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  1. Free, publicly-accessible full text available June 1, 2024
  2. Abstract We investigate an inverse scattering problem for a thin inhomogeneous scatterer in R m , m = 2, 3, which we model as an m − 1 dimensional open surface. The scatterer is referred to as a screen. The goal is to design target signatures that are computable from scattering data in order to detect changes in the material properties of the screen. This target signature is characterized by a mixed Steklov eigenvalue problem for a domain whose boundary contains the screen. We show that the corresponding eigenvalues can be determined from appropriately modified scattering data by using the generalized linear sampling method. A weaker justification is provided for the classical linear sampling method. Numerical experiments are presented to support our theoretical results. 
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  3. In this paper we consider the inverse problem of determining structural properties of a thin anisotropic and dissipative inhomogeneity in \begin{document}$ {\mathbb R}^m $\end{document}, \begin{document}$ m = 2, 3 $\end{document} from scattering data. In the asymptotic limit as the thickness goes to zero, the thin inhomogeneity is modeled by an open \begin{document}$ m-1 $\end{document} dimensional manifold (here referred to as screen), and the field inside is replaced by jump conditions on the total field involving a second order surface differential operator. We show that all the surface coefficients (possibly matrix valued and complex) are uniquely determined from far field patterns of the scattered fields due to infinitely many incident plane waves at a fixed frequency. Then we introduce a target signature characterized by a novel eigenvalue problem such that the eigenvalues can be determined from measured scattering data, adapting the approach in [20]. Changes in the measured eigenvalues are used to identified changes in the coefficients without making use of the governing equations that model the healthy screen. In our investigation the shape of the screen is known, since it represents the object being evaluated. We present some preliminary numerical results indicating the validity of our inversion approach

     
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  4. In recent years, a new approach has been proposed in the study of the inverse scattering problem for electromagnetic waves. In particular, a study is made of the analytic properties of the scattering operator, and the results of this study are used to design target signatures that respond to changes in the electromagnetic parameters of the scattering medium. These target signatures are characterized by novel eigenvalue problems such that the eigenvalues can be determined from measured scattering data. Changes in the structural properties of the material or the presence of flaws cause changes in the measured eigenvalues. In this article, we provide a general framework for developing target signatures and numerical evidence of the efficacy of new target signatures based on recently introduced eigenvalue problems arising in electromagnetic scattering theory for anisotropic media. 
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  5. We provide a graduate student accessible survey of the fascinating topic of transmission eigenvalues 
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  6. null (Ed.)
    This short note was motivated by our e orts to investigate whether there exists a half plane free of transmission eigenvalues for Maxwell's equations. This question is related to solvability of the time domain interior transmission problem which plays a fundamental role in the justi cation of linear sampling and factorization methods with time dependent data. Our original goal was to adapt semiclassical analysis techniques developed in [21, 23] to prove that for some combination of electromagnetic parameters, the transmission eigenvalues lie in a strip around the real axis. Unfortunately we failed. To try to understand why, we looked at the particular example of spherically symmetric media, which provided us with some insight on why we couldn't prove the above result. Hence this paper reports our ndings on the location of all transmission eigenvalues and the existence of complex transmission eigenvalues for Maxwell's equations for spherically strati ed media. We hope that these results can provide reasonable conjectures for general electromagnetic media. 
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  7. null (Ed.)