Recovery of an embedded obstacle and the surrounding medium for Maxwell's system

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

2 Scopus Citations
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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)2192-2209
Journal / PublicationJournal of Differential Equations
Volume267
Issue number4
Online published15 Mar 2019
Publication statusPublished - 5 Aug 2019
Externally publishedYes

Abstract

In this paper, we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric far-field data. The complex scatterer consists of an inhomogeneous medium and a possibly embedded perfectly electric conducting (PEC) obstacle. The far-field data are collected corresponding to incident plane waves with a fixed incident direction and a fixed polarisation, but frequencies from an open interval. It is shown that the embedded obstacle can be uniquely recovered by the aforementioned far-field data, independent of the surrounding medium. Furthermore, if the surrounding medium is piecewise homogeneous, then the medium can be recovered as well. Those unique recovery results are new to the literature. Our argument is based on low-frequency expansions of the electromagnetic fields and certain harmonic analysis techniques.

Research Area(s)

  • Embedded obstacle, Inverse electromagnetic scattering, Maxwell system, Surrounding medium, Uniqueness