Title

Formulation For Stable And Efficient Implementation Of The Rigorous Coupled-Wave Analysis Of Binary Gratings

Abstract

The rigorous coupled-wave analysis technique for describing the diffraction of electromagnetic waves by periodic grating structures is reviewed. Formulations for a stable and efficient numerical implementation of the analysis technique are presented for one-dimensional binary gratings for both TE and TM polarization and forthe general case of conical diffraction. It is shown that by exploitation of the symmetry of the diffraction problem a very efficient formulation, with up to an order-of-magnitude improvement in the numerical efficiency, is produced. The rigorous coupled-wave analysis is shown to be inherently stable. The sources of potentialnumerical problems associated with underflow and overflow, inherent in digital calculations, are presented. A formulation that anticipates and preempts these instability problems is presented. The calculated diffraction efficiencies for dielectric gratings are shown to converge to the correct value with an increasing number of space harmonics over a wide range of parameters, including very deep gratings. The effect of the number ofharmonics on the convergence of the diffraction efficiencies is investigated. More field harmonics are shownto be required for the convergence of gratings with larger grating periods, deeper gratings, TM polarization, and 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

1068-1076

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1364/JOSAA.12.001068

Socpus ID

0029307028 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0029307028

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