Abstract

Separable binary-phase array illuminators for fan-out up to 1024 × 1024 and ~65% two-dimensional efficiency are designed by simulated annealing with constraints for maximizing the minimum feature size. A new nonseparable trapezoidal coding technique is introduced and applied to design high-efficiency(~ 75%–80%) array generators for fan-out up to 16 × 16. A rigorous electromagnetic diffraction theory is used to evaluate the range of validity of the scalar designs (both grating period and input angle are considered), to analyze fabrication errors (slanted groove walls and undercutting), and to design binary resonance-domain one-dimensional array generators with 90%–100% efficiency. Trapezoidal gratings for low fan-out (8 × 8), separable gratings for high fan-out (up to 128 × 128), and a 1 × 5 resonance domain (100% efficient) reflection grating are demonstrated experimentally.

© 1992 Optical Society of America

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1992 (1)

1991 (5)

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Rigorous diffraction analysis of Dammann gratings,” Opt. Commun. 81, 337–342 (1991). [There is a typographical error in Figs. (2)–(4) of this paper: the uniformities ΔR without the zeroth order (dotted lines) should be multiplied by a factor of 2.]
[CrossRef]

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

H. Stark, W. C. Catino, J. L. LoCicero, “Design of phase gratings by generalized projections,” J. Opt. Soc. Am. A 8, 566–571 (1991).
[CrossRef]

C.-M. Yuan, A. J. Strojwas, “Modeling optical microscope images of integrated-circuit structures,” J. Opt. Soc. Am. A 8, 778–790 (1991).
[CrossRef]

J. Bruning, “Optical lithography: where will it end? ”Opt. Photon. News 2(5), 23–27 (1991).
[CrossRef]

1990 (16)

J. L. Jewell, Y. H. Lee, A. Scherer, S. L. McCall, N. A. Olsson, J. P. Harbison, L. T. Florez, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29, 210–214 (1990).
[CrossRef]

H. P. Herzig, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Phys. 29, L1307–L1309 (1990).
[CrossRef]

N. Kawatsuki, M. Uetsuki, “Optical phase gratings made from photorefractive polymers,” Appl. Opt. 29, 210–215 (1990).
[CrossRef] [PubMed]

J. Westerholm, J. Turunen, A. Vasara, “Optimization of optical components for optical computer systems,” Phys. Scr. T33, 193–196 (1990).
[CrossRef]

M. R. Taghizadeh, J. Turunen, A. Vasara, “Binary-phase wavefronts reconstructed from internal-reflection metal on glass holograms,” Appl. Phys. Lett. 56, 1195–1197 (1990).
[CrossRef]

J. N. Mait, “Design of binary-phase and multiphase Fourier gratings for array generation,” J. Opt. Soc. Am. A 7, 1514–1528 (1990).
[CrossRef]

M. Heissmeier, U. Krackhardt, N. Streibl, “A Dammann grating with diffraction orders of arbitrary intensity etched into Al2O3,” Opt. Commun. 76, 103–106 (1990).
[CrossRef]

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “Fabrication of space-invariant fan-out components in dichromated gelatin,” Appl. Opt. 29, 1134–1141 (1990).
[CrossRef] [PubMed]

J. T. Sheridan, C. J. R. Sheppard, “An examination of the theories for the calculation of diffraction by square wave gratings: 2. Angular variation,” Optik 85, 57–66 (1990).

J. R. Leger, G. J. Swanson, “Efficient array illuminator using binary-optics phase plates at fractional Talbot planes,” Opt. Lett. 15, 288–290 (1990).
[CrossRef] [PubMed]

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “High efficiency, wide bandwidth optical fan-out elements in dichromated gelatin,” Opt. Lett. 15, 694–696 (1990).
[CrossRef] [PubMed]

J. Turunen, J. Fagerholm, A. Vasara, M. R. Taghizadeh, “Detour-phase kinoform interconnects: the concept and fabrication considerations,” J. Opt. Soc. Am. A 7, 1202–1208 (1990).
[CrossRef]

M. E. Prise, N. C. Craft, R. E. LaMarche, M. M. Downs, S. J. Walker, L. A. D’Asaro, L. M. F. Chirovsky, “Module for optical logic circuits using symmetric self-electrooptic effect devices,” Appl. Opt. 29, 2164–2170 (1990).
[CrossRef] [PubMed]

A. W. Lohmann, J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337–4340 (1990).
[CrossRef] [PubMed]

S. J. Walker, J. Jahns, “Array generation with multilevel phase gratings,” J. Opt. Soc. Am. A 7, 1509–1513 (1990).
[CrossRef]

J. Jahns, S. J. Walker, “Two-dimensional array of diffractive microlenses fabricated by thin film deposition,” Appl. Opt. 29, 931–936 (1990).
[CrossRef] [PubMed]

1989 (14)

J. Jahns, A. Huang, “Planar integration of free-space optical components,” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

A. W. Lohmann, J. Schwider, N. Streibl, J. A. Thomas, “An array illuminator based on the phase contrast method,” Appl. Opt. 27, 2915–2921 (1989).
[CrossRef]

A. W. Lohmann, S. Sinzinger, W. Stork, “Array of Brewster telescopes,” Appl. Opt. 28, 3835–3837 (1989).
[CrossRef] [PubMed]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

J. N. Mait, “Design of Dammann gratings for two-dimensional, nonseparable, noncentrosymmetric responses,” Opt. Lett. 14, 196–198 (1989).
[CrossRef] [PubMed]

M. R. Feldman, C. C. Guest, “Iterative encoding of high-efficiency holograms for generation of spot arrays,” Opt. Lett. 14, 479–481 (1989).
[CrossRef] [PubMed]

J. Turunen, A. Vasara, J. Westerholm, “Stripe-geometry two-dimensional Dammann gratings,” Opt. Commun. 74, 245–252 (1989).
[CrossRef]

A. W. Lohmann, F. Sauer, “Staircase telescope arrays for local beam compression in one dimension,” Appl. Opt. 28, 3830–3834 (1989).
[CrossRef] [PubMed]

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1969 (1989).
[CrossRef]

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

F. B. McCormick, “Generation of large spot arrays from a single laser beam by multiple imaging with binary phase gratings,” Opt. Eng. 28, 299–304 (1989).

