Nonlinear eigenvalue problems for coupled Helmholtz equations modeling gradient-index graphene waveguides

JOURNAL OF COMPUTATIONAL PHYSICS

卷:423

Article

Song, Jung Heon¹  Maier, Matthias²  Luskin, Mitchell¹ 

[1] Univ Minnesota, Sch Math, 206 Church St SE, Minneapolis, MN 55455 USA

[2] Texas A&M Univ, Dept Math, 3368 TAMU, College Stn, TX 77843 USA

关键词: Guided mode;    Time-harmonic Maxwell's equations;    Surface plasmon polariton;    Nonlinear eigenvalue problem;    Quartic eigenvalue problem;    Quadratification;   

DOI  :  10.1016/j.jcp.2020.109871

来源: Elsevier

【 摘 要 】

We discuss a quartic eigenvalue problem arising in the context of an optical waveguiding problem involving atomically thick 2D materials. The waveguide configuration we consider consists of a gradient-index (spatially dependent) dielectric equipped with conducting interior interfaces. This leads to a quartic eigenvalue problem with mixed transverse electric and transverse magnetic modes, and strongly coupled electric and magnetic fields. We derive a weak formulation of the quartic eigenvalue problem and introduce a numerical solver based on a quadratification approach in which the quartic eigenvalue problem is transformed to a spectrally equivalent companion problem. We verify our numerical framework against analytical solutions for prototypical geometries. As a practical example, we demonstrate how an improved quality factor (defined by the ratio of the real and the imaginary part of the computed eigenvalues) can be obtained for a family of gradient-index host materials with internal conducting interfaces. We outline how this result lays the groundwork for solving related shape optimization problems. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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