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

Youjun Deng, Hongyu LIU*, Xiaodong Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)2192-2209
Number of pages18
JournalJournal of Differential Equations
Volume267
Issue number4
DOIs
Publication statusPublished - 5 Aug 2019

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

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

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