X. Lu, Y. Wang, M. Wu, G. Jin, “The fabrication of a 25 × 25 multiple beam splitter,” Opt. Commun. 72, 157–162 (1989).
[CrossRef]

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasara, J. Westerholm, “Optimization and fabrication of gratingbeam-splitters in silicon nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

U. Krackhardt, N. Streibl, “Design of Dammann-gratings for array generation,” Opt. Commun. 74, 31–36 (1989).
[CrossRef]

1988 (6)

J. N. Mait, K.-H. Brenner, “Optical symbolic substitution: system design using phase-only holograms,” Appl. Opt. 27, 1692–1700 (1988).
[CrossRef] [PubMed]

J. Turunen, X. Bien, G. Jin, “Optimization of grating multi-beamsplitters,” Acta Opt. Sinica 8, 946–953 (1988).

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1988).

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimisation and fabrication of grating beamsplitters,” J. Phys. D 21, S102–S105 (1988).
[CrossRef]

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

A. W. Lohmann, “An array illuminator based on the Talbot-effect,” Optik 79, 41–45 (1988).

1987 (1)

1986 (1)

1985 (2)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

L. C. Botten, R. C. McPhedran, “Completeness and modal expansion methods in diffraction theory,” Opt. Acta 32, 1479–1488 (1985).
[CrossRef]

1983 (1)

C.-Y. Han, Y. Ishii, K. Murata, “Reshaping collimated laser beams with Gaussian profile to uniform profiles,” Appl. Opt. 22, 3644–3647 (1983).
[CrossRef] [PubMed]

1982 (2)

U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratio,” Fiber Integrated Opt. 4, 159–167 (1982).
[CrossRef]

R. C. Fairchild, J. R. Fienup, “Computer-originated aspheric holographic optical elements,” Opt. Eng. 21, 133–140 (1982).

1981 (3)

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffractiongrating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1102–1106 (1981).

1980 (1)

1979 (2)

W.-H. Lee, “High efficiency multiple beam gratings,” Appl. Opt. 18, 2152–2158 (1979).
[CrossRef] [PubMed]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[CrossRef]

1978 (1)

1977 (1)

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

1973 (1)

1972 (2)

L. P. Boivin, “Multiple imaging using various types of simple phase gratings,” Appl. Opt. 11, 1782–1792 (1972).
[CrossRef] [PubMed]

D. Maystre, R. Petit, “Diffraction par un reseau lamellaire infinement conducteur,” Opt. Commun. 5, 90–93 (1972).
[CrossRef]

1971 (1)

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

1966 (1)

Adams, J. L.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffractiongrating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Allebach, J. P.

Andrewartha, J. R.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffractiongrating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[CrossRef]

Beckmann, P.

P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam1967), Vol. VI, pp. 53–69.
[CrossRef]

Bergstrom, J.

J. A. Cox, T. Werner, J. Lee, S. Nelson, B. Fritz, J. Bergstrom, “Diffraction efficiency of binary optical elements,” in Computer and Optically Formed Holographic Optics, I. N. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 116–124 (1990).

Berkowitz, H. L.

H. L. Berkowitz, C. F. Cook, J. H. Kwiatkowski, W. M. Goordeau, “Edge-controlled self-consistent proximity effect corrections,” in Semiconductor Processing, D. C. Gupta, ed. (American Society for Testing and Materials, Baltimore, Md., 1984).
[CrossRef]

Bien, X.

J. Turunen, X. Bien, G. Jin, “Optimization of grating multi-beamsplitters,” Acta Opt. Sinica 8, 946–953 (1988).

Boivin, L. P.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1986).

Botten, L. C.

L. C. Botten, R. C. McPhedran, “Completeness and modal expansion methods in diffraction theory,” Opt. Acta 32, 1479–1488 (1985).
[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffractiongrating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1102–1106 (1981).

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Brenner, K.-H.

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1969 (1989).
[CrossRef]

J. N. Mait, K.-H. Brenner, “Optical symbolic substitution: system design using phase-only holograms,” Appl. Opt. 27, 1692–1700 (1988).
[CrossRef] [PubMed]

Bruning, J.

J. Bruning, “Optical lithography: where will it end? ”Opt. Photon. News 2(5), 23–27 (1991).
[CrossRef]

Bryngdahl, O.

O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. XXVIII, pp. 1–86.
[CrossRef]

Buchholz, D. B.

L. M. F. Chirovsky, M. W. Focht, J. M. Freund, G. D. Guth, R. E. Leibenguth, G. J. Przybylek, L. E. Smith, L. A. D’Asaro, A. L. Lentine, R. A. Novotny, D. B. Buchholz, “Large arrays of symmetric self electro-optic effect devices,” in Photonic Switching, Vol. 8 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 56–59.

Buller, G. S.

A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

Burckhardt, C. B.

Campbell, R. J.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Catino, W. C.

Chirovsky, L. M. F.

M. E. Prise, N. C. Craft, R. E. LaMarche, M. M. Downs, S. J. Walker, L. A. D’Asaro, L. M. F. Chirovsky, “Module for optical logic circuits using symmetric self-electrooptic effect devices,” Appl. Opt. 29, 2164–2170 (1990).
[CrossRef] [PubMed]

L. M. F. Chirovsky, M. W. Focht, J. M. Freund, G. D. Guth, R. E. Leibenguth, G. J. Przybylek, L. E. Smith, L. A. D’Asaro, A. L. Lentine, R. A. Novotny, D. B. Buchholz, “Large arrays of symmetric self electro-optic effect devices,” in Photonic Switching, Vol. 8 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 56–59.

Cook, C. F.

H. L. Berkowitz, C. F. Cook, J. H. Kwiatkowski, W. M. Goordeau, “Edge-controlled self-consistent proximity effect corrections,” in Semiconductor Processing, D. C. Gupta, ed. (American Society for Testing and Materials, Baltimore, Md., 1984).
[CrossRef]

Cox, J. A.

J. A. Cox, T. Werner, J. Lee, S. Nelson, B. Fritz, J. Bergstrom, “Diffraction efficiency of binary optical elements,” in Computer and Optically Formed Holographic Optics, I. N. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 116–124 (1990).

Craft, N. C.

Craig, M. S.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1102–1106 (1981).

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffractiongrating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Craig, R. G. A.

A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

D’Asaro, L. A.

M. E. Prise, N. C. Craft, R. E. LaMarche, M. M. Downs, S. J. Walker, L. A. D’Asaro, L. M. F. Chirovsky, “Module for optical logic circuits using symmetric self-electrooptic effect devices,” Appl. Opt. 29, 2164–2170 (1990).
[CrossRef] [PubMed]

L. M. F. Chirovsky, M. W. Focht, J. M. Freund, G. D. Guth, R. E. Leibenguth, G. J. Przybylek, L. E. Smith, L. A. D’Asaro, A. L. Lentine, R. A. Novotny, D. B. Buchholz, “Large arrays of symmetric self electro-optic effect devices,” in Photonic Switching, Vol. 8 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 56–59.

