Full wave analysis of plane wave diffraction by a finite sinusoidal grating: E-polarization case

Elena D. Vinogradova, Kazuya Kobayashi, Toru Eizawa

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    Plane wave diffraction studies of a finite sinusoidal grating have previously assumed that the grating length is large in wavelengths and the depth of its corrugations is small compared to a wavelength. This paper introduces a rigorous technique, the Method of Analytical Regularization (MAR), which removes these restrictions. The solution obtained by this method is free from limitations on the parameters of sinusoidal grating and possesses the capability to achieve predetermined accuracy of computations uniformly in a wide frequency band. The results of previous studies, which employed the Wiener-Hopf technique combined with a perturbation method, are compared with those obtained by the MAR; excellent concordance of results in the common parameter regimes of applicability of both methods is found. The different regimes of applicability of each approach are identified; within these, the MAR provides effective and efficient solutions to benchmark problems for testing other approximate techniques.
    LanguageEnglish
    Pages44-62
    Number of pages19
    JournalWave Motion
    Volume86
    DOIs
    Publication statusPublished - 1 Mar 2019

    Fingerprint

    Wave Diffraction
    wave diffraction
    Diffraction gratings
    Plane Wave
    Gratings
    plane waves
    Polarization
    Diffraction
    gratings
    Wavelength
    polarization
    Regularization
    Frequency bands
    wavelengths
    Wiener-Hopf Technique
    constrictions
    Testing
    Concordance
    perturbation
    Perturbation Method

    Keywords

    • scattering of E-polarized plane wave
    • finite sinusoidal grating
    • method of analytical regularization
    • Wiener-Hopf technique combined with perturbation method
    • efficient computational algorithm in wide frequency band
    • Floquet modes for finite grating

    Cite this

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    abstract = "Plane wave diffraction studies of a finite sinusoidal grating have previously assumed that the grating length is large in wavelengths and the depth of its corrugations is small compared to a wavelength. This paper introduces a rigorous technique, the Method of Analytical Regularization (MAR), which removes these restrictions. The solution obtained by this method is free from limitations on the parameters of sinusoidal grating and possesses the capability to achieve predetermined accuracy of computations uniformly in a wide frequency band. The results of previous studies, which employed the Wiener-Hopf technique combined with a perturbation method, are compared with those obtained by the MAR; excellent concordance of results in the common parameter regimes of applicability of both methods is found. The different regimes of applicability of each approach are identified; within these, the MAR provides effective and efficient solutions to benchmark problems for testing other approximate techniques.",
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    Full wave analysis of plane wave diffraction by a finite sinusoidal grating : E-polarization case. / Vinogradova, Elena D.; Kobayashi, Kazuya; Eizawa, Toru.

    In: Wave Motion, Vol. 86, 01.03.2019, p. 44-62.

    Research output: Contribution to journalArticleResearchpeer-review

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    T1 - Full wave analysis of plane wave diffraction by a finite sinusoidal grating

    T2 - Wave Motion

    AU - Vinogradova, Elena D.

    AU - Kobayashi, Kazuya

    AU - Eizawa, Toru

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    AB - Plane wave diffraction studies of a finite sinusoidal grating have previously assumed that the grating length is large in wavelengths and the depth of its corrugations is small compared to a wavelength. This paper introduces a rigorous technique, the Method of Analytical Regularization (MAR), which removes these restrictions. The solution obtained by this method is free from limitations on the parameters of sinusoidal grating and possesses the capability to achieve predetermined accuracy of computations uniformly in a wide frequency band. The results of previous studies, which employed the Wiener-Hopf technique combined with a perturbation method, are compared with those obtained by the MAR; excellent concordance of results in the common parameter regimes of applicability of both methods is found. The different regimes of applicability of each approach are identified; within these, the MAR provides effective and efficient solutions to benchmark problems for testing other approximate techniques.

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    KW - Wiener-Hopf technique combined with perturbation method

    KW - efficient computational algorithm in wide frequency band

    KW - Floquet modes for finite grating

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