVHOE surface normal.

Fig. 3
Fig. 3

Relative buffer-layer thicknesses and total thicknesses of two sets of SVHOE’s. The SVHOE’s in case A all have the same buffer-layer thickness (150 μm), whereas the SVHOE’s in case B have the same total thickness (1500 μm). The angular sensitivities of the first diffraction orders for these sets of SVHOE’s are compared in Figs. 4 and 5. Note that the 11-layer SVHOE has the same buffer-layer thickness and total thickness in both cases.

Fig. 4
Fig. 4

First-order diffraction efficiency as a function of readout beam incidence angle for the 2-, 5-, and 11-layer [(a), (b), and (c), respectively] SVHOE’s of case A.

Fig. 5
Fig. 5

First-order diffraction efficiency as a function of readout beam incidence angle for the two- and five- layer [(a) and (b), respectively] SVHOE’s of case B. The angular response of the case B 11-layer SVHOE is the same as that shown in Fig. 4(c).

Fig. 6
Fig. 6

Propagation of the zeroth and first orders between SVHOE layers, with an incidence angle of θ0. The first order propagates at an angle θ1 with respect to the surface normal of the SVHOE.

Fig. 7
Fig. 7

Summary of SVHOE +1-order angular diffraction behavior.

Fig. 8
Fig. 8

Angular diffraction sensitivity of the +1 (solid curve) and −1 (dashed curve) orders of a 1500-μm-thick volume hologram. The grating recorded in the material has a period of 3.0 μm. The material is assumed to have the same refractive index (3.4) as the SVHOE’s in cases A and B.

Fig. 9
Fig. 9

Angular sensitivity of the +1 order (solid curve) and −1 order (dashed curve) of the 1500-μm-thick 11-layer SVHOE in cases A and B.

Fig. 10
Fig. 10

Schematic diagram showing an SVHOE operating as a 1-D array generator for readout with an uncollimated beam. Two 1-D arrays of beams are generated, one associated with the +1 order and the other associated with the −1 order.

Fig. 11
Fig. 11

Angular sensitivity of the ±1 orders for a five-layer SVHOE for (a) Qb/2π = 4.0 and (b) Qb/2π = 4.5.

Fig. 12
Fig. 12

Positions of SVHOE +1-order and −1-order diffraction peaks (solid and dashed curves, respectively) as a function of the normalized incidence angle α and the normalized buffer-layer thickness Qb/2π. At integer values of Qb/2π, the ±1-order diffraction peaks occur at the same incidence angles.

Fig. 13
Fig. 13

First-order diffraction efficiency as a function of the normalized buffer-layer thickness Qb/2π for a five-layer SVHOE parameterized by the grating strength υ.

Fig. 14
Fig. 14

First-order diffraction efficiency as a function of grating strength for a five-layer SVHOE for different values of the normalized buffer-layer thickness Qb/2π.

Fig. 15
Fig. 15

Propagation angles of the −1 to +2 diffraction orders between two SVHOE modulation layers.

Fig.16
Fig.16

First-order diffraction efficiency as a function of the normalized buffer-layer thickness Qb/2π for different numbers of modulation layers. The total grating strength in each case is chosen as 3.83 rad, which results in zero diffraction efficiency at the center of each notch.

Fig. 17
Fig. 17

First-order diffraction efficiency as a function of readout beam wavelength for a 21-layer SVHOE. Bragg incidence is assumed at each wavelength.

Fig. 18
Fig. 18

First-order diffraction efficiency as a function of grating spatial frequency for a five-layer SVHOE for different values of the total grating strength υ. Bragg incidence is assumed at each grating spatial frequency.

Equations (9)

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Q b = 2 π λ 0 d b / ( n Λ 2 ) ,
υ = 2 π Δ n D mod / λ 0 ,
ϕ 1 = 2 π n d b ( cos θ 1 cos θ 0 ) / λ 0 π n d b ( θ 0 2 θ 1 2 ) / λ 0 ,
θ 0 = λ 0 / ( 2 n Λ ) + l 1 Λ / d b = θ B + l 1 Δ θ p ,
θ 0 = θ B + l 1 Δ θ p ,
p = 2 θ B / Δ θ p ,
p = Q b / ( 2 π ) ,
ϕ m / 2 π = n d b ( θ 0 2 θ m 2 ) / ( 2 λ 0 )
= m ( α m / 2 ) Q b / 2 π ,

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