Abstract

A rigorous coupled-wave approach is used to analyze diffraction by general planar gratings bounded by two different media. The grating fringes may have any orientation (slanted or unslanted) with respect to the grating surfaces. The analysis is based on a state-variables representation and results in a unifying, easily computer-implementable matrix formulation of the general planar-grating diffraction problem. Accurate diffraction characteristics are presented for the first time to the authors’ knowledge for general slanted gratings. This present rigorous formulation is compared with rigorous modal theory, approximate two-wave modal theory, approximate multiwave coupled-wave theory, and approximate two-wave coupled-wave theory. Typical errors in the diffraction characteristics introduced by these various approximate theories are evaluated for transmission, slanted, and reflection gratings. Inclusion of higher-order waves in a theory is important for obtaining accurate predictions when forward-diffracted orders are dominant (transmission-grating behavior). Conversely, when backward-diffracted orders dominate (reflection-grating behavior), second derivatives of the field amplitudes and boundary diffraction need to be included to produce accurate results.

© 1981 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. R. Aggrawal, "Diffraction of light by ultrasonic waves," Proc. Indian Acad. Sci. 31, 417–426 (1950).
  2. P. Phariseau, "On the diffraction of light by progressive supersonic waves," Proc. Indian Acad. Sci. Sect. A 44, 165–170 (1965).
  3. W. R. Klein and B. D. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonic Ultrason. SU-14, 123–134 (1967).
  4. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).
  5. G. L. Fillmore and R. F. Tynan, "Sensitometric characteristics of hardened dichromated-gelatin films," J. Opt. Soc. Am. 61, 199–203 (1971).
  6. J. A. Kong, "Second-order coupled-mode equations for spatially periodic media," J. Opt. Soc. Am. 67, 825–829 (1977).
  7. R. Magnusson and T. K. Gaylord, "Analysis of multiwave diffraction by thick gratings," J. Opt. Soc. Am. 67, 1165–1170 (1977).
  8. T. Tamir, H. C. Wang, and A. A. Oliner, "Wave propagation in sinusoidally stratified dielectric media," IEEE Trans. Microwave Theory Tech. MTT-12, 323–335 (1964).
  9. T. Tamir and H. C. Wang, "Scattering of electromagnetic waves by a sinusoidally stratified half-space: I. Formal solution and analysis approximations," Can. J. Phys. 44, 2073–2094 (1966).
  10. T. Tamir, "Scattering of electromagnetic waves by a sinusoidally stratified half-space: II. Diffraction aspects of the Rayleigh and Bragg wavelengths," Can. J. Phys. 44, 2461–2494 (1966).
  11. C. B. Burckhardt, "Diffraction of a plane wave at a sinusoidally stratified dielectric grating," J. Opt. Soc. Am. 56, 1502–1509 (1966).
  12. L. Bergstein and D. Kermisch, "Image storage and reconstruction in volume holography," Proc. Symp. Modern Opt. 17, 655–680 (1967).
  13. 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).
  14. R. S. Chu and T. Tamir, "Wave propagation and dispersion in space-time periodic media," Proc. IEE 119, 797–806 (1972).
  15. F. G. Kaspar, "Diffraction by thick periodically stratified gratings with complex dielectric constant," J. Opt. Soc. Am. 63, 37–45 (1973).
  16. S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
  17. R. S. Chu and J. A. Kong, "Modal theory of spatially periodic media," IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).
  18. R. Magnusson and T. K. Gaylord, "Equivalence of multiwave coupled-wave theory and modal theory of periodic-media diffraction," J. Opt. Soc. Am. 68, 1777–1779 (1978).
  19. M. G. Moharam and T. K. Gaylord, "Coupled-wave analysis of reflection gratings," Appl. Opt., 20, 240–244 (1981).
  20. M. G. Moharam, T. K. Gaylord, and R. Magnusson, "Criteria for Bragg regime diffraction by phase gratings," Opt. Commun. 32, 14–18 (1980).

1981

1980

M. G. Moharam, T. K. Gaylord, and R. Magnusson, "Criteria for Bragg regime diffraction by phase gratings," Opt. Commun. 32, 14–18 (1980).

1978

1977

1975

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

1973

1972

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

1971

1970

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

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

1967

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

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

1966

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

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

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

1965

P. Phariseau, "On the diffraction of light by progressive supersonic waves," Proc. Indian Acad. Sci. Sect. A 44, 165–170 (1965).

1964

T. Tamir, H. C. Wang, and A. A. Oliner, "Wave propagation in sinusoidally stratified dielectric media," IEEE Trans. Microwave Theory Tech. MTT-12, 323–335 (1964).

1950

R. R. Aggrawal, "Diffraction of light by ultrasonic waves," Proc. Indian Acad. Sci. 31, 417–426 (1950).

Aggrawal, R. R.

R. R. Aggrawal, "Diffraction of light by ultrasonic waves," Proc. Indian Acad. Sci. 31, 417–426 (1950).

Bergstein, L.

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

Bertoni, H. L.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

Burckhardt, C. B.

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

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).

Cook, B. D.

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

Fillmore, G. L.

Gaylord, T. K.

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. Sonic 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).

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

Magnusson, R.

Moharam, M. G.

M. G. Moharam and T. K. Gaylord, "Coupled-wave analysis of reflection gratings," Appl. Opt., 20, 240–244 (1981).

M. G. Moharam, T. K. Gaylord, and R. Magnusson, "Criteria for Bragg regime diffraction by phase gratings," Opt. Commun. 32, 14–18 (1980).

Oliner, A. A.

T. Tamir, H. C. Wang, and A. A. Oliner, "Wave propagation in sinusoidally stratified dielectric media," IEEE Trans. Microwave Theory Tech. MTT-12, 323–335 (1964).

Peng, S. T.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

Phariseau, P.

P. Phariseau, "On the diffraction of light by progressive supersonic waves," Proc. Indian Acad. Sci. Sect. A 44, 165–170 (1965).

Tamir, T.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

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

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 analysis approximations," Can. J. Phys. 44, 2073–2094 (1966).

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

T. Tamir, H. C. Wang, and A. A. Oliner, "Wave propagation in sinusoidally stratified dielectric media," IEEE Trans. Microwave Theory Tech. MTT-12, 323–335 (1964).

Tynan, R. F.

Wang, H. C.

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

T. Tamir, H. C. Wang, and A. A. Oliner, "Wave propagation in sinusoidally stratified dielectric media," IEEE Trans. Microwave Theory Tech. MTT-12, 323–335 (1964).

Appl. Opt.

Bell Syst. Tech. J.

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

Can. J. Phys.

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

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

IEEE Trans. Microwave Theory Tech.

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, H. C. Wang, and A. A. Oliner, "Wave propagation in sinusoidally stratified dielectric media," IEEE Trans. Microwave Theory Tech. MTT-12, 323–335 (1964).

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

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

IEEE Trans. Sonic Ultrason.

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

J. Opt. Soc. Am.

Opt. Commun.

M. G. Moharam, T. K. Gaylord, and R. Magnusson, "Criteria for Bragg regime diffraction by phase gratings," Opt. Commun. 32, 14–18 (1980).

Proc. IEE

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

Proc. Indian Acad. Sci.

R. R. Aggrawal, "Diffraction of light by ultrasonic waves," Proc. Indian Acad. Sci. 31, 417–426 (1950).

Proc. Indian Acad. Sci. Sect. A

P. Phariseau, "On the diffraction of light by progressive supersonic waves," Proc. Indian Acad. Sci. Sect. A 44, 165–170 (1965).

Proc. Symp. Modern Opt.

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.