On the inverse scattering from anisotropic periodic layers and transmission eigenvalues

被引：3

作者：

Harris, Isaac ^{[1
]}

Nguyen, Dinh-Liem ^{[2
]}

Sands, Jonathan ^{[2
]}

Truong, Trung ^{[2
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Kansas State Univ, Dept Math, Manhattan, KS 66506 USA

来源：

APPLICABLE ANALYSIS | 2022年 / 101卷 / 08期

关键词：

Inverse scattering; Factorization method; transmission eigenvalues; anisotropic periodic structure; TM polarization; FACTORIZATION METHOD; GRATINGS;

D O I：

10.1080/00036811.2020.1836349

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the inverse scattering and the transmission eigenvalues for anisotropic periodic layers. For the inverse scattering problem, we study the Factorization method for shape reconstruction of the periodic layers from near field scattering data. This method provides a fast numerical algorithm as well as a unique determination for the shape reconstruction of the scatterer. We present a rigorous justification and numerical examples for the factorization method. The transmission eigenvalue problem in scattering have recently attracted a lot of attentions. Transmission eigenvalues can be determined from scattering data and they can provide information about the material parameters of the scatterers. In this paper, we formulate the interior transmission eigenvalue problem and prove the existence of infinitely many transmission eigenvalues for the scattering from anisotropic periodic layers.

引用

页码：3065 / 3081

页数：17

共 21 条

[1]

[Anonymous], 2008, Oxford Lecture Series in Mathematics and its Applications

[2]

[Anonymous], 2013, Inverse Problems

[3] A complete factorization method for scattering by periodic surfaces [J].