Abstract

A simple but rigorous chain-matrix analysis is used to determine the plane-wave diffraction efficiencies and angular selectivities of planar pure-reflection gratings (zero-slant angle) of arbitrary thickness, arbitrary-starting and arbitrary-ending conditions, and arbitrary incidence angle. The results from rigorous coupled-wave theory in the angular limit as the fringes become parallel to the surfaces are shown to approach these results in a particular average sense.

© 1982 Optical Society of America

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  1. C. B. Burckhardt, "Diffraction of a plane wave at a sinusoidally stratified dielectric grating," J. Opt. Soc. Am. 56, 1502–1509 (1966).
  2. T. Tamir and H. C. Wang, "Scattering of electromagnetic waves by a sinusoidally stratified half-space: I. Formal solution and analytic approximations," Can. J. Phys. 44, 2073–2094 (1966).
  3. T. Tamir, "Scattering of electromagnetic waves by a sinusoidally stratified half-space: II. Diffraction aspects at the Rayleigh and Bragg wavelengths," Can. J. Phys. 44, 2461–2494 (1966).
  4. L. Bergstein and D. Kermisch, "Image storage and reconstruction in volume holography," Proc. Symp. Modern Opt. 17, 655–680 (1967).
  5. S. T. Peng and E. S. Cassedy, "Scattering of light waves at boundaries to parametrically modulated media," Proc. Symp. Modern Opt. 17, 299–342 (1967).
  6. F. G. Kaspar, "Diffraction by thick periodically stratified gratings with complex dielectric constant," J. Opt. Soc. Am. 63, 37–45 (1973).
  7. R. S. Chu and T. Tamir, "Wave propagation and dispersion in space-time periodic media," Proc. IEE 119, 797–806 (1972).
  8. R. S. Chu and J. A. Kong, "Modal theory of spatially periodic media," IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).
  9. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).
  10. R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).
  11. D. L. Jaggard and C. Elachi, "Floquet and coupled-wave analysis of higher-order Bragg coupling in a periodic medium," J. Opt. Soc. Am. 66, 674–682 (1976).
  12. W. R. Klein and B. D. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
  13. R. Magnusson and T. K. Gaylord, "Analysis of multiwave diffraction of thick gratings," J. Opt. Soc. Am. 67, 1165–1170 (1977).
  14. M. G. Moharam and T. K. Gaylord, "Coupled-wave analysis of reflection gratings," Appl. Opt. 20, 240–244 (1981).
  15. M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar grating diffraction," J. Opt. Soc. Am. 71, 811–818 (1981).
  16. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 55–70.
  17. R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), pp. 79–94.
  18. W. W. Rigrod, "Diffraction efficiency of nonsinusoidal Bragg reflection gratings," J. Opt. Soc. Am. 64, 97–99 (1974); Erratum, J. Opt. Soc. Am. 64, 895 (1974).

1981 (2)

1977 (2)

R. Magnusson and T. K. Gaylord, "Analysis of multiwave diffraction of thick gratings," J. Opt. Soc. Am. 67, 1165–1170 (1977).

R. S. Chu and J. A. Kong, "Modal theory of spatially periodic media," IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).

1976 (1)

1974 (1)

1973 (1)

1970 (1)

R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).

1969 (1)

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

1967 (3)

L. Bergstein and D. Kermisch, "Image storage and reconstruction in volume holography," Proc. Symp. Modern Opt. 17, 655–680 (1967).

S. T. Peng and E. S. Cassedy, "Scattering of light waves at boundaries to parametrically modulated media," Proc. Symp. Modern Opt. 17, 299–342 (1967).

W. R. Klein and B. D. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).

1966 (3)

C. B. Burckhardt, "Diffraction of a plane wave at a sinusoidally stratified dielectric grating," J. Opt. Soc. Am. 56, 1502–1509 (1966).

T. Tamir and H. C. Wang, "Scattering of electromagnetic waves by a sinusoidally stratified half-space: I. Formal solution and analytic approximations," Can. J. Phys. 44, 2073–2094 (1966).

T. Tamir, "Scattering of electromagnetic waves by a sinusoidally stratified half-space: II. Diffraction aspects at the Rayleigh and Bragg wavelengths," Can. J. Phys. 44, 2461–2494 (1966).

Bergstein, L.

L. Bergstein and D. Kermisch, "Image storage and reconstruction in volume holography," Proc. Symp. Modern Opt. 17, 655–680 (1967).

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 55–70.

Burckhardt, C. B.

Cassedy, E. S.

S. T. Peng and E. S. Cassedy, "Scattering of light waves at boundaries to parametrically modulated media," Proc. Symp. Modern Opt. 17, 299–342 (1967).

Chu, R. S.

R. S. Chu and J. A. Kong, "Modal theory of spatially periodic media," IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).

R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).

R. S. Chu and T. Tamir, "Wave propagation and dispersion in space-time periodic media," Proc. IEE 119, 797–806 (1972).

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), pp. 79–94.

Cook, B. D.

W. R. Klein and B. D. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).

Elachi, C.

Gaylord, T. K.

Jaggard, D. L.

Kaspar, F. G.

Kermisch, D.

L. Bergstein and D. Kermisch, "Image storage and reconstruction in volume holography," Proc. Symp. Modern Opt. 17, 655–680 (1967).

Klein, W. R.

W. R. Klein and B. D. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).

Kogelnik, H.

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

Kong, J. A.

R. S. Chu and J. A. Kong, "Modal theory of spatially periodic media," IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).

Magnusson, R.

Moharam, M. G.

Peng, S. T.

S. T. Peng and E. S. Cassedy, "Scattering of light waves at boundaries to parametrically modulated media," Proc. Symp. Modern Opt. 17, 299–342 (1967).

Rigrod, W. W.

Tamir, T.

R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).

T. Tamir, "Scattering of electromagnetic waves by a sinusoidally stratified half-space: II. Diffraction aspects at the Rayleigh and Bragg wavelengths," Can. J. Phys. 44, 2461–2494 (1966).

T. Tamir and H. C. Wang, "Scattering of electromagnetic waves by a sinusoidally stratified half-space: I. Formal solution and analytic approximations," Can. J. Phys. 44, 2073–2094 (1966).

R. S. Chu and T. Tamir, "Wave propagation and dispersion in space-time periodic media," Proc. IEE 119, 797–806 (1972).

Wang, H. C.

T. Tamir and H. C. Wang, "Scattering of electromagnetic waves by a sinusoidally stratified half-space: I. Formal solution and analytic approximations," Can. J. Phys. 44, 2073–2094 (1966).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 55–70.

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

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

Can. J. Phys. (2)

T. Tamir and H. C. Wang, "Scattering of electromagnetic waves by a sinusoidally stratified half-space: I. Formal solution and analytic approximations," Can. J. Phys. 44, 2073–2094 (1966).

T. Tamir, "Scattering of electromagnetic waves by a sinusoidally stratified half-space: II. Diffraction aspects at the Rayleigh and Bragg wavelengths," Can. J. Phys. 44, 2461–2494 (1966).

IEEE Trans. Microwave Theory Tech. (2)

R. S. Chu and J. A. Kong, "Modal theory of spatially periodic media," IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).

R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).

IEEE Trans. Sonics Ultrason. (1)

W. R. Klein and B. D. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).

J. Opt. Soc. Am. (6)

Proc. Symp. Modern Opt. (2)

L. Bergstein and D. Kermisch, "Image storage and reconstruction in volume holography," Proc. Symp. Modern Opt. 17, 655–680 (1967).

S. T. Peng and E. S. Cassedy, "Scattering of light waves at boundaries to parametrically modulated media," Proc. Symp. Modern Opt. 17, 299–342 (1967).

Other (3)

R. S. Chu and T. Tamir, "Wave propagation and dispersion in space-time periodic media," Proc. IEE 119, 797–806 (1972).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 55–70.

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), pp. 79–94.

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