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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 19 — Sep. 14, 2009
  • pp: 17102–17117

Numerical demonstration of the validity of the Rayleigh hypothesis

Alexandre V. Tishchenko  »View Author Affiliations

Optics Express, Vol. 17, Issue 19, pp. 17102-17117 (2009)

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The Rayleigh hypothesis and the related method of diffraction analysis are revisited. It is shown that the Rayleigh method can be applied to deep grating modeling without numerical problems and that it gives any desired accuracy whatever the groove depth. This proves the validity of the Rayleigh hypothesis and rehabilitates the Rayleigh method.

© 2009 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(290.0290) Scattering : Scattering

ToC Category:
Diffraction and Gratings

Original Manuscript: April 13, 2009
Revised Manuscript: June 8, 2009
Manuscript Accepted: June 11, 2009
Published: September 11, 2009

Alexandre V. Tishchenko, "Numerical demonstration of the validity of the Rayleigh hypothesis," Opt. Express 17, 17102-17117 (2009)

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  1. Lord Rayleigh (J. W. Strutt), "On the incidence of aerial and electromagnetic waves upon small obstacles in the form of ellipsoids or elliptic cylinders, and the passage of electric waves through a circular aperture in a conducting screen," Phil. Mag. 44, 28-52 (1897).
  2. Lord Rayleigh (J. W. Strutt), "On the dynamical theory of gratings," Proc. R. Soc. London Ser. A 79, 399-416 (1907). [CrossRef]
  3. L. N. Deryugin, "Equations for coefficients of wave reflections from a periodically uneven surface," Dokl. Akad. Nauk SSSR 87,913-916 (1952).
  4. B. A. Lippmann, "Note on the theory of gratings," J. Opt. Soc. Am. 43,408 (1953). [CrossRef]
  5. J. L. Uretski, "The scattering of plane waves from periodic surfaces," Ann. Phys. 33, 400-427 (1965). [CrossRef]
  6. R. Petit, M. Cadilhac, "Sur la diffraction d’une onde plane par un réseau infinement conducteur, C. R. Acad. Sci. Paris 262B, 468-471 (1966).
  7. R. F. Millar, "On the Rayleigh assumption in scattering by a periodic surface, II," Proc. Cambridge Philos. Soc. 69,217-225 (1971). [CrossRef]
  8. J. Pavageau, "Sur la méthode des spectres d’ondes planes dans les problèmes de diffraction," C. R. Acad. Sci. Paris 266B, 135-138 (1968).
  9. R. H. T. Bates, "Analytic constraints on electromagnetic field computations," IEEE Trans. Microwave Theory and Tech. MTT-23, 605-623 (1975). [CrossRef]
  10. A. Wirgin, "On Rayleigh’s theory of sinusoidal diffraction gratings," Opt. Acta 27, 1671-1692 (1980). [CrossRef]
  11. K. Yasuura and H. Ikuno, "On the modified Rayleigh hypothesis and the mode-matching method," in Summaries Int. Symp. Antennas and Propagation, Sendai, Japan, 173-174, (1971).
  12. P. C. Waterman, "Scattering by periodic surfaces," J. Acoust. Soc. Am. 57, 791 (1975). [CrossRef]
  13. J. B. Davies, "A least-squares boundary residual method for the numerical solution of scattering problems," IEEE Trans. Microwave Theory and Tech. MTT-21, 99-103 (1973). [CrossRef]
  14. V. I. Tatarskii, "Relation between the Rayleigh equation in diffraction theory and the equation based on Green’s formula, " J. Opt. Soc. Am. 12, 1254-1260 (1995). [CrossRef]
  15. J. Wauer, T. Rother, "Considerations to Rayleigh’s hypothesis," Opt. Commun. 282, 339 (2009). [CrossRef]
  16. L. Kazandjian, "Rayleigh methods applied to electromagnetic scattering from gratings in general homogeneous media," Phys. Rev. E 54, 6802-6815 (1996). [CrossRef]
  17. V. A. Sychugov and A. V. Tishchenko, "Light emission from a corrugated dielectric waveguide," Sov. J. Quantum Electron. 10, 186-189 (1980). [CrossRef]
  18. V. A. Sychugov and A. V. Tishchenko, "Propagation and conversion of light in corrugated waveguide structures," Sov. J. Quantum Electron. 12, 923-926 (1982). [CrossRef]
  19. G. A. Golubenko, A. A. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985). [CrossRef]
  20. J. Turunen, "Diffraction theory of dielectric surface relief gratings," in Micro-optics, H.P. Herzig ed. (Taylor&Francis Inc., 1997).
  21. A. M. Prokhorov, V. A. Sychugov, A. V. Tishchenko, and A. A. Khakimov, "Kinetics of the rippling of a germanium surface bombarded by an intense laser beam," Sov. Tech. Phys. Lett. 8, 605-606 (1982).
  22. V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, "Waveguide coupling gratings for high-sensitivity biochemical sensors," Sens. Actuators B 38-39 360-364 (1997). [CrossRef]
  23. I. F. Salakhutdinov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, and F. A. Pudonin, "Anomalous light reflection at the surface of a corrugated thin metal film," IEEE J. Quantum Electron. 34, 1054-1060 (1998). [CrossRef]
  24. I. A. Avrutsky, V. A. Sychugov, and A. V. Tishchenko, "The study of excitation, radiation, and reflection processes in corrugated waveguides," in Waveguide Corrugated Structures in Integrated and Fiber Optics, IOFAN Proc. 34, 3-98 (Nauka, Moscow, 1991, in Russian).
  25. P. Sheng, R. S. Stepleman, and P. N. Sanda, "Exact eigenfunctions for square-wave gratings: Application to diffraction and surface-plasmon calculations," Phys. Rev. B 262907-2916 (1982). [CrossRef]
  26. J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J. Opt. Paris 11, 235-241 (1980).
  27. M. Greenberg, Advanced Engineering Mathematics, 2nd ed., (Prentice Hall, 1998).
  28. G. H. Golub, C. F. Van Loan, Matrix computations, 3rd ed., (Johns Hopkins, Baltimore, 1996).
  29. P. M. van den Berg, "Reflection by a grating: Rayleigh methods," J. Opt. Soc. Am. 71, 1224-1229 (1981). [CrossRef]
  30. E. Popov, B. Chernov, M. Nevière, and N. Bonod, "Differential theory: Application to highly conducting gratings," J. Opt. Soc. Am. A 21, 199-206 (2004). [CrossRef]
  31. D. E. Knuth, The Art of Computer Programming, vol. 2: Seminumerical Algorithms, 3rd ed. (Reading, MA: Addison-Wesley, 1998).
  32. M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982). [CrossRef]
  33. A. G. Ramm, "Modified Rayleigh conjecture and applications," J. Phys. A 35, L357-L361 (2002). [CrossRef]
  34. J. A. Fawcett, "Modeling acousto-elastic waveguide/object scattering with the Rayleigh hypothesis," J. Acoust. Soc. Am. 106, 164-168 (1999). [CrossRef]
  35. N. Garcia, G. Armand, and J. Lapujoulade, "Diffraction intensities in helium scattering; Topographic curves," Surf. Sci. 68, 399-407 (1977). [CrossRef]
  36. V. Pan, "Complexity of computations with matrices and polynomials," SIAM Rev. 34, 225-262 (1992). [CrossRef]

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Fig. 1. Fig. 2.

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