Abstract

The equivalence of generalized multiwave coupled-wave theory and rigorous modal theory for describing diffraction by volume periodic structures is established. The detailed connection between these theories is presented. The coupled-wave approach, which provides simple formulation and good physical insight, may thus also be used to obtain exact results.

© 1979 Optical Society of America

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  1. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).
  2. 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).
  3. 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).
  4. S. F. Su and T. K. Gaylord, "Calculation of arbitrary-order diffraction efficiencies of thick gratings with arbitrary grating shape," J. Opt. Soc. Am. 65, 59–64 (1975).
  5. W. R. Klein and B. D. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrasonics SU-14, 123–134 (1967).
  6. R. Magnusson and T. K. Gaylord, "Analysis of multiwave diffraction of thick gratings," J. Opt. Soc. Am. 67, 1165–1170 (1977).
  7. J. A. Kong, "Second-order coupled-mode equations for spatially periodic media," J. Opt. Soc. Am. 67, 825–829 (1977).
  8. C. B. Burckhardt, "Diffraction of a plane wave at a sinusoidally stratified dielectric grating," J. Opt. Soc. Am. 56, 1502–1509 (1966).
  9. 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).
  10. 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).
  11. L. Bergstein and D. Kermisch, "Image storage and reconstruction in volume holography," Proc. Symp. Modern Opt. 17, 655–680 (1967).
  12. 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).
  13. F. G. Kaspar, "Diffraction by thick periodically stratified gratings with complex dielectric constant," J. Opt. Soc. Am. 63, 37–45 (1973).
  14. R. S. Chu and T. Tamir, "Wave propagation and dispersion in space-time periodic media," Proc. IEE 119, 797–806 (1972).
  15. R. S. Chu and J. A. Kong, "Modal theory of spatially periodic media," IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).
  16. R. Magnusson and T. K. Gaylord, "Diffraction regimes of transmission gratings," J. Opt. Soc. Am. 68 809–814 (1978).
  17. H. Kogelnik and C. V. Shank, "Coupled-wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327–2335 (1972).
  18. A. Yariv and A. Gover, "Equivalence of the coupled-mode and FloquetBloch formalisms in periodic optical waveguides," Appl. Phys. Lett. 26, 537–539 (1975).
  19. S. R. Seshadri, "Reflection and transmission coefficients of a periodic dielectric slab," Proc. IEEE 66, 699–700 (1978).
  20. H. Kogelnik, "Bragg diffraction in hologram gratings with multiple internal reflections," J. Opt. Soc. Am. 57, 431–433 (1967).
  21. R. Magnusson and T. K. Gaylord, "Diffraction efficiencies of thin phase gratings with arbitrary grating shape," J. Opt. Soc. Am. 68 806–809 (1978).

1978 (2)

1977 (3)

1976 (1)

1975 (2)

S. F. Su and T. K. Gaylord, "Calculation of arbitrary-order diffraction efficiencies of thick gratings with arbitrary grating shape," J. Opt. Soc. Am. 65, 59–64 (1975).

A. Yariv and A. Gover, "Equivalence of the coupled-mode and FloquetBloch formalisms in periodic optical waveguides," Appl. Phys. Lett. 26, 537–539 (1975).

1973 (1)

1972 (1)

H. Kogelnik and C. V. Shank, "Coupled-wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327–2335 (1972).

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 (4)

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

H. Kogelnik, "Bragg diffraction in hologram gratings with multiple internal reflections," J. Opt. Soc. Am. 57, 431–433 (1967).

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).

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).

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).

Cook, B. D.

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

Elachi, C.

Gaylord, T. K.

Gover, A.

A. Yariv and A. Gover, "Equivalence of the coupled-mode and FloquetBloch formalisms in periodic optical waveguides," Appl. Phys. Lett. 26, 537–539 (1975).

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 Ultrasonics SU-14, 123–134 (1967).

Kogelnik, H.

H. Kogelnik and C. V. Shank, "Coupled-wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327–2335 (1972).

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

H. Kogelnik, "Bragg diffraction in hologram gratings with multiple internal reflections," J. Opt. Soc. Am. 57, 431–433 (1967).

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).

J. A. Kong, "Second-order coupled-mode equations for spatially periodic media," J. Opt. Soc. Am. 67, 825–829 (1977).

Magnusson, R.

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).

Seshadri, S. R.

S. R. Seshadri, "Reflection and transmission coefficients of a periodic dielectric slab," Proc. IEEE 66, 699–700 (1978).

Shank, C. V.

H. Kogelnik and C. V. Shank, "Coupled-wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327–2335 (1972).

Su, S. F.

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 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).

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).

Yariv, A.

A. Yariv and A. Gover, "Equivalence of the coupled-mode and FloquetBloch formalisms in periodic optical waveguides," Appl. Phys. Lett. 26, 537–539 (1975).

Appl. Phys. Lett. (1)

A. Yariv and A. Gover, "Equivalence of the coupled-mode and FloquetBloch formalisms in periodic optical waveguides," Appl. Phys. Lett. 26, 537–539 (1975).

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 Ultrasonics (1)

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

J. Appl. Phys. (1)

H. Kogelnik and C. V. Shank, "Coupled-wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327–2335 (1972).

J. Opt. Soc. Am. (9)

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 (2)

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

S. R. Seshadri, "Reflection and transmission coefficients of a periodic dielectric slab," Proc. IEEE 66, 699–700 (1978).

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