Dammann, H.

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Dempsey, J.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Downs, M. M.

Ekberg, M.

M. Ekberg, M. Larsson, S. Hard, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. (to be published).

Fagerholm, J.

J. Turunen, J. Fagerholm, A. Vasara, M. R. Taghizadeh, “Detour-phase kinoform interconnects: the concept and fabrication considerations,” J. Opt. Soc. Am. A 7, 1202–1208 (1990).
[CrossRef]

J. Fagerholm, J. Turunen, A. Vasara, J. Westerholm, “Computer-generated Fourier-transform holograms of optical computing,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 253–260 (1989).

Fairchild, R. C.

R. C. Fairchild, J. R. Fienup, “Computer-originated aspheric holographic optical elements,” Opt. Eng. 21, 133–140 (1982).

Feldman, M. R.

Fienup, J. R.

R. C. Fairchild, J. R. Fienup, “Computer-originated aspheric holographic optical elements,” Opt. Eng. 21, 133–140 (1982).

Florez, L. T.

J. L. Jewell, Y. H. Lee, A. Scherer, S. L. McCall, N. A. Olsson, J. P. Harbison, L. T. Florez, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29, 210–214 (1990).
[CrossRef]

Focht, M. W.

L. M. F. Chirovsky, M. W. Focht, J. M. Freund, G. D. Guth, R. E. Leibenguth, G. J. Przybylek, L. E. Smith, L. A. D’Asaro, A. L. Lentine, R. A. Novotny, D. B. Buchholz, “Large arrays of symmetric self electro-optic effect devices,” in Photonic Switching, Vol. 8 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 56–59.

Fox, J. R.

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[CrossRef]

Freund, J. M.

L. M. F. Chirovsky, M. W. Focht, J. M. Freund, G. D. Guth, R. E. Leibenguth, G. J. Przybylek, L. E. Smith, L. A. D’Asaro, A. L. Lentine, R. A. Novotny, D. B. Buchholz, “Large arrays of symmetric self electro-optic effect devices,” in Photonic Switching, Vol. 8 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 56–59.

Fritz, B.

J. A. Cox, T. Werner, J. Lee, S. Nelson, B. Fritz, J. Bergstrom, “Diffraction efficiency of binary optical elements,” in Computer and Optically Formed Holographic Optics, I. N. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 116–124 (1990).

Gallagher, N. C.

N. C. Gallagher, S. S. Naqvi, “Diffractive optics:scalar and non-scalar design analysis,” in Holographic Optics: Optically and Computer Generated, I. N. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 32–40 (1989).

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Geng, W.-Z.

L. Wang, W.-Z. Geng, R. Kostuk, “An efficient multiple-image holographic optical element” in Holographic Optics: Optically and Computer Generated, I. N. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 97–107 (1989).

Goodman, J. W.

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

Goordeau, W. M.

H. L. Berkowitz, C. F. Cook, J. H. Kwiatkowski, W. M. Goordeau, “Edge-controlled self-consistent proximity effect corrections,” in Semiconductor Processing, D. C. Gupta, ed. (American Society for Testing and Materials, Baltimore, Md., 1984).
[CrossRef]

Görtler, K.

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Guest, C. C.

Guth, G. D.

L. M. F. Chirovsky, M. W. Focht, J. M. Freund, G. D. Guth, R. E. Leibenguth, G. J. Przybylek, L. E. Smith, L. A. D’Asaro, A. L. Lentine, R. A. Novotny, D. B. Buchholz, “Large arrays of symmetric self electro-optic effect devices,” in Photonic Switching, Vol. 8 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 56–59.

Han, C.-Y.

C.-Y. Han, Y. Ishii, K. Murata, “Reshaping collimated laser beams with Gaussian profile to uniform profiles,” Appl. Opt. 22, 3644–3647 (1983).
[CrossRef] [PubMed]

Harbison, J. P.

J. L. Jewell, Y. H. Lee, A. Scherer, S. L. McCall, N. A. Olsson, J. P. Harbison, L. T. Florez, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29, 210–214 (1990).
[CrossRef]

Hard, S.

M. Ekberg, M. Larsson, S. Hard, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. (to be published).

Heissmeier, M.

M. Heissmeier, U. Krackhardt, N. Streibl, “A Dammann grating with diffraction orders of arbitrary intensity etched into Al2O3,” Opt. Commun. 76, 103–106 (1990).
[CrossRef]

Herzig, H. P.

H. P. Herzig, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Phys. 29, L1307–L1309 (1990).
[CrossRef]

Huang, A.

J. Jahns, A. Huang, “Planar integration of free-space optical components,” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1969 (1989).
[CrossRef]

Ichikawa, H.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

H. Ichikawa, M. R. Taghizadeh, J. Turunen, “Non-interferometric fabrication of computer-generated phase holograms on silver halide photographic emulsion,” Opt. Eng. (to be published).

Ishii, Y.

C.-Y. Han, Y. Ishii, K. Murata, “Reshaping collimated laser beams with Gaussian profile to uniform profiles,” Appl. Opt. 22, 3644–3647 (1983).
[CrossRef] [PubMed]

Jahns, J.

S. J. Walker, J. Jahns, “Array generation with multilevel phase gratings,” J. Opt. Soc. Am. A 7, 1509–1513 (1990).
[CrossRef]

J. Jahns, S. J. Walker, “Two-dimensional array of diffractive microlenses fabricated by thin film deposition,” Appl. Opt. 29, 931–936 (1990).
[CrossRef] [PubMed]

J. Jahns, A. Huang, “Planar integration of free-space optical components,” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1969 (1989).
[CrossRef]

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1988).

Jewell, J.

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1969 (1989).
[CrossRef]

Jewell, J. L.

J. L. Jewell, Y. H. Lee, A. Scherer, S. L. McCall, N. A. Olsson, J. P. Harbison, L. T. Florez, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29, 210–214 (1990).
[CrossRef]

Jin, G.

X. Lu, Y. Wang, M. Wu, G. Jin, “The fabrication of a 25 × 25 multiple beam splitter,” Opt. Commun. 72, 157–162 (1989).
[CrossRef]

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimisation and fabrication of grating beamsplitters,” J. Phys. D 21, S102–S105 (1988).
[CrossRef]

J. Turunen, X. Bien, G. Jin, “Optimization of grating multi-beamsplitters,” Acta Opt. Sinica 8, 946–953 (1988).

Kaspar, F. G.

Kawatsuki, N.

N. Kawatsuki, M. Uetsuki, “Optical phase gratings made from photorefractive polymers,” Appl. Opt. 29, 210–215 (1990).
[CrossRef] [PubMed]

Killat, U.

U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratio,” Fiber Integrated Opt. 4, 159–167 (1982).
[CrossRef]

Klotz, E.

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Knop, K.

Kostuk, R.

L. Wang, W.-Z. Geng, R. Kostuk, “An efficient multiple-image holographic optical element” in Holographic Optics: Optically and Computer Generated, I. N. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 97–107 (1989).

Krackhardt, U.

U. Krackhardt, J. N. Mait, N. Streibl, “Upper bound on the diffraction efficiency of phase-only fan-out elements,” Appl. Opt. 31, 27–37 (1992).
[CrossRef] [PubMed]

M. Heissmeier, U. Krackhardt, N. Streibl, “A Dammann grating with diffraction orders of arbitrary intensity etched into Al2O3,” Opt. Commun. 76, 103–106 (1990).
[CrossRef]

U. Krackhardt, N. Streibl, “Design of Dammann-gratings for array generation,” Opt. Commun. 74, 31–36 (1989).
[CrossRef]

Kwiatkowski, J. H.

H. L. Berkowitz, C. F. Cook, J. H. Kwiatkowski, W. M. Goordeau, “Edge-controlled self-consistent proximity effect corrections,” in Semiconductor Processing, D. C. Gupta, ed. (American Society for Testing and Materials, Baltimore, Md., 1984).
[CrossRef]

LaMarche, R. E.

Lanczos, C.

C. Lanczos, Applied Analysis (Dover, New York, 1988).

Larsson, M.

M. Ekberg, M. Larsson, S. Hard, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. (to be published).

Lebreton, G.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Lee, J.

J. A. Cox, T. Werner, J. Lee, S. Nelson, B. Fritz, J. Bergstrom, “Diffraction efficiency of binary optical elements,” in Computer and Optically Formed Holographic Optics, I. N. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 116–124 (1990).

Lee, W.-H.

Lee, Y. H.

J. L. Jewell, Y. H. Lee, A. Scherer, S. L. McCall, N. A. Olsson, J. P. Harbison, L. T. Florez, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29, 210–214 (1990).
[CrossRef]

Leger, J. R.

Leibenguth, R. E.

L. M. F. Chirovsky, M. W. Focht, J. M. Freund, G. D. Guth, R. E. Leibenguth, G. J. Przybylek, L. E. Smith, L. A. D’Asaro, A. L. Lentine, R. A. Novotny, D. B. Buchholz, “Large arrays of symmetric self electro-optic effect devices,” in Photonic Switching, Vol. 8 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 56–59.

Lentine, A. L.

L. M. F. Chirovsky, M. W. Focht, J. M. Freund, G. D. Guth, R. E. Leibenguth, G. J. Przybylek, L. E. Smith, L. A. D’Asaro, A. L. Lentine, R. A. Novotny, D. B. Buchholz, “Large arrays of symmetric self electro-optic effect devices,” in Photonic Switching, Vol. 8 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 56–59.

LoCicero, J. L.

Lohmann, A. W.

A. W. Lohmann, J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337–4340 (1990).
[CrossRef] [PubMed]

A. W. Lohmann, J. Schwider, N. Streibl, J. A. Thomas, “An array illuminator based on the phase contrast method,” Appl. Opt. 27, 2915–2921 (1989).
[CrossRef]

A. W. Lohmann, S. Sinzinger, W. Stork, “Array of Brewster telescopes,” Appl. Opt. 28, 3835–3837 (1989).
[CrossRef] [PubMed]

A. W. Lohmann, F. Sauer, “Staircase telescope arrays for local beam compression in one dimension,” Appl. Opt. 28, 3830–3834 (1989).
[CrossRef] [PubMed]

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1969 (1989).
[CrossRef]

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A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

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A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

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N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1969 (1989).
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Noponen, E.

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Rigorous diffraction analysis of Dammann gratings,” Opt. Commun. 81, 337–342 (1991). [There is a typographical error in Figs. (2)–(4) of this paper: the uniformities ΔR without the zeroth order (dotted lines) should be multiplied by a factor of 2.]
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J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
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A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, J. Tuovinen, “Rigorous diffraction theory of binary optical interconnects,” in Holographic Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1507, 224–238 (1991).

J. M. Miller, J. Turunen, A. Vasara, M. R. Taghizadeh, E. Noponen, “Rigorous modal theory for perfectly conducting lamellar gratings,” in Proceedings of the Third International Conference on Holographic Systems, Components, and Applications (Institution of Electrical Engineers, London, 1991), pp. 99–102.

Novotny, R. A.

L. M. F. Chirovsky, M. W. Focht, J. M. Freund, G. D. Guth, R. E. Leibenguth, G. J. Przybylek, L. E. Smith, L. A. D’Asaro, A. L. Lentine, R. A. Novotny, D. B. Buchholz, “Large arrays of symmetric self electro-optic effect devices,” in Photonic Switching, Vol. 8 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 56–59.

Olsson, N. A.

J. L. Jewell, Y. H. Lee, A. Scherer, S. L. McCall, N. A. Olsson, J. P. Harbison, L. T. Florez, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29, 210–214 (1990).
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Petit, R.

D. Maystre, R. Petit, “Diffraction par un reseau lamellaire infinement conducteur,” Opt. Commun. 5, 90–93 (1972).
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M. E. Prise, N. C. Craft, R. E. LaMarche, M. M. Downs, S. J. Walker, L. A. D’Asaro, L. M. F. Chirovsky, “Module for optical logic circuits using symmetric self-electrooptic effect devices,” Appl. Opt. 29, 2164–2170 (1990).
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N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1969 (1989).
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J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1988).

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L. M. F. Chirovsky, M. W. Focht, J. M. Freund, G. D. Guth, R. E. Leibenguth, G. J. Przybylek, L. E. Smith, L. A. D’Asaro, A. L. Lentine, R. A. Novotny, D. B. Buchholz, “Large arrays of symmetric self electro-optic effect devices,” in Photonic Switching, Vol. 8 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 56–59.

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U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratio,” Fiber Integrated Opt. 4, 159–167 (1982).
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A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

Redmond, I. R.

A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

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A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

Rhodes, P. W.

Robertson, B.

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “High efficiency, wide bandwidth optical fan-out elements in dichromated gelatin,” Opt. Lett. 15, 694–696 (1990).
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B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “Fabrication of space-invariant fan-out components in dichromated gelatin,” Appl. Opt. 29, 1134–1141 (1990).
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B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “Space-invariant holographic optical interconnects in dichromated gelatin,” in Proceedings of the Second International Conference on Holographic Systems, Components, and Applications (Institution of Electrical Engineers, London, 1989) pp. 200–203.

