Abstract

Resonance-domain diffractive optics covers the region where the characteristic feature sizes in the surface-relief modulation structure of the diffractive optical element are comparable to the wavelength of light; it may be viewed as a bridge between synthetic holography and the electromagnetic theory of diffraction gratings and rough surfaces. We consider the problem of synthesizing, in the framework of the electromagnetic theory, various types of periodic resonance-domain diffractive optical elements that utilize several diffraction orders. Parametric optimization is used to design one-to-N fan-out elements, N-to-N star couplers, and polarization-controlled optical beam splitters and switches with close to 100% efficiencies and no undesired diffraction orders in the image half-space. Reflection-type fan-out gratings with six and seven output beams are demonstrated experimentally at λ = 10.6 μm.

© 1992 Optical Society of America

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1986).
  2. W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. XVI, pp. 121–231.
  3. N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
    [CrossRef]
  4. 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]
  5. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).
  6. P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1967), Vol. VI, pp. 53–69.
    [CrossRef]
  7. R. Petit, ed., Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  8. D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. XXI, pp. 1–67.
    [CrossRef]
  9. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [CrossRef]
  10. 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).
    [CrossRef]
  11. 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).
    [CrossRef]
  12. 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]
  13. 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).
    [CrossRef]
  14. Two monochromatic waves with the same wavelength and the same state of polarization but incident at different angles are, strictly speaking, mutually coherent. However, mutual noncorrelation is assumed here, meaning, e.g., that independent (quasi-monochromatic) sources are used.
  15. H. Dammann, “Color separation gratings,” Appl. Opt. 17, 2273–2279 (1978).
    [CrossRef] [PubMed]
  16. J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miler, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
    [CrossRef]
  17. A. Roger, D. Maystre, “Inverse scattering method in electromagnetic optics: application to diffraction gratings,”J. Opt. Soc. Am. 70, 1483–1495 (1980).
    [CrossRef]
  18. A. Roger, “Grating profile optimizations by inverse scattering methods,” Opt. Commun. 32, 11–13 (1980).
    [CrossRef]
  19. J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and fabrication of grating beamsplitter,”J. Phys. D 21, S102–S105 (1988).
    [CrossRef]
  20. 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, 3320–3336 (1992).
    [CrossRef] [PubMed]
  21. C. B. Burckhardt, “Diffraction of a plane wave at a sinusoidally stratified dielectric grating,”J. Opt. Soc. Am. 56, 1502–1509 (1966).
    [CrossRef]
  22. F. G. Kaspar, “Diffraction by thick, periodically stratified gratings with complex dielectric constant,”J. Opt. Soc. Am. 63, 37–45 (1973).
    [CrossRef]
  23. K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,”J. Opt. Soc. Am. 68, 1206–1210 (1978).
    [CrossRef]
  24. J. M. Miller, J. Turunen, M. R. Taghizadeh, A. Vasara, E. Noponen, “Rigorous modal theory for perfectly conducting lamellar gratings,”IEEE Conf. Publ. 342, 99–102 (1991).
  25. D. Maystre, R. Petit, “Diffraction par un reseau lamellaire infinement conducteur,” Opt. Commun. 5, 90–93 (1972).
    [CrossRef]
  26. F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
    [CrossRef]
  27. F. Wyrowski, “Theory of digital holography,”IEEE Conf. Publ. 342, 93–97 (1991).
  28. F. Wyrowski, “Characteristics of diffractive optical elements/digital holograms,” in Computer and Optically Formed Holographic Optics, I. N. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 2–10 (1990).
    [CrossRef]
  29. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1967).
  30. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,”J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  31. H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  32. U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratio,” Fiber Integr. Opt. 4, 159–167 (1982).
    [CrossRef]

1992 (1)

1991 (5)

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miler, “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).
[CrossRef]

J. M. Miller, J. Turunen, M. R. Taghizadeh, A. Vasara, E. Noponen, “Rigorous modal theory for perfectly conducting lamellar gratings,”IEEE Conf. Publ. 342, 99–102 (1991).

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

F. Wyrowski, “Theory of digital holography,”IEEE Conf. Publ. 342, 93–97 (1991).

1989 (1)

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

1988 (1)

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

1985 (1)

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

1982 (2)

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

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,”J. Opt. Soc. Am. 72, 1385–1392 (1982).
[CrossRef]

1980 (2)

1978 (2)

1973 (1)

1972 (1)

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]

1967 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1967).

