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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

  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 12 — Dec. 1, 2007
  • pp: 3781–3788

Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings

Nikolay M. Lyndin, Olivier Parriaux, and Alexander V. Tishchenko  »View Author Affiliations


JOSA A, Vol. 24, Issue 12, pp. 3781-3788 (2007)
http://dx.doi.org/10.1364/JOSAA.24.003781


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Abstract

The Fourier modal method (FMM), often also referred to as rigorous coupled-wave analysis (RCWA), is known to suffer from numerical instabilities when applied to low-loss metallic gratings under TM incidence. This problem has so far been attributed to the imperfect conditioning of the matrices to be diagonalized. The present analysis based on a modal vision reveals that the so-called instabilities are true features of the solution of the mathematical problem of a binary metal grating dealt with by truncated Fourier representation of Maxwell’s equations. The extreme sensitivity of this solution to the optogeometrical parameters is the result of the excitation, propagation, coupling, interference, and resonance of a finite number of very slow propagating spurious modes. An astute management of these modes permits a complete and safe removal of the numerical instabilities at the price of an arbitrarily small and controllable reduction in accuracy as compared with the referenced true-mode method.

© 2007 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory

ToC Category:
Diffraction and Gratings

History
Original Manuscript: August 20, 2007
Revised Manuscript: September 25, 2007
Manuscript Accepted: September 27, 2007
Published: November 21, 2007

Citation
Nikolay M. Lyndin, Olivier Parriaux, and Alexander V. Tishchenko, "Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings," J. Opt. Soc. Am. A 24, 3781-3788 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-12-3781

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