M. R. Taghizadeh, J. Turunen, B. Robertson, A. Vasara, J. Westerholm, “Passive optical array generators,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 148–151.

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J. L. Jewell, Y. H. Lee, A. Scherer, S. L. McCall, N. A. Olsson, J. P. Harbison, L. T. Florez, “Surface-emitting microlasers for photonic switching and interchip connections,” Opt. Eng. 29, 210–214 (1990).
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J. T. Sheridan, C. J. R. Sheppard, “An examination of the theories for the calculation of diffraction by square wave gratings: 2. Angular variation,” Optik 85, 57–66 (1990).

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Sinzinger, S. O.

A. W. Lohmann, S. O. Sinzinger, “Spatial noise reduction in array illuminators,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 38–40.

Sizer, T.

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1969 (1989).
[CrossRef]

Smith, L. E.

L. M. F. Chirovsky, M. W. Focht, J. M. Freund, G. D. Guth, R. E. Leibenguth, G. J. Przybylek, L. E. Smith, L. A. D’Asaro, A. L. Lentine, R. A. Novotny, D. B. Buchholz, “Large arrays of symmetric self electro-optic effect devices,” in Photonic Switching, Vol. 8 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 56–59.

Smith, S. D.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

Snowdon, J. F.

A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

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Stork, W.

Streibl, N.

U. Krackhardt, J. N. Mait, N. Streibl, “Upper bound on the diffraction efficiency of phase-only fan-out elements,” Appl. Opt. 31, 27–37 (1992).
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M. Heissmeier, U. Krackhardt, N. Streibl, “A Dammann grating with diffraction orders of arbitrary intensity etched into Al2O3,” Opt. Commun. 76, 103–106 (1990).
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N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
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N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1969 (1989).
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U. Krackhardt, N. Streibl, “Design of Dammann-gratings for array generation,” Opt. Commun. 74, 31–36 (1989).
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A. W. Lohmann, J. Schwider, N. Streibl, J. A. Thomas, “An array illuminator based on the phase contrast method,” Appl. Opt. 27, 2915–2921 (1989).
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J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1988).

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C.-M. Yuan, A. J. Strojwas, “Modeling optical microscope images of integrated-circuit structures,” J. Opt. Soc. Am. A 8, 778–790 (1991).
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Swanson, G. J.

Sweeney, D. W.

Taghizadeh, M. R.

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Rigorous diffraction analysis of Dammann gratings,” Opt. Commun. 81, 337–342 (1991). [There is a typographical error in Figs. (2)–(4) of this paper: the uniformities ΔR without the zeroth order (dotted lines) should be multiplied by a factor of 2.]
[CrossRef]

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “Fabrication of space-invariant fan-out components in dichromated gelatin,” Appl. Opt. 29, 1134–1141 (1990).
[CrossRef] [PubMed]

M. R. Taghizadeh, J. Turunen, A. Vasara, “Binary-phase wavefronts reconstructed from internal-reflection metal on glass holograms,” Appl. Phys. Lett. 56, 1195–1197 (1990).
[CrossRef]

J. Turunen, J. Fagerholm, A. Vasara, M. R. Taghizadeh, “Detour-phase kinoform interconnects: the concept and fabrication considerations,” J. Opt. Soc. Am. A 7, 1202–1208 (1990).
[CrossRef]

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “High efficiency, wide bandwidth optical fan-out elements in dichromated gelatin,” Opt. Lett. 15, 694–696 (1990).
[CrossRef] [PubMed]

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasara, J. Westerholm, “Optimization and fabrication of gratingbeam-splitters in silicon nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “Space-invariant holographic optical interconnects in dichromated gelatin,” in Proceedings of the Second International Conference on Holographic Systems, Components, and Applications (Institution of Electrical Engineers, London, 1989) pp. 200–203.

J. M. Miller, J. Turunen, A. Vasara, M. R. Taghizadeh, E. Noponen, “Rigorous modal theory for perfectly conducting lamellar gratings,” in Proceedings of the Third International Conference on Holographic Systems, Components, and Applications (Institution of Electrical Engineers, London, 1991), pp. 99–102.

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, J. Tuovinen, “Rigorous diffraction theory of binary optical interconnects,” in Holographic Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1507, 224–238 (1991).

A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

H. Ichikawa, M. R. Taghizadeh, J. Turunen, “Non-interferometric fabrication of computer-generated phase holograms on silver halide photographic emulsion,” Opt. Eng. (to be published).

M. R. Taghizadeh, J. Turunen, B. Robertson, A. Vasara, J. Westerholm, “Passive optical array generators,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 148–151.

M. Ekberg, M. Larsson, S. Hard, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. (to be published).

Thomas, J. A.

Tuovinen, J.

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, J. Tuovinen, “Rigorous diffraction theory of binary optical interconnects,” in Holographic Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1507, 224–238 (1991).

Turunen, J.

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Rigorous diffraction analysis of Dammann gratings,” Opt. Commun. 81, 337–342 (1991). [There is a typographical error in Figs. (2)–(4) of this paper: the uniformities ΔR without the zeroth order (dotted lines) should be multiplied by a factor of 2.]
[CrossRef]

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

M. R. Taghizadeh, J. Turunen, A. Vasara, “Binary-phase wavefronts reconstructed from internal-reflection metal on glass holograms,” Appl. Phys. Lett. 56, 1195–1197 (1990).
[CrossRef]

J. Westerholm, J. Turunen, A. Vasara, “Optimization of optical components for optical computer systems,” Phys. Scr. T33, 193–196 (1990).
[CrossRef]

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “Fabrication of space-invariant fan-out components in dichromated gelatin,” Appl. Opt. 29, 1134–1141 (1990).
[CrossRef] [PubMed]

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “High efficiency, wide bandwidth optical fan-out elements in dichromated gelatin,” Opt. Lett. 15, 694–696 (1990).
[CrossRef] [PubMed]

J. Turunen, J. Fagerholm, A. Vasara, M. R. Taghizadeh, “Detour-phase kinoform interconnects: the concept and fabrication considerations,” J. Opt. Soc. Am. A 7, 1202–1208 (1990).
[CrossRef]

J. Turunen, A. Vasara, J. Westerholm, “Stripe-geometry two-dimensional Dammann gratings,” Opt. Commun. 74, 245–252 (1989).
[CrossRef]

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasara, J. Westerholm, “Optimization and fabrication of gratingbeam-splitters in silicon nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimisation and fabrication of grating beamsplitters,” J. Phys. D 21, S102–S105 (1988).
[CrossRef]

J. Turunen, X. Bien, G. Jin, “Optimization of grating multi-beamsplitters,” Acta Opt. Sinica 8, 946–953 (1988).

J. Fagerholm, J. Turunen, A. Vasara, J. Westerholm, “Computer-generated Fourier-transform holograms of optical computing,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 253–260 (1989).

