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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 73, Iss. 5 — May. 1, 1983
  • pp: 702–706

Mathematical analysis of gratings with circularly concentric grooves

J. M. Elson  »View Author Affiliations


JOSA, Vol. 73, Issue 5, pp. 702-706 (1983)
http://dx.doi.org/10.1364/JOSA.73.000702


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Abstract

A mathematical method of analysis of gratings having circularly concentric grooves is presented. The main emphasis is not on the ultimate calculation of the diffracted or scattered fields but rather on reducing the problem to a tractable form with clear physical interpretation, to which the point-matching method can be applied. This is done by starting with the Rayleigh–Fano equation for scattering from rough surfaces. For circular geometry, the problem initially appears intractable. However, by a series of Laplace and inverse Laplace transforms, the problem is reduced to a tractable form.

© 1983 Optical Society of America

Citation
J. M. Elson, "Mathematical analysis of gratings with circularly concentric grooves," J. Opt. Soc. Am. 73, 702-706 (1983)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-73-5-702


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References

  1. J. Dyson, "Circular and spiral diffraction gratings," Proc. R. Soc. London Ser. A 248, 93–106 (1958).
  2. U. Fano, "The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld's waves)," J. Opt. Soc. Am. 31, 213–222 (1941); R. Petit, "Electromagnetisme- diffraction d'une onde plane monochromatique par un réseau périodique infiniment conducteur," C. R. Acad. Sci. 257, 2018–2021 (1963); F. Toigo, A. Marvin, V. Celli, and N. R. Hill, "Optical properties of rough surfaces: general theory and the small roughness limit," Phys. Rev. B 15, 5618–5626 (1977).
  3. J. M. Eison, "High efficiency diffraction grating theory," Proc. Soc. Photo-Opt. Instrum. Eng. 240, 128–131 (1981).
  4. J. Vlieger and D. Bedeaux, "A phenomenological theory of light scattering by surfaces," Physica 85A, 389–398 (1976).
  5. F. Toigo, A. Marvin, V. Celli, and N. R. Hill, "Optical properties of rough surfaces: general theory and the small roughness limit," Phys. Rev. B 15, 5618–5626 (1977).

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