Abstract

Using rigorous electromagnetic diffraction theory, we evaluate the potential performance and the limitations of coding diffractive optical elements in the form of a pulse-frequency-modulated carrier grating. This coding scheme employs the first diffraction order of an ultrahigh-frequency binary carrier grating, with a period below 1.5 wavelengths. We establish that the pulse-frequency-modulation structure can be designed with the standard synthesis techniques based on paraxial scalar diffraction theory. However, we had to optimize the groove depth, the aspect ratio, and the carrier period with rigorous electromagnetic theory to achieve close to 100% efficiency and the desired polarization properties. Our method is compared with another recent coding scheme that utilizes the zeroth order of a subwavelength-period pulse-width-modulated binary carrier grating.

© 1994 Optical Society of America

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    [CrossRef]
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  15. J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
    [CrossRef]
  16. E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
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  29. J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel-grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1992).
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    [CrossRef]
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1993 (5)

P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultrahigh resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
[CrossRef]

H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
[CrossRef]

J. Turunen, P. Blair, J. M. Miller, M. R. Taghizadeh, E. Noponen, “Bragg holograms with binary synthetic surface-relief profile,” Opt. Lett. 18, 1022–1024 (1993).
[CrossRef] [PubMed]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
[CrossRef]

1992 (8)

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3220–3236 (1992).
[CrossRef]

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel graing array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

P. Ehbets, H. P. Herzig, D. Prongué, M. T. Gale, “High-efficiency continuous surface-relief gratings for two-dimensional array generation,” Opt. Lett. 17, 908–910 (1992).
[CrossRef] [PubMed]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel-grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1992).
[CrossRef]

E. Noponen, J. Turunen, A. Vasara, “Parametric optimization of multilevel diffractive optical elements by electromagnetic theory,” Appl. Opt. 32, 5010–5012 (1992).

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[CrossRef]

M. W. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 31, 4453–4458 (1992).
[CrossRef] [PubMed]

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1992).

1991 (3)

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

W. Stork, N. Steibl, H. Haidner, P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991).
[CrossRef] [PubMed]

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Rigorous diffraction analysis of Dammann gratings,” Opt. Commun. 81, 337–342 (1991).
[CrossRef]

1990 (1)

1989 (3)

T. Shiono, M. Kitagawa, K. Setsune, T. Mitsuyu, “Reflection micro-Fresnel lenses and their use in an integrated focus sensor,” Appl. Opt. 28, 3434–3442 (1989).
[CrossRef] [PubMed]

N. C. Gallagher, D. W. Sweeney, “Computer-generated microwave kinoforms,” Opt. Eng. 28, 599–604 (1989).
[CrossRef]

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

1986 (1)

1979 (1)

1978 (1)

1977 (2)

1975 (1)

1972 (1)

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

1967 (1)

1965 (1)

M. R. Schroeder, “Binaural dissimilarity and optimum ceilings for concert halls: more lateral sound diffusion,” J. Acoust. Soc. Am. 65, 958–963 (1965).
[CrossRef]

Baird, V. E.

Blair, P.

Bryngdahl, O.

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

Cheo, L. S.

Chou, S. Y.

P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultrahigh resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
[CrossRef]

Ebbeson, G. R.

Ehbets, P.

Ekberg, M.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel graing array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

Farn, M. W.

Fischer, P. B.

P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultrahigh resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
[CrossRef]

Gale, M. T.

Gallagher, N. C.

N. C. Gallagher, D. W. Sweeney, “Computer-generated microwave kinoforms,” Opt. Eng. 28, 599–604 (1989).
[CrossRef]

Gaylord, T. K.

Haidner, H.

H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
[CrossRef]

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1992).

W. Stork, N. Steibl, H. Haidner, P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991).
[CrossRef] [PubMed]

Hård, S.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel graing array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

Heath, J. W.

Herzig, H. P.

Hessel, A.

Ichikawa, H.

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3220–3236 (1992).
[CrossRef]

Jaakkola, T.

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3220–3236 (1992).
[CrossRef]

Jahns, J.

Jull, E. V.

Kipfer, P.

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1992).

W. Stork, N. Steibl, H. Haidner, P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991).
[CrossRef] [PubMed]

Kitagawa, M.

Knop, K.

Kuisma, S.

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3220–3236 (1992).
[CrossRef]

Larsson, M.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel graing array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

Loewen, E. G.

Lohmann, A. W.

Maystre, D.

Miller, J. M.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

J. Turunen, P. Blair, J. M. Miller, M. R. Taghizadeh, E. Noponen, “Bragg holograms with binary synthetic surface-relief profile,” Opt. Lett. 18, 1022–1024 (1993).
[CrossRef] [PubMed]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[CrossRef]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3220–3236 (1992).
[CrossRef]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel-grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1992).
[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).
[CrossRef]

J. Turunen, E. Noponen, A. Vasara, J. M. Miller, M. R. Taghizadeh, “Electromagnetic theory of diffractive optics,” in Workshop on Digital Holography 19– 21 May 1992, Prague, Czechoslovakia, A. A. Pesl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1718, 90–99 (1992).

