Imaging of periodic dielectrics

Lechleiter, Armin

doi:10.1007/s10543-010-0255-7

Cited by 18 publications

(10 citation statements)

References 12 publications

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“…Since we are interested in numerical reconstructions, we will mainly discuss related results in this direction. We first refer to [1,2,[7][8][9]14,16,18,22,26,27] and references therein for an unexhausted list of results in the case of scalar equations of Helmholtz type. However, to our knowledge, there has been only a limited number of studies on numerical reconstructions for the case of full Maxwell's equations, see [4,10,15,20,24].…”

Section: Introductionmentioning

confidence: 99%

Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

Nguyen

Truong

2020

Journal of Inverse and Ill-Posed Problems

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This paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

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Section: Introductionmentioning

confidence: 99%

Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

Nguyen

Truong

2020

Journal of Inverse and Ill-Posed Problems

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“…Reconstruction using phaseless data for perfectly conducting grating profiles appeared in [6]. The factorization method and the linear sampling method were developed in [15] and [22], respectively. For shallow penetrable gratings, an iterative method was given in [17].…”

Section: Introductionmentioning

confidence: 99%

Efficient finite element method for grating profile reconstruction

Zhang

Sun

2015

Journal of Computational Physics

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“…There are several numerical methods for reconstructing diffraction gratings (see, e.g., [3][4][5] for the factorization method of Kirsch and [6][7][8][9] for an optimization method). The purpose of this paper is to study the important uniqueness issue for such inverse problems.…”

Section: Introductionmentioning

confidence: 99%

Uniqueness results in the inverse scattering problem for periodic structures

Yang

Zhang

2012

Math Methods in App Sciences

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This paper is concerned with the inverse electromagnetic scattering by a 2D (impenetrable or penetrable) smooth periodic curve. Precisely, we establish global uniqueness results on the inverse problem of determining the grating profile from the scattered fields corresponding to a countably infinite number of quasiperiodic incident waves. For the case of an impenetrable and partially coated perfectly reflecting grating, we prove that the grating profile and its physical property can be uniquely determined from the scattered field measured above the periodic structure. For the case of a penetrable grating, we show that the periodic interface can be uniquely recovered by the scattered field measured only above the interface. A key ingredient in our proofs is a novel mixed reciprocity relation that is derived in this paper for the periodic structures and seems to be new.

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Imaging of periodic dielectrics

Abstract: International audienc

Cited by 18 publications

References 12 publications

Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

Efficient finite element method for grating profile reconstruction

Uniqueness results in the inverse scattering problem for periodic structures

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