Determination of electromagnetic Bloch variety in a medium with frequency-dependent coefficients

被引：7

作者：

Lackner, C. ^{[1
]}

Meng, S. ^{[2
]}

Monk, P. ^{[3
]}

机构：

[1] Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 358卷

基金：

奥地利科学基金会; 美国国家科学基金会;

关键词：

Bloch variety; Quadratic eigenvalue; Composite materials; Frequency-dependent materials; BAND-STRUCTURE CALCULATIONS; FINITE-ELEMENTS; APPROXIMATION;

D O I：

10.1016/j.cam.2019.03.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a functional framework and a numerical algorithm to compute the Bloch variety for Maxwell's equations when the electric permittivity is frequency dependent. We incorporate the idea of a mixed formulation for Maxwell's equations to obtain a quadratic eigenvalue for the wave-vector in terms of the frequency. We reformulate this problem as a larger linear eigenvalue problem and prove that this results in the need to compute eigenvalues of a compact operator. Using finite elements, we provide preliminary numerical examples of the scheme for both frequency independent and frequency dependent permittivity. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：359 / 373

页数：15

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