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

    Authors

    M. G. Moharam; E. B. Grann; D. A. Pommet;T. K. Gaylord

    Comments

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    Abbreviated Journal Title

    J. Opt. Soc. Am. A-Opt. Image Sci. Vis.

    Keywords

    SURFACE-RELIEF GRATINGS; DIFFRACTION ANALYSIS; Optics

    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 for the 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 potential numerical 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 of harmonics on the convergence of the diffraction efficiencies is investigated. More field harmonics are shown to be required for the convergence of gratings with larger grating periods, deeper gratings, TM polarization, and conical diffraction.

    Journal Title

    Journal of the Optical Society of America a-Optics Image Science and Vision

    Volume

    12

    Issue/Number

    5

    Publication Date

    1-1-1995

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    1068

    Last Page

    1076

    WOS Identifier

    WOS:A1995QV02900027

    ISSN

    0740-3232

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