A contour integral-based method for nonlinear eigenvalue problems for semi-infinite photonic crystals

IF 7.2 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computer Physics Communications Pub Date : 2024-09-30 DOI:10.1016/j.cpc.2024.109377

Xing-Long Lyu , Tiexiang Li , Wen-Wei Lin

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Abstract

In this study, we introduce an efficient method for determining isolated singular points of two-dimensional semi-infinite and bi-infinite photonic crystals, equipped with perfect electric conductor and quasi-periodic mixed boundary conditions. This specific problem can be modeled by a Helmholtz equation and is recast as a generalized eigenvalue problem involving an infinite-dimensional block quasi-Toeplitz matrix. Through an intelligent implementation of cyclic structure-preserving matrix transformations, the contour integral method is elegantly employed to calculate the isolated eigenvalue and to extract a component of the associated eigenvector. Moreover, a propagation formula for electromagnetic fields is derived. This formulation enables rapid computation of field distributions across the expansive semi-infinite and bi-infinite domains, thus highlighting the attributes of edge states. The preliminary MATLAB implementation is available at https://github.com/FAME-GPU/2D_Semi-infinite_PhC.

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基于轮廓积分的半无限光子晶体非线性特征值问题方法

在本研究中，我们介绍了一种确定二维半无限和双无限光子晶体孤立奇异点的有效方法，该晶体配有完美电导体和准周期混合边界条件。这一具体问题可以用亥姆霍兹方程建模，并被重构为涉及无限维块准托普利兹矩阵的广义特征值问题。通过循环结构保留矩阵变换的智能实现，轮廓积分法被优雅地用于计算孤立特征值和提取相关特征向量的一个分量。此外，还推导出了电磁场的传播公式。这种公式可以快速计算扩展的半无限域和双无限域的场分布，从而突出边缘状态的属性。初步的 MATLAB 实现可在 https://github.com/FAME-GPU/2D_Semi-infinite_PhC 上获得。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.