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “Space-invariant holographic optical interconnects in dichromated gelatin,” in Proceedings of the Second International Conference on Holographic Systems, Components, and Applications (Institution of Electrical Engineers, London, 1989) pp. 200–203.

J. M. Miller, J. Turunen, A. Vasara, M. R. Taghizadeh, E. Noponen, “Rigorous modal theory for perfectly conducting lamellar gratings,” in Proceedings of the Third International Conference on Holographic Systems, Components, and Applications (Institution of Electrical Engineers, London, 1991), pp. 99–102.

J. Turunen, A. Vasara, J. Westerholm, “Generalized two-dimensional binary phase gratings,” in Annual Meeting 1988, Vol. 11 of OSA 1988 Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 126.

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, J. Tuovinen, “Rigorous diffraction theory of binary optical interconnects,” in Holographic Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1507, 224–238 (1991).

M. R. Taghizadeh, J. Turunen, B. Robertson, A. Vasara, J. Westerholm, “Passive optical array generators,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 148–151.

M. Ekberg, M. Larsson, S. Hard, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. (to be published).

H. Ichikawa, M. R. Taghizadeh, J. Turunen, “Non-interferometric fabrication of computer-generated phase holograms on silver halide photographic emulsion,” Opt. Eng. (to be published).

Uetsuki, M.

N. Kawatsuki, M. Uetsuki, “Optical phase gratings made from photorefractive polymers,” Appl. Opt. 29, 210–215 (1990).
[CrossRef] [PubMed]

Vasara, A.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Rigorous diffraction analysis of Dammann gratings,” Opt. Commun. 81, 337–342 (1991). [There is a typographical error in Figs. (2)–(4) of this paper: the uniformities ΔR without the zeroth order (dotted lines) should be multiplied by a factor of 2.]
[CrossRef]

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “Fabrication of space-invariant fan-out components in dichromated gelatin,” Appl. Opt. 29, 1134–1141 (1990).
[CrossRef] [PubMed]

J. Westerholm, J. Turunen, A. Vasara, “Optimization of optical components for optical computer systems,” Phys. Scr. T33, 193–196 (1990).
[CrossRef]

M. R. Taghizadeh, J. Turunen, A. Vasara, “Binary-phase wavefronts reconstructed from internal-reflection metal on glass holograms,” Appl. Phys. Lett. 56, 1195–1197 (1990).
[CrossRef]

J. Turunen, J. Fagerholm, A. Vasara, M. R. Taghizadeh, “Detour-phase kinoform interconnects: the concept and fabrication considerations,” J. Opt. Soc. Am. A 7, 1202–1208 (1990).
[CrossRef]

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “High efficiency, wide bandwidth optical fan-out elements in dichromated gelatin,” Opt. Lett. 15, 694–696 (1990).
[CrossRef] [PubMed]

J. Turunen, A. Vasara, J. Westerholm, “Stripe-geometry two-dimensional Dammann gratings,” Opt. Commun. 74, 245–252 (1989).
[CrossRef]

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasara, J. Westerholm, “Optimization and fabrication of gratingbeam-splitters in silicon nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimisation and fabrication of grating beamsplitters,” J. Phys. D 21, S102–S105 (1988).
[CrossRef]

J. Fagerholm, J. Turunen, A. Vasara, J. Westerholm, “Computer-generated Fourier-transform holograms of optical computing,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 253–260 (1989).

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “Space-invariant holographic optical interconnects in dichromated gelatin,” in Proceedings of the Second International Conference on Holographic Systems, Components, and Applications (Institution of Electrical Engineers, London, 1989) pp. 200–203.

J. M. Miller, J. Turunen, A. Vasara, M. R. Taghizadeh, E. Noponen, “Rigorous modal theory for perfectly conducting lamellar gratings,” in Proceedings of the Third International Conference on Holographic Systems, Components, and Applications (Institution of Electrical Engineers, London, 1991), pp. 99–102.

J. Turunen, A. Vasara, J. Westerholm, “Generalized two-dimensional binary phase gratings,” in Annual Meeting 1988, Vol. 11 of OSA 1988 Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 126.

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, J. Tuovinen, “Rigorous diffraction theory of binary optical interconnects,” in Holographic Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1507, 224–238 (1991).

M. R. Taghizadeh, J. Turunen, B. Robertson, A. Vasara, J. Westerholm, “Passive optical array generators,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 148–151.

M. Ekberg, M. Larsson, S. Hard, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. (to be published).

Veldkamp, W. B.

Wakelin, S.

A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

Walker, A. C.

A. C. Walker, M. R. Taghizadeh, J. G. H. Mathew, I. Redmond, R. J. Campbell, S. D. Smith, J. Dempsey, G. Lebreton, “Optically bistable thin-film interference devices and holographic techniques for experiments in digital optics,” Opt. Eng. 27, 38–44 (1988).

A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

Walker, S. J.

Walker, S. L.

R. L. Morrison, S. L. Walker, “Progress in diffractive phase gratings used for spot array generation,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 144–147.

R. L. Morrison, S. L. Walker, “Binary phase gratings generating even numbered spot arrays,” in Annual Meeting 1989, Vol. 18 of OSA 1989 Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 111.

Wang, L.

L. Wang, W.-Z. Geng, R. Kostuk, “An efficient multiple-image holographic optical element” in Holographic Optics: Optically and Computer Generated, I. N. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 97–107 (1989).

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X. Lu, Y. Wang, M. Wu, G. Jin, “The fabrication of a 25 × 25 multiple beam splitter,” Opt. Commun. 72, 157–162 (1989).
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J. A. Cox, T. Werner, J. Lee, S. Nelson, B. Fritz, J. Bergstrom, “Diffraction efficiency of binary optical elements,” in Computer and Optically Formed Holographic Optics, I. N. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 116–124 (1990).

Westerholm, J.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

J. Westerholm, J. Turunen, A. Vasara, “Optimization of optical components for optical computer systems,” Phys. Scr. T33, 193–196 (1990).
[CrossRef]

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasara, J. Westerholm, “Optimization and fabrication of gratingbeam-splitters in silicon nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

J. Turunen, A. Vasara, J. Westerholm, “Stripe-geometry two-dimensional Dammann gratings,” Opt. Commun. 74, 245–252 (1989).
[CrossRef]

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimisation and fabrication of grating beamsplitters,” J. Phys. D 21, S102–S105 (1988).
[CrossRef]

J. Fagerholm, J. Turunen, A. Vasara, J. Westerholm, “Computer-generated Fourier-transform holograms of optical computing,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 253–260 (1989).