1966 (1)

Beckmann, P.

P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1967), 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).
[CrossRef]

Born, M.

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

Bryngdahl, O.

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

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]

Burckhardt, C. B.

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).
[CrossRef]

Dammann, H.

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

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

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).
[CrossRef]

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).
[CrossRef]

Gaylord, T. K.

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

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,”J. Opt. Soc. Am. 72, 1385–1392 (1982).
[CrossRef]

Goodman, J. W.

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

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]

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, 3320–3336 (1992).
[CrossRef] [PubMed]

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

Jaakkola, T.

Jin, G.

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

Kaspar, F. G.

Killat, U.

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

Knop, K.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1967).

Kuisma, S.

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).
[CrossRef]

Lee, W.-H.

W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. XVI, pp. 121–231.

Maystre, D.

A. Roger, D. Maystre, “Inverse scattering method in electromagnetic optics: application to diffraction gratings,”J. Opt. Soc. Am. 70, 1483–1495 (1980).
[CrossRef]

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

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. XXI, pp. 1–67.
[CrossRef]

Miler, J. M.

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

Miller, J. M.

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, 3320–3336 (1992).
[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]

J. M. Miller, J. Turunen, M. R. Taghizadeh, A. Vasara, E. Noponen, “Rigorous modal theory for perfectly conducting lamellar gratings,”IEEE Conf. Publ. 342, 99–102 (1991).

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).
[CrossRef]

Moharam, M. G.

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

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,”J. Opt. Soc. Am. 72, 1385–1392 (1982).
[CrossRef]

Naqvi, S. S.

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).
[CrossRef]

Nelson, S.

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).
[CrossRef]

Noponen, E.

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, 3320–3336 (1992).
[CrossRef] [PubMed]

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miler, “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).
[CrossRef]

J. M. Miller, J. Turunen, M. R. Taghizadeh, A. Vasara, E. Noponen, “Rigorous modal theory for perfectly conducting lamellar gratings,”IEEE Conf. Publ. 342, 99–102 (1991).

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).
[CrossRef]

Petit, R.

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

Rabe, G.

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

Rave, W.

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

Roger, A.

Salin, A.

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

Streibl, N.

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

Taghizadeh, M. R.

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, 3320–3336 (1992).
[CrossRef] [PubMed]

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miler, “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).
[CrossRef]

J. M. Miller, J. Turunen, M. R. Taghizadeh, A. Vasara, E. Noponen, “Rigorous modal theory for perfectly conducting lamellar gratings,”IEEE Conf. Publ. 342, 99–102 (1991).

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).
[CrossRef]

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).
[CrossRef]

Turunen, J.

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, 3320–3336 (1992).
[CrossRef] [PubMed]

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miler, “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).
[CrossRef]

J. M. Miller, J. Turunen, M. R. Taghizadeh, A. Vasara, E. Noponen, “Rigorous modal theory for perfectly conducting lamellar gratings,”IEEE Conf. Publ. 342, 99–102 (1991).

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

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).
[CrossRef]

Vasara, A.

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, 3320–3336 (1992).
[CrossRef] [PubMed]

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miler, “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).
[CrossRef]

J. M. Miller, J. Turunen, M. R. Taghizadeh, A. Vasara, E. Noponen, “Rigorous modal theory for perfectly conducting lamellar gratings,”IEEE Conf. Publ. 342, 99–102 (1991).

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

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).
[CrossRef]

Werner, T.

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).
[CrossRef]

Westerholm, J.

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, 3320–3336 (1992).
[CrossRef] [PubMed]

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

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

Wolf, E.

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

Wyrowski, F.

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

F. Wyrowski, “Theory of digital holography,”IEEE Conf. Publ. 342, 93–97 (1991).

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]

F. Wyrowski, “Characteristics of diffractive optical elements/digital holograms,” in Computer and Optically Formed Holographic Optics, I. N. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 2–10 (1990).
[CrossRef]

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1967).

Fiber Integr. Opt. (1)

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

IEEE Conf. Publ. (2)

J. M. Miller, J. Turunen, M. R. Taghizadeh, A. Vasara, E. Noponen, “Rigorous modal theory for perfectly conducting lamellar gratings,”IEEE Conf. Publ. 342, 99–102 (1991).