Mitsuyu, T.

Moharam, M. G.

Nevière, M.

Noponen, E.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

J. Turunen, P. Blair, J. M. Miller, M. R. Taghizadeh, E. Noponen, “Bragg holograms with binary synthetic surface-relief profile,” Opt. Lett. 18, 1022–1024 (1993).
[CrossRef] [PubMed]

E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
[CrossRef]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3220–3236 (1992).
[CrossRef]

E. Noponen, J. Turunen, A. Vasara, “Parametric optimization of multilevel diffractive optical elements by electromagnetic theory,” Appl. Opt. 32, 5010–5012 (1992).

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[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).
[CrossRef]

J. Turunen, E. Noponen, A. Vasara, J. M. Miller, M. R. Taghizadeh, “Electromagnetic theory of diffractive optics,” in Workshop on Digital Holography 19– 21 May 1992, Prague, Czechoslovakia, A. A. Pesl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1718, 90–99 (1992).

Paris, D. P.

Petit, R.

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

Prongué, D.

Ross, N.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel-grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1992).
[CrossRef]

Schmoys, J.

Schroeder, M. R.

M. R. Schroeder, “Binaural dissimilarity and optimum ceilings for concert halls: more lateral sound diffusion,” J. Acoust. Soc. Am. 65, 958–963 (1965).
[CrossRef]

Schwider, J.

H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
[CrossRef]

Setsune, K.

Sheridan, J. T.

H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
[CrossRef]

Shiono, T.

Steibl, N.

Stork, W.

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1992).

W. Stork, N. Steibl, H. Haidner, P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991).
[CrossRef] [PubMed]

Streibl, N.

H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
[CrossRef]

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1992).

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

Sweeney, D. W.

N. C. Gallagher, D. W. Sweeney, “Computer-generated microwave kinoforms,” Opt. Eng. 28, 599–604 (1989).
[CrossRef]

Taghizadeh, M. R.

J. Turunen, P. Blair, J. M. Miller, M. R. Taghizadeh, E. Noponen, “Bragg holograms with binary synthetic surface-relief profile,” Opt. Lett. 18, 1022–1024 (1993).
[CrossRef] [PubMed]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[CrossRef]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3220–3236 (1992).
[CrossRef]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel-grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1992).
[CrossRef]

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel graing array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[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).
[CrossRef]

J. Turunen, E. Noponen, A. Vasara, J. M. Miller, M. R. Taghizadeh, “Electromagnetic theory of diffractive optics,” in Workshop on Digital Holography 19– 21 May 1992, Prague, Czechoslovakia, A. A. Pesl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1718, 90–99 (1992).

Tseng, D. Y.

Turunen, J.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

J. Turunen, P. Blair, J. M. Miller, M. R. Taghizadeh, E. Noponen, “Bragg holograms with binary synthetic surface-relief profile,” Opt. Lett. 18, 1022–1024 (1993).
[CrossRef] [PubMed]

E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
[CrossRef]

E. Noponen, J. Turunen, A. Vasara, “Parametric optimization of multilevel diffractive optical elements by electromagnetic theory,” Appl. Opt. 32, 5010–5012 (1992).

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel graing array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel-grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1992).
[CrossRef]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3220–3236 (1992).
[CrossRef]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[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).
[CrossRef]

J. Turunen, E. Noponen, A. Vasara, J. M. Miller, M. R. Taghizadeh, “Electromagnetic theory of diffractive optics,” in Workshop on Digital Holography 19– 21 May 1992, Prague, Czechoslovakia, A. A. Pesl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1718, 90–99 (1992).

Vasara, A.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
[CrossRef]

E. Noponen, J. Turunen, A. Vasara, “Parametric optimization of multilevel diffractive optical elements by electromagnetic theory,” Appl. Opt. 32, 5010–5012 (1992).

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel graing array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain,” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[CrossRef]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3220–3236 (1992).
[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).
[CrossRef]

J. Turunen, E. Noponen, A. Vasara, J. M. Miller, M. R. Taghizadeh, “Electromagnetic theory of diffractive optics,” in Workshop on Digital Holography 19– 21 May 1992, Prague, Czechoslovakia, A. A. Pesl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1718, 90–99 (1992).

Walker, S. J.

Westerholm, J.

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel graing array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3220–3236 (1992).
[CrossRef]

Wyrowski, F.

