Uniqueness in inverse electromagnetic scattering problem with phaseless far-field data at a fixed frequency

Author:

Xu Xiaoxu1,Zhang Bo23,Zhang Haiwen4

Affiliation:

1. Beijing Computational Science Research Center, Beijing 100193, China

2. LSEC, NCMIS and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

4. NCMIS and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Abstract

Abstract This paper is concerned with uniqueness in inverse electromagnetic scattering with phaseless far-field pattern at a fixed frequency. In our previous work (2018,SIAM J. Appl. Math. 78, 3024–3039), by adding a known reference ball into the acoustic scattering system, it was proved that the impenetrable obstacle and the index of refraction of an inhomogeneous medium can be uniquely determined by the acoustic phaseless far-field patterns generated by infinitely many sets of superpositions of two plane waves with different directions at a fixed frequency. In this paper, we extend these uniqueness results to the inverse electromagnetic scattering case. The phaseless far-field data are the modulus of the tangential component in the orientations ${\boldsymbol{e}}_\phi $ and ${\boldsymbol{e}}_\theta $, respectively, of the electric far-field pattern measured on the unit sphere and generated by infinitely many sets of superpositions of two electromagnetic plane waves with different directions and polarizations. Our proof is mainly based on Rellich’s lemma and the Stratton–Chu formula for radiating solutions to the Maxwell equations.

Funder

National Natural Science Foundation of China

China Postdoctoral Science Foundation

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics

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