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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 4 — Apr. 1, 1978
  • pp: 496–502

On an asymptotic theory of diffraction gratings used in the scalar domain

Erwin G. Loewen, Michel Nevière, and Daniel Maystre  »View Author Affiliations


JOSA, Vol. 68, Issue 4, pp. 496-502 (1978)
http://dx.doi.org/10.1364/JOSA.68.000496


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Abstract

Starting from the electromagnetic theory, we derive an asymptotic formalism to investigate the behavior of perfectly conducting gratings used at small wavelengths to groove pitch ratios and near normal incidence. The theory is applied to study three classical types of profiles: sinusoidal, lamellar, and blazed gratings. Results are given for both -1 and -2 Littrow (or near Littrow) mounts. The accuracy of the theory and the limits of the domain where it applies are studied by the use of rigorous electromagnetic computations. The role of a finite conductivity of the surface is also investigated.

© 1978 Optical Society of America

Citation
Erwin G. Loewen, Michel Nevière, and Daniel Maystre, "On an asymptotic theory of diffraction gratings used in the scalar domain," J. Opt. Soc. Am. 68, 496-502 (1978)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-68-4-496


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References

  1. D. Maystre, "Sur la Diffraction d'une onde plane par un réseau mé tallique de conductivite finie," Opt. Commun. 6, 50 (1972).
  2. M. Nevière, P. Vincent, and R. Petit, "Sur la theorie du réseaux conducteur et ses applications a l’optique," Nouv. Rev. Opt. 5, 65 (1974).
  3. E. Loewen, M. Nevière, and D. Maystre, "Grating Efficiency Theory as it Applies to Blazed and Holographic Gratings," Appl. Opt. 16, 2711 (1977).
  4. B. A. Lippman, "Note on the Theory of Gratings," J. Opt. Soc. Am. 43, 408 (1953).
  5. R. Petit and M. Cadilhac, "Sur la diffraction d'une onde plane par un réseau infiniment conducteur," C. R. Acad. Sci. Ser. B 262, 468 (1966).
  6. R. F. Millar, "On the Rayleigh Assumption in Scattering by a Periodic Surface," Proc. Camb. Philos. Soc. 65, 773 (1969).
  7. R. F. Millar, "Singularities of Two-Dimensional Exterior Solutions of the Helmholtz Equation," Proc. Camb. Philos. Soc. 69, 175 (1971).
  8. R.G. Barentsev, Vestn. Leningr. Univ. 1, 66 (1965).
  9. J. Pavageau, "Equation intégrale pour la diffraction electromagné tique par des conducteurs parfaits dans les problèmes à deux dimensions- Application aux ré seaux," C. R. Acad. Sci. Ser. B 264, 424 (1967).
  10. J. L. Uretsky, "The Scattering of Plane Waves from Periodic Surfaces," Ann. Phys. (Leipzig) 33, 400 (1965).
  11. A. Wirgin, "Considé rations thé oriques sur la diffraction par ré flexion sur des surfaces quasiment planes; application a la diffraction par des ré seaux," C. R. Acad. Sci. (Paris), 259, 1486 (1964).
  12. M. Neviè re, M. Cadilhac, "Sur la Validité du Developement de Rayleigh," Opt. Commun. 2, 235 (1970).
  13. R. Petit and D. Maystre, "Application des lois de l'é lectromagnetique a l'é tude des ré seaux," Rev. Phys. Appl. 7, 427 (1972).
  14. M. Neviè re, M. Cadilhac, and R. Petit, "Applications of Conformal Mappings to the Diffraction of Electromagnetic Waves by a Grating," IEEE Trans. Antennas Propag. AP-21, 37 (1973).
  15. R. F. Millar, "On the Rayleigh Assumption in Scattering by a Periodic Surface," Proc. Camb. Philos. Soc. 69, 217 (1971).
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 64.
  17. E. G. Loewen, M. Nevière and D. Maystre, "Efficiency Optimization of Rectangular Groove Gratings in Visible and IR Regions," (unpublished).
  18. D. Maystre and R. Petit, "Diffraction par un ré seau lamellaire infiniment conducteur," Opt. Commun. 5, 90 (1972).
  19. E. G. Loewen and M. Neviè re, "Simple Selection Rules for VUV and XUV Diffraction Gratings," Appl. Opt. (to be published).

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