Uniqueness in phaseless inverse