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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


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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

History
Original Manuscript: September 11, 1997
Revised Manuscript: January 13, 1998
Manuscript Accepted: January 26, 1998
Published: June 1, 1998

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

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