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

F. Wyrowski, “Characteristics of diffractive optical elements/ digital holograms,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 2–10 (1991).
[CrossRef]

Appl. Opt. (8)

Appl. Phys. Lett. (1)

P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultrahigh resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
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[CrossRef]

J. Mod. Opt. (2)

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

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (3)

Opt. Commun. (4)

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Rigorous diffraction analysis of Dammann gratings,” Opt. Commun. 81, 337–342 (1991).
[CrossRef]

H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
[CrossRef]

M. Ekberg, M. Larsson, S. Hård, J. Turunen, M. R. Taghizadeh, J. Westerholm, A. Vasara, “Multilevel graing array illuminators manufactured by electron-beam lithography,” Opt. Commun. 88, 37–41 (1992).
[CrossRef]

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[CrossRef]

Opt. Eng. (1)

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[CrossRef]

Opt. Lett. (3)

Optik (1)

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as an artificial distributed index medium,” Optik 89, 107–112 (1992).

Rep. Prog. Phys. (1)

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

Other (3)

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

J. Turunen, E. Noponen, A. Vasara, J. M. Miller, M. R. Taghizadeh, “Electromagnetic theory of diffractive optics,” in Workshop on Digital Holography 19– 21 May 1992, Prague, Czechoslovakia, A. A. Pesl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1718, 90–99 (1992).

F. Wyrowski, “Characteristics of diffractive optical elements/ digital holograms,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 2–10 (1991).
[CrossRef]

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Figures (17)

Fig. 1
Fig. 1

(a) Linear carrier phase ϕc(x) and the desired phase modulation ϕ(x) of the carrier, (b) the unmodulated high-frequency carrier grating. Various coding methods of ϕ(x): (c) pulse-position modulation, (d) pulse-width modulation, and (e) pulse-frequency modulation.

Fig. 2
Fig. 2

Geometry of a transmission-type binary high-frequency grating illuminated by a monochromatic plane wave.

Fig. 3
Fig. 3

(a) Maximum first-order efficiency of a transmission-type binary high-frequency grating as a function of period length, assuming Bragg incidence and an aspect ratio of c/dc = 0.5; (b) optimal relief depth h for each period.

Fig. 4
Fig. 4

Explanation of discontinuities in Fig. 3: double-peaked first-order efficiency curves (as a function of groove depth h/λ) for several values of the grating period dc/λ around the discontinuity at dc/λ = 0.88.

Fig. 5
Fig. 5

First-order efficiency of several transmission-type grating solutions from Fig. 3, with dc {0.6,0.8,1.0,1.2,1.4}, when (a) the angle of incidence θ, (b) the aspect ratio c/dc, and (c) the relief depth h are varied. In (a), the exact Bragg angles are indicated by upward-pointing arrows.

Fig. 6
Fig. 6

Effects of slanted (tilt angle α > 0) or undercut (α < 0) groove sidewalls on the first-order efficiency η−1 of a transmission-type grating, without (solid curve) and with (dashed curve) transition-point compensation.

Fig. 7
Fig. 7

Same as Fig. 3 but for perfectly conducting reflection-type gratings.

Fig. 8
Fig. 8

Same as Fig. 5 but for perfectly conducting reflection-type gratings.

Fig. 9
Fig. 9

Sensitivity to grating-period modulation with three constant angles of incidence.

Fig. 10
Fig. 10

(a) Diffraction efficiency η and (b) array uniformity error E for transmission-type pulse-frequency-modulated binary array illuminators generating 4 (solid curves), 8 (dashed curves), and 16 (dotted curves) beams, analyzed as a function of the grating period d = Ldc.

Fig. 11
Fig. 11

Same as Fig. 10 but for perfectly conducting reflection-type gratings.

Fig. 12
Fig. 12

Same as Fig. 11 but with the angle of incidence θ = 60.28°.

Fig. 13
Fig. 13

Same as Fig. 11 but with the angle of incidence θ = 70.56°.

Fig. 14
Fig. 14

Zeroth-order (a) phase and (b) diffraction efficiency of a transmission-type grating with period dc/λ = 0.8, analyzed as a function of the aspect ratio c/dc, for TE (solid curves) and TM (dashed curves) polarization.

Fig. 15
Fig. 15

Same as Fig. 14 but for a period dc/λ = 0.4.

Fig. 16
Fig. 16

(a) Diffraction efficiency and (b) array nonuniformity error for transmission-type pulse-width-modulated binary array illuminators generating 4 (solid curves), 8 (dashed curves), and 16 (dotted curves) beams, plotted as a function of the grating period d = Ldc with dc/λ = 0.8.

Fig. 17
Fig. 17

Same as Fig. 16 but for a period dc/λ = 0.4.

Tables (2)

Tables Icon

Table 1 Solutions for Transmission-Type Binary High-Frequency Gratingsa

Tables Icon

Table 2 Solutions for Reflection-Type Binary High-Frequency Gratingsa

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