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Validation and Numerical Convergence of the Hankel-Bessel and Mathieu Rigorous Coupled Wave Analysis Algorithms for Radially and Azimuthally --- Inhomogeneous, Elliptical, Cylindrical Systems

John Jarem

Dr. John Jarem

Electrical and Computer Engineering Department

University of Alabama in Huntsville

USA

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, Vol. 36, 153-177, 2002

doi:10.2528/PIER02012503 | Google Scholar

Abstract

A Rigorous Coupled Wave Analysis (RCWA) algorithm for electromagnetic (EM) scattering from radially and azimuthally inhomogeneous material elliptical systems based on State Variable (SV) techniques and based on circular-cylindrical Hankel-Bessel expansion modes is developed for the first time. The algorithm in conjunction with the elliptical system RCWA algorithm [1], which was based on SV techniques and Mathieu expansion modes, is used to validate and study numerical convergence of both elliptical RCWA algorithms. The formulation of the SV, Hankel-Bessel elliptical algorithm is presented. Two numerical elliptical examples are studied in detail by both algorithms, a homogeneous one which consists of three different uniform materials located in three elliptical regions and an inhomogeneous one which consists of an azimuthal, dielectric, step profile which is located between two uniform material elliptical regions. In this paper EM field scattering from a step profile which possessed a much larger dielectric step profile difference than was studied in [1] is presented. Validation and numerical convergence data of the Hankel-Bessel and the Mathieu [1] RCWA algorithm is presented for the first time, both in plot figures and in tables, when different numbers of expansion modes were used, when different number of layers were used, and when different numbers of SV harmonics were used. Validation of the RCWA algorithms was further carried out for the homogeneous case, by using Mathieu expansion modes in all regions and was carried out by using Hankel-Bessel expansion modes and Mathieu expansion modes in different regions. Validation of the Hankel-Bessel and Mathieu [1] RCWA algorithms was observed to a high degree of accuracy. It was found for the numerical example tested, that the number of modes used in the RCWA algorithms needed to exceed a critical minimum value in order to obtain meaningful, accurate results, and after this critical number of modes was exceeded, that convergence occurred rapidly as the number of modes increased. It was also found that as the number of layers used in the algorithm increased that the numerical accuracy of the RCWA solution slowly increased.

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John Jarem, "Validation and Numerical Convergence of the Hankel-Bessel and Mathieu Rigorous Coupled Wave Analysis Algorithms for Radially and Azimuthally --- Inhomogeneous, Elliptical, Cylindrical Systems," , Vol. 36, 153-177, 2002.
doi:10.2528/PIER02012503

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