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PIER PIER B PIER C PIER M PIER Letters
2024-02-05
Fast Calculations of Vector Electromagnetics in 3D Periodic Structures Based on Multiple Scattering Theory and Broadband Green's Function
By
Leung Tsang,

    Professor Leung Tsang

    Department of Electrical Engineering and Computer Science

    University of Michigan

    USA

    Homepage

Tien-Hao Liao,

    Dr. Tien-Hao Liao

    Department of Electrical Engineering and Computer Science

    University of Michigan

    USA

    Homepage

Shurun Tan,

    Dr. Shurun Tan

    College of Information Science and Electronic Engineering

    Zhejiang University

    China

    Homepage

Xiaolan Xu,

    Dr. Xiaolan Xu

    California Institute of Technology

    USA

    Homepage

Xuyang Bai,

    Dr. Xuyang Bai

    Zhejiang University-University of Illinois at Urbana-Champaign Institute

    Zhejiang University

    China

    Homepage

Rouxing Gao

    Dr. Rouxing Gao

    University of Michigan

    USA

    Homepage

Progress In Electromagnetics Research, Vol. 179, 19-36, 2024
doi:10.2528/PIER23091003
Abstract
We have developed a fast method of using Multiple Scattering Theory-Broadband Green's Function (MST-BBGF) for band field calculations. In this paper, we successfully extended the method to the vector electromagnetic case of 3D periodic structures. In the MST-BBGF approach, the broadband transformation to vector spherical waves for 3D is derived using the Broadband Green's function. The band eigenvalue problem is expressed in terms of the single scatterer T matrix which is independent of the periodic lattice nor the Bloch vector. For the first five bands, the dimension of the KKR eigen equation is merely 6, as 6 vector spherical waves are utilized for the scattered waves. We make extensive comparisons of the results with the commercial software COMSOL in both accuracy and computation efficiency. The CPU requirementon a standard laptop for the MST-BBGF method is merely 0.309 seconds for the first 5 bands. The MST-BBGF method is accurate and is at least two orders of magnitude faster than commercial software COMSOL. In the band field calculations, we employ the approach of extended coefficient to use the low order eigenvector of 6 to extend to 240 vector spherical wave coefficients without the need of re-calculating the eigenvalue nor the eigenvector of the KKR equation. The extended coefficients approach gives accurate band field solutions for the entire (0,0,0) cell.
Citation
Leung Tsang, Tien-Hao Liao, Shurun Tan, Xiaolan Xu, Xuyang Bai, and Rouxing Gao, "Fast Calculations of Vector Electromagnetics in 3D Periodic Structures Based on Multiple Scattering Theory and Broadband Green's Function," Progress In Electromagnetics Research, Vol. 179, 19-36, 2024.
doi:10.2528/PIER23091003
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