A sampling method for the inverse transmission problem for periodic media

Yang, Jiaqing; Zhang, Bo; Zhang, Ruming

doi:10.1088/0266-5611/28/3/035004

Cited by 20 publications

(27 citation statements)

References 14 publications

(15 reference statements)

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“…We refer to [10,11,15,25] for an account of recent developments of these methods. The case of periodic media has been treated by several authors and without being exhaustive, we refer to [1,2,17,22,30,31,33,36]. For the inverse problem in locally perturbed periodic waveguides we refer to [8,34] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Sampling methods for reconstructing the geometry of a local perturbation in unknown periodic layers

Haddar¹,

Nguyen²

2017

Computers & Mathematics with Applications

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International audienceThis paper is dedicated to the design and analysis of sampling methods to reconstruct the shape of a local perturbation in a periodic layer from measurements of scattered waves at a fixed frequency. We first introduce the model problem that corresponds with the semi-discretized version of the continous model with respect to the Floquet-Bloch variable. We then present the inverse problem setting where (propagative and evanescent) plane waves are used to illuminate the structure and measurements of the scattered wave at a parallel plane to the periodicity directions are performed. We introduce the near field operator and analyze two possible factorizations of this operator. We then establish sampling methods to identify the defect and the periodic background geometry from this operator measurement. We also show how one can recover the geometry of the background independently from the defect. We then introduce and analyze the single Floquet-Bloch mode measurement operators and show how one can exploit them to built an indicator function of the defect independently from the background geometry. Numerical validating results are provided for simple and complex backgrounds

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Section: Introductionmentioning

confidence: 99%

Sampling methods for reconstructing the geometry of a local perturbation in unknown periodic layers

Haddar¹,

Nguyen²

2017

Computers & Mathematics with Applications

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“…One can find recent developments of the linear sampling method in [10,11]. The linear sampling method has been extended to inverse scattering involving periodic media, in [15,16,33]. However, in spite of the advantages of the method, a full mathematical justification still remains open, see [10].…”

Section: Introductionmentioning

confidence: 99%

Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

Lechleiter¹,

Nguyen²

2013

SIAM J. Imaging Sci.

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This paper is concerned with the inverse scattering problem of electromagnetic waves from penetrable biperiodic structures in three dimensions. We study the Factorization method as a tool for reconstructing the periodic media from measured data consisting of scattered electromagnetic waves for incident plane electromagnetic waves. We propose a rigorous analysis for the method. A simple criterion is provided to reconstruct the biperiodic structures. We also provide three-dimensional numerical experiments to indicate the performance of the method.

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“…There also exist some numerical methods in reconstructing periodic structures. For example, a linear sampling method was developed in [20,22] for determining the shape of partially coated bi-periodic structures, and in [35] a novel linear sampling method was introduced for simultaneously reconstructing dielectric grating structures in an inhomogeneous periodic medium. See also [10] for a finite element method or [3,4,17] for the factorization method in determining the periodic structures, or [30] for the uniquely reconstruction of a locally perturbed infinite plane.…”

Section: Introductionmentioning

confidence: 99%

A novel method in determining a layered periodic structure

Cui

2020

Bound Value Probl

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This paper is concerned with the inverse scattering of time-harmonic waves by a penetrable structure. By applying the integral equation method, we establish the uniform $L^{p}_{\alpha }\ (1< p\leq 2)$ L α p ( 1 < p ≤ 2 ) estimates for the scattered and transmitted wave fields corresponding to a series of incident point sources. Based on these a priori estimates and a mixed reciprocity relation, we prove that the penetrable structure can be uniquely identified by means of the scattered field measured only above the structure induced by a countably infinite number of quasi-periodic incident plane waves.

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A sampling method for the inverse transmission problem for periodic media

Cited by 20 publications

References 14 publications

Sampling methods for reconstructing the geometry of a local perturbation in unknown periodic layers

Sampling methods for reconstructing the geometry of a local perturbation in unknown periodic layers

Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

A novel method in determining a layered periodic structure

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