J. Turunen, A. Vasara, J. Westerholm, “Generalized two-dimensional binary phase gratings,” in Annual Meeting 1988, Vol. 11 of OSA 1988 Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 126.

M. R. Taghizadeh, J. Turunen, B. Robertson, A. Vasara, J. Westerholm, “Passive optical array generators,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 148–151.

M. Ekberg, M. Larsson, S. Hard, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel grating array illuminators manufactured by electron-beam lithography,” Opt. Commun. (to be published).

Wherrett, B. S.

A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

Wilson, I. J.

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
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Wilson, J. I. B.

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasara, J. Westerholm, “Optimization and fabrication of gratingbeam-splitters in silicon nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

Wilson, R. A.

A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

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M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1986).

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X. Lu, Y. Wang, M. Wu, G. Jin, “The fabrication of a 25 × 25 multiple beam splitter,” Opt. Commun. 72, 157–162 (1989).
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O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. XXVIII, pp. 1–86.
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C.-M. Yuan, A. J. Strojwas, “Modeling optical microscope images of integrated-circuit structures,” J. Opt. Soc. Am. A 8, 778–790 (1991).
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Acta Opt. Sinica (1)

J. Turunen, X. Bien, G. Jin, “Optimization of grating multi-beamsplitters,” Acta Opt. Sinica 8, 946–953 (1988).

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J. N. Mait, K.-H. Brenner, “Optical symbolic substitution: system design using phase-only holograms,” Appl. Opt. 27, 1692–1700 (1988).
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N. Kawatsuki, M. Uetsuki, “Optical phase gratings made from photorefractive polymers,” Appl. Opt. 29, 210–215 (1990).
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M. R. Taghizadeh, J. Turunen, A. Vasara, “Binary-phase wavefronts reconstructed from internal-reflection metal on glass holograms,” Appl. Phys. Lett. 56, 1195–1197 (1990).
[CrossRef]

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasara, J. Westerholm, “Optimization and fabrication of gratingbeam-splitters in silicon nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
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J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimisation and fabrication of grating beamsplitters,” J. Phys. D 21, S102–S105 (1988).
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J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
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J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

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J. Fagerholm, J. Turunen, A. Vasara, J. Westerholm, “Computer-generated Fourier-transform holograms of optical computing,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 253–260 (1989).

B. Robertson, M. R. Taghizadeh, J. Turunen, A. Vasara, “Space-invariant holographic optical interconnects in dichromated gelatin,” in Proceedings of the Second International Conference on Holographic Systems, Components, and Applications (Institution of Electrical Engineers, London, 1989) pp. 200–203.

L. Wang, W.-Z. Geng, R. Kostuk, “An efficient multiple-image holographic optical element” in Holographic Optics: Optically and Computer Generated, I. N. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 97–107 (1989).

A. C. Walker, R. G. A. Craig, D. J. McKnight, I. R. Redmond, J. F. Snowdon, G. S. Buller, E. J. Restall, R. A. Wilson, S. Wakelin, N. McArdle, P. Meredith, J. M. Miller, G. MacKinnon, M. R. Taghizadeh, S. D. Smith, B. S. Wherrett, “Design and construction of a programmable optical 16 × 16 array processor,” in Optical Computing, Vol. 6 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 199–202.

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[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Grating geometry considered in the amplitude transmission theory of binary array illuminators.

Fig. 2
Fig. 2

Coding schemes for 2D binary grating array generators: (a) arbitrary shapes, (b) trapezoidal shapes confined in stripes, (c) separable Dammann grating, (d) pixellated grating.

Fig. 3
Fig. 3

Aperture geometry of the EOM grating; all even diffracted orders are suppressed.

Fig. 4
Fig. 4

The set consisting of N signal orders (solid circles) inside the image window S (orders bounded by the dashed line).

Fig. 5
Fig. 5

Structure of one period of a trapezoidal 16 × 16 fan-out grating with R = 80 stripes.

Fig. 6
Fig. 6

Diffraction of a plane wave (wavelength λ in vacuum) by a multilevel lamellar surface-relief grating of period d.

Fig. 7
Fig. 7

Comparison of the perfect conductor (PC) method of Appendix B with the BKK method of Appendix A for a 7-beam gold Dammann grating with d = 100λ. Rayleigh order intensities Pm, m = −3, …, 3, are evaluated for four different wavelengths λ.

Fig. 8
Fig. 8

Redesign of relief depth H as a function of grating period d for a 5-beam Dammann grating with structure (a1, b1) = (0, 0.2647d) and (a2, b2) = (0.6145d, 0.6529d). For polarity A (solid curve) the central order is too weak, while for polarity B (dashed curve) it was too bright, and a redesign of H (dashed-dotted curve, right-hand scale) yields a better uniformity (dotted curve).

Fig. 9
Fig. 9

Shadowing effects at an oblique angle of incidence: (a) 7-beam Dammann grating with the relief depth readjusted, (b) 8-beam EOM design.

Fig. 10
Fig. 10

Effects of slanted or undercut groove side walls on the reconstruction error of 7- and 8-beam gratings. The angle α denotes the tilt angle measured from the surface normal. (a) Gratings outside the local resonance domain d = 100λ. (b) Dielectric resonance domain gratings of Table III.

Fig. 11
Fig. 11

Spot array produced by a separable 64 × 64 Dammann grating.

Fig. 12
Fig. 12

Photograph of the mask for a trapezoidal 8 × 8 design covering ~3 × 4 periods.

Fig. 13
Fig. 13

Array generated by the 8 × 8 trapezoidal phase grating fabricated by reactive ion etching on fused silica.

Fig. 14
Fig. 14

(a) SEM photograph of the 1 × 5 resonance-domain reflection grating. (b) Slanted groove boundary produced by reactive ion etching.

Tables (6)

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Table I Fan-Out N , Efficiency PE, Uniformity ΔR, and the Number of Transition Point Pairs J for 1D Dammann Gratings with ϕ = π

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Table II Fan-Out N , Efficiency PE, Uniformity ΔR, Phase Delay ϕ, Total Number of Trapezoids ∑J, and the Number of Stripes R for Trapezoidal Stripe-Geometry Binary Gratingsa

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Table III Optimized Dielectric Resonance Domain Fan-Out Gratings: Fan-Out N , Efficiency PE, Uniformity ΔR, Period d, Relief Depth H, Angle of Incidence θ, Minimum Feature Size Δmin, and the Number of Grooves Ja

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Table IV Optimized Perfectly Conducting Resonance-Domain Fan-Out Gratings: Fan-Out N , Uniformity ΔR, Period d, Relief Depth H, Angle of Incidence θ, Minimum Feature Size Δmin, and Number of Grooves Ja

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Table V Patterning Error Analysis of 1D Dammann Gratings With Different Models

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Table VI Measured Array Uniformities ΔR of Dammann Gratings With Period d, Fabricated for Wavelength λa

Equations (43)

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t ( x , y ) = exp [ i 2 π λ - H 0 n ( x , y , z ) d z ] .
U ( x , y , 0 ) = t ( x , y ) U inc ( x , y , - H )
t ( x , y ) = m = - n = - T m n exp [ i 2 π ( m x / d x + n y / d y ) ] ,
T m n = 1 d x d y 0 d x 0 d y t ( x , y ) exp [ - i 2 π ( m x / d x + n y / d y ) ] d x d y .
V ( ξ , η ) m = - n = - T m n U ˜ inc [ ( ξ - m f λ / d x ) / f λ , ( η - n f λ / d y ) / f λ ] ,
P m n = T m n 2 ,
t ( x , y ) = { t 1 = τ 1 exp ( i ϕ ) when A ˜ ( x , y ) = 1 t 2 = τ 2 when A ˜ ( x , y ) = 0 .
T m n = ( t 1 - t 2 ) F m n + t 2 δ m 0 δ n 0 ,
F m n = 0 1 0 1 A ( x , y ) exp [ - i 2 π ( m x + n y ) ] d x d y ,
F m n = i 2 π m R r = 1 R j = 1 J r ( exp { - i π [ m ( b j r + d j r ) + n ( 2 r - ) / R ] } sinc [ m ( d j r - b j r ) + n / R ] - exp { - i π [ m ( a j r + c j r ) + n ( 2 r - 1 ) / R ] } + sinc [ m ( c j r - a j r ) + n / R ] ) ,
F 0 n = i 2 π n r = 1 R j = 1 J r exp ( - i 2 π n r / R ) { d j r + c j r - b j r - a j r ) [ r - ( r - 1 ) exp ( i 2 π n / R ) ] + [ r ( b j r - a j r ) + ( 1 - r ) ( d j r - c j r ) - i R 2 π n ( d j r + c j r - b j r - a j r ) ] [ 1 - exp ( i 2 π n / R ] } ,
F 00 = 1 2 R r = 1 R j = 1 J r ( b j r + d j r - a j r - c j r ) ,
{ A ( x , y ) = 1 x ( a j , b j ) y ( a ˜ r , b ˜ r ) or x ( b j , a j + 1 ) y ( b ˜ r , a ˜ r + 1 ) , A ( x , y ) = 0 otherwise
F m n = F m F ˜ n + ( δ m 0 - F m ) ( δ n 0 - F ˜ n ) ,
F m = j = 1 J ( b j - a j ) sinc [ m ( b j - a j ) ] exp [ - i π m ( a j + b j ) ] .
T m n = [ τ 1 exp ( i ϕ ) - τ 2 ] ( 2 F m F ˜ n - F m δ n 0 - F ˜ n δ m 0 ) + τ 1 exp ( i ϕ ) δ m 0 δ n 0 .
A ( x , y ) = A ( x + 1 / 2 ) , y + 1 / 2 ) = 1 - A ( x , y + 1 / 2 ) = 1 - A ( x + 1 / 2 , y ) .
F m n = 4 0 1 / 2 0 1 / 2 A ( x , y ) exp [ - i 2 π ( m x + n y ) ] d x d y + 2 π 2 m n
P m n = { P E / N when ( m , n ) M 0 when ( m , n ) S \ M ,
P E = ( m , n ) M P m n
Δ R = max ( m , n ) M 1 - N P m n / P E
r off = max ( m , n ) S \ M ( N P mn / P E )
Mf = ( m , n ) M ( P m n - P ^ E / N ) 2 ,
Δ min = min j = 1 , , J ( b j - a j , a j + 1 - b j ) ,
r = 1 + N P E [ sin 2 ( ϕ / 2 ) sin 2 ( φ / 2 ) - 1 ] ,
r = N P E cot 2 ( φ 2 ) ,
Δ R = C 1 α C 2 N C 3 ,
Δ R ~ 300 α N % .
Δ R = 400 Δ x / λ %
U inc ( x , z < - H ) = exp { i [ 2 π ξ x + r 0 ( z + H ) ] } .
2 U ( x , z ) x 2 + 2 U ( x , z ) z 2 + k 2 ( x , z ) U ( x , z ) = 0 ,
x [ 1 ( x , z ) U ( x , z ) x ] + z [ 1 ( x , z ) U ( x , z ) z ] + k 2 U ( x , z ) = 0 ,
U R ( x , z < - H ) = m = - R m exp ( i 2 π m x / d ) exp { i [ 2 π ξ x - r m ( z + h ) ] } ,
U T ( x , z > 0 ) = m = - T m exp ( i 2 π m x / d ) exp [ i ( 2 π ξ x + t m z ) ] ,
r m = { n 0 k [ 1 - ( λ / n 0 ) 2 ξ m 2 ] 1 / 2 ( λ / n 0 ) ξ m 1 i n 0 k [ ( λ / n 0 ) 2 ξ m 2 - 1 ] 1 / 2 ( λ / n 0 ) ξ m > 1 ,
t m = { n 3 k [ 1 - ( λ / n 3 ) 2 ξ m 2 ] 1 / 2 ( λ / n 3 ) ξ m 1 i n 3 k [ ( λ / n 3 ) 2 ξ m 2 - 1 ( λ / n 3 ) ξ m > 1 ,
P R , m = Re ( r m ) r 0 R m 2 ,             P T , m = C Re ( t m ) r 0 T m 2 ,
U q ( x , z ) = l = - p = - B l p , q exp ( i 2 π ξ l x ) { A p , q exp [ i α p , q ( z - h q - 1 ) ] + A p , q exp [ - i α p , q ( z - h q ) ] } .
l = - D n l , q B l , q = α q 2 B n , q ,             n = - , , ,
D n l , q = k 2 n - l , q - 4 π 2 δ n l ξ l 2 ,
D n l , q = k 2 n - l , q - 4 π 2 r = - n - r , q η r - l , q ξ r ξ l ,
U I I , j ( x , z ) = { l = 1 A l j sin ( μ l j z ) X l j ( x ) TE polarization l = 0 A l j cos ( μ l j z ) X l j ( x ) TM polarization ,
X l j = { ( 2 / c j ) 1 / 2 sin [ l π ( x - a j ) / c j ] TE polarization ( 2 / c j ) 1 / 2 cos [ l π ( x - a j ) / c j ] TM polarization , l 0 ,

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