F. Wyrowski, “Theory of digital holography,”IEEE Conf. Publ. 342, 93–97 (1991).

J. Mod. Opt. (1)

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Figures (9)

Fig. 1
Fig. 1

Diffraction of a plane wave by a binary, periodic diffractive optical element.

Fig. 2
Fig. 2

Fan-out to two with resonance-domain transmission gratings: geometries. (a) Normal incidence: orders m = ±1 are used. (b) Bragg incidence: orders m = 0 and m = −1 are used.

Fig. 3
Fig. 3

Fan-out to two with resonance-domain transmission gratings: results. (a) Amplitude and (b) phase of the response (transmission) function t(x) for the geometry of Fig. 2(a). Solid curves: the summation extends over a large number of evanescent waves. Dashed curves: the summation extends over propagating waves only. In (c) and (d) the corresponding results are given for the geometry of Fig. 2(b).

Fig. 4
Fig. 4

Operating principle of a resonance-domain star coupler connecting N sources to N detectors: (a) odd fan-out, (b) even fan-out with incident waves at Bragg angles.

Fig. 5
Fig. 5

Response functions r(x) and the wave-front transformations r W (x) for the 4-to-4 reflective star coupler at the two angles of incidence.

Fig. 6
Fig. 6

Operating principle of a polarization-sensitive node that either lets through or swaps two mutually uncorrelated inputs at ±θ, depending on their (common) state of polarization.

Fig. 7
Fig. 7

Operating principle of a diffractive polarization beam splitter: TM-polarized light is passed straight through (zeroth order), while TE-polarized light is diffracted into the first order.

Fig. 8
Fig. 8

Scanning electron microscope photograph of a one-to-six resonance-domain fan-out grating.

Fig. 9
Fig. 9

Optical reconstruction of the resonance-domain one-to-six fan-out grating.

Equations (27)

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t ( x , y ) = exp [ i k - H 0 n ( x , y , x ) d z ] ,
n ( x , z ) = { n 1 when x [ a j , b j ) n 2 otherwise ,
U I ( x , z ) = exp [ i k n 0 ( x sin θ + z cos θ ) ] ,
U R ( x , z ) = m = - R m exp [ i ( γ m x - r m z ) ] ,
U T ( x , z ) = m = - T m exp [ i ( γ m x + t m z ) ] ,
γ m = k n 0 sin θ + 2 π m / d ,
r m = { [ ( k n 0 ) 2 - γ m 2 ] 1 / 2 when γ m k n 0 i [ γ m 2 - ( k n 0 ) 2 ] 1 / 2 when γ m > k n 0 ,
t m = { [ ( k n 3 ) 2 - γ m 2 ] 1 / 2 when γ m k n 3 i [ γ m 2 - ( k n 3 ) 2 ] 1 / 2 when γ m > k n 3 .
r ( x ) = U R ( x , - H ) U I ( x , - H ) = m = - R m exp ( i 2 π m x / d ) ,
t ( x ) = U T ( x , 0 ) U I ( x , 0 ) = m = - T m exp ( i 2 π m x / d )
I m = ( r m / r 0 ) R m 2 ,
I m = C ( t m / r 0 ) T m 2 ,
P = { I ^ m I ^ m { 0 , 1 } , m W }
N = m W I ^ m
η = m W I ^ m I m
E = max m W I ^ m 1 - N I m / η
r W ( x ) = m W R m exp ( i 2 π m x / d ) ,
t W ( x ) = m W T m exp ( i 2 π m x / d )
U I , q ( x , z ) = exp [ i k q n 0 ( x sin θ q + z cos θ q ) ] ,
P q = { I ^ m , q I ^ m , q = { 0 , 1 } , m W q }
N q = m W q I ^ m , q ,
η q = m W q I ^ m , q I m , q ,
E q = max m W q I ^ m , q 1 - N q I m , q / η q ,
M f = q = 1 Q m W q ( I m , q - I ^ m , q η ^ q / N q ) 2 ,
t ^ W ( x ) = exp ( i α ) cos ( 2 π x / d - α )
t ( x ) = { exp ( 8.77 i ) when x / λ [ 0 , 0.322 ) 1 otherwise ,
t ^ W ( x ) = exp ( i α ) exp ( - i π x / d ) cos ( π x / d - α )

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