Title

Stable Implementation Of The Rigorous Coupled-Wave Analysis For Surface-Relief Gratings:Enhanced Transmittance Matrix Approach

Abstract

An enhanced, numerically stable transmittance matrix approach is developed and is applied to the implementation of the rigorous coupled-wave analysis for surface-relief and multilevel gratings. The enhanced approach is shown to produce numerically stable results for excessively deep multilevel surface-relief dielectric gratings. The nature of the numerical instability for the classic transmission matrix approach in thepresence of evanescent fields is determined. The finite precision of the numerical representation on digitalcomputers results in insufficient accuracy in numerically representing the elements produced by invertingan ill-conditioned transmission matrix. These inaccuracies will result in numerical instability in the calculations for successive field matching between the layers. The new technique that we present anticipatesand preempts these potential numerical problems. In addition to the full-solution approach whereby all thereflected and the transmitted amplitudes are calculated, a simpler, more efficient formulation is proposed forcases in which only the reflected amplitudes (or the transmitted amplitudes) are required. Incorporatingthis enhanced approach into the implementation of the rigorous coupled-wave analysis, we obtain numericallystable and convergent results for excessively deep (50 wavelengths), 16-level, asymmetric binary gratings.Calculated results are presented for both TE and TM polarization and for conical diffraction. © 1995 Optical Society of America.

Publication Date

1-1-1995

Publication Title

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volume

12

Issue

5

Number of Pages

1077-1086

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1364/JOSAA.12.001077

Socpus ID

0029306568 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0029306568

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