Communications in Mathematical Sciences

Volume 22 (2024)

Number 3

Analysis and computation for the scattering problem of electromagnetic waves in chiral media

Pages: 721 – 746

DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n3.a5

Authors

Gang Bao (School of Mathematical Sciences, Zhejiang University, Hangzhou, China)

Lei Zhang (Department of Mathematics, Zhejiang University of Technology, Hangzhou, China)

Abstract

This paper considers an obstacle scattering problem in a chiral medium under circularly polarized oblique plane wave incidence, which can be represented as a combination of a left-circularly polarized plane wave and a right-circularly polarized one. We apply a reduced model problem with coupled oblique derivative boundary conditions, describing the cross-coupling effect of electric and magnetic fields. A novel boundary integral equation is constructed by introducing single-layer potential operators and the corresponding normal and tangential derivative operators. The corresponding properties are obtained by splitting techniques to overcome the singularity of integral operators. A numerical method for solving the boundary integral equation is developed, whose convergence is proved. Numerical results are presented to show the performance of the proposed method.

Keywords

Maxwell’s equations, chiral medium, boundary integral equations, collocation method, convergence

2010 Mathematics Subject Classification

35Q61, 65N12, 65R20, 78A25

Full Text (PDF format)

Bao was supported by the National Natural Science Foundation of China (No. U21A20425), and by a Key Laboratory of Zhejiang Province, China.

Zhang was supported by the National Natural Science Foundation of China (No. 12271482), by the Zhejiang Provincial Natural Science Foundation of China (No. LZ23A010006; LY23A010004), and by the Scientific Research Starting Foundation (No. 2022109001429).

Received 13 November 2022

Received revised 13 July 2023

Accepted 22 August 2023

Published 4 March 2024