The two-dimensional electromagnetic inverse scattering problem for chiral media

Gerlach, Thomas

doi:10.1088/0266-5611/15/6/315

Cited by 16 publications

(10 citation statements)

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“…However, to the knowledge of the author, the number of works related to the inverse problem for chiral media is relatively small. Results on uniqueness can be found in [6,7,16,[31][32][33]41]. The paper [16] has further presented an iterative method of Newton-type for identifying shape of two-dimensional chiral scatterers.…”

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confidence: 99%

The factorization method for the Drude-Born-Fedorov model for periodic chiral structures

Nguyen¹

2016

IPI

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We consider the electromagnetic inverse scattering problem for the Drude-Born-Fedorov model for periodic chiral structures known as chiral gratings both in R 2 and R 3. The Factorization method is studied as an analytical as well as a numerical tool for solving this inverse problem. The method constructs a simple criterion for characterizing shape of the periodic scatterer which leads to a fast imaging algorithm. This criterion is necessary and sufficient which gives a uniqueness result in shape reconstruction of the scatterer. The required data consists of certain components of Rayleigh sequences of (measured) scattered fields caused by plane incident electromagnetic waves. We propose in this electromagnetic plane wave setting a rigorous analysis for the Factorization method. Numerical examples in two and three dimensions are also presented for showing the efficiency of the method.

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confidence: 99%

The factorization method for the Drude-Born-Fedorov model for periodic chiral structures

Nguyen¹

2016

IPI

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“…Indeed, this follows from (3.50) and the point (9) in Proposition 3.8. Note that (3.54) and (3.55) prove the p = 2-version of the decomposition we seek.…”

Section: )mentioning

confidence: 76%

“…also [4], [15] and [16]. The papers [23], [3] deal with transmission problems, [1] studies the behavior of the solution with respect to the chirality parameter, while [9] considers a two-dimensional inverse problem. See also [2], [11] for related work and more references.…”

Section: Theorem 13mentioning

confidence: 99%

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The method of layer potentials for electromagnetic waves in chiral media

Mitrea¹

2001

Forum Mathematicum

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Statement of the problem and main results Let Ω be a bounded domain in R 3 , with surface measure dσ and outward unit normal n. Throughout the paper we shall assume that Ω is Lipschitz (i.e., ∂Ω can be locally described by means of graphs of Lipschitz continuous functions in appropriate systems of coordinates) and that ∂Ω is connected. Also, we set Ω + := Ω and Ω − := R 3 \Ω. The classical Faraday-Amperé-Maxwell equations in Ω + or Ω − read curl E = iωB,

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“…The solution depends continuously on the data as expressed in (3.4). §4 Uniqueness of solution for the inverse scattering problem In [8], Gerlach studied the uniqueness of inverse problem by the point source method. In this section we discuss the uniqueness result by another method.…”

Section: Problem 1 (Direct Problem) For Given Incident Fieldsmentioning

confidence: 99%

Analysis of two-dimensional electromagnetic scattering by a perfectly conducting obstacle in a homogeneous chiral environment

Gao

Zhang

2007

Appl. Math. Chin. Univ.

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The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered. A two-dimensional direct scattering model is established and the existence and uniqueness of solutions to the problem are discussed by an integral equation approach. The inverse scattering problem to find the shape of scatterer with the given far-field data is formulated. Result on the uniqueness of the inverse problem is proved. §1 IntroductionThe phenomenon of optical activity in special materials has been known since the beginning of the last century. In recent years chiral materials have been studied intensively in electromagnetic theory literature. Chiral media are examples of media responding with both electric and magnetic polarization to either electric or magnetic excitation. They can be characterized by a set of constitutive relations in which the electric and magnetic fields are coupled. In this paper we use the Drude-Born-Fedorov constitutive equations.Scattering by an obstacle in a chiral medium-although somewhat exotic at a first glanceconstitutes an attractive problem. Some illustrative examples are the turbid chiral media [1] , the Bruggeman homogenization of chiral composites [2] , the method of moments for scattering by a chiral obstacle in a chiral environment [1] ; and the solvability of the latter scattering problem is studied in [3].In this paper, a direct and an inverse scattering problems by a perfectly conducting obstacle in a homogeneous chiral environment are discussed. We confine ourselves to the two-dimensional case.We start our consideration with time-harmonic Maxwell's equationsReceived: 2005-12-16. MR Subject Classification: 65N06.

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The two-dimensional electromagnetic inverse scattering problem for chiral media

Cited by 16 publications

References 11 publications

The factorization method for the Drude-Born-Fedorov model for periodic chiral structures

The factorization method for the Drude-Born-Fedorov model for periodic chiral structures

The method of layer potentials for electromagnetic waves in chiral media

Analysis of two-dimensional electromagnetic scattering by a perfectly conducting obstacle in a homogeneous chiral environment

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