OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 6 — Jun. 1, 1998
  • pp: 1566–1576

Waterman and Rayleigh methods for diffraction grating problems: extension of the convergence domain

M. Bagieu and D. Maystre  »View Author Affiliations


JOSA A, Vol. 15, Issue 6, pp. 1566-1576 (1998)
http://dx.doi.org/10.1364/JOSAA.15.001566


View Full Text Article

Acrobat PDF (384 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We show that the Waterman method, a classical and rigorous method of electromagnetics for scattering by surfaces or objects, can be significantly improved. In a first step, it is shown, in the case of scattering by gratings, that the origin of the instabilities encountered in the numerical implementation of the method must be found in the ill conditioning of the equations. A well-adapted regularization process allows us to extend the domain of convergence of the method by a factor of approximately 40% in the range of groove depth for one-dimensional gratings and s polarization. Finally, we show that the same kind of regularization can extend the domain of convergence of the Rayleigh method.

© 1998 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(050.2770) Diffraction and gratings : Gratings
(260.2110) Physical optics : Electromagnetic optics
(290.0290) Scattering : Scattering

Citation
M. Bagieu and D. Maystre, "Waterman and Rayleigh methods for diffraction grating problems: extension of the convergence domain," J. Opt. Soc. Am. A 15, 1566-1576 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-6-1566


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. P. C. Waterman, “Scattering by periodic surfaces,” J. Acoust. Soc. Am. 57, 791–802 (1975).
  2. A. Wirgin, “Sur trois variantes de la théorie de Rayleigh de la diffraction d’une onde par une surface sinusoidale,” C.R. Acad. Sci. Ser. A 289, 259–262 (1979).
  3. A. Wirgin, “Aspects numeriques du problème de la diffraction d’une onde par une surface sinusoidale,” C. R. Acad. Sci. Ser. B 289, 273–276 (1979).
  4. Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London Ser. A 79, 399–415 (1907).
  5. Lord Rayleigh, The Theory of Sound (Dover, New York, 1945), Vol. 2.
  6. D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics XXI, E. Wolf, ed. (Elsevier, Amsterdam, 1984), pp. 1–67.
  7. D. Maystre, “Integral methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 63–100.
  8. J. Hadamard, Le problème de Cauchy (Hermann, Paris, 1932).
  9. K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed. (Springer-Verlag, Berlin, 1989).
  10. A. Tikhonov and V. Arsenine, Méthode de Résolution de Problèmes Mal Posés (Editions de Moscou, Moscow, 1976).
  11. N. Garcia, V. Celli, N. R. Hill, and N. Cabrera, “Illconditioned matrices in the scattering of waves from hard corrugated surfaces,” Phys. Rev. B 18, 5184–5189 (1978).
  12. G. Armand and J. R. Manson, “Scattering from a corrugated hard wall: comparison of boundary conditions,” Phys. Rev. B 19, 4091–4099 (1979).
  13. J. L. Uretsky, “The scattering of plane waves from periodic surfaces,” Ann. Phys. (New York) 33, 400–427 (1965).
  14. R. Petit, “Quelques propriétés des réseaux métalliques,” Opt. Acta 14, 301–310 (1967).
  15. D. Maystre and R. C. McPhedran, “Le théorème de réciprocité pour les réseaux de conductivité finie: démonstration et applications,” Opt. Commun. 12, 164–167 (1974).
  16. M. Cadilhac, “Some mathematical aspects of the grating theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980).
  17. M. Abramowitz and A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1968).
  18. R. Petit and M. Cadilhac, “Sur la diffraction d’une onde plane par un réseau infiniment conducteur,” C. R. Acad. Sci. 262, 468–471 (1966).
  19. A. Roger, D. Maystre, and M. Cadilhac, “On a problem of inverse scattering in optics: the dielectric inhomogeneous medium,” J. Opt. (Paris) 9, 83–90 (1978).
  20. J. M. Chesneaux and A. Wirgin, “Reflection from a corrugated surface revisited,” J. Acoust. Soc. Am. 96, 1116–1129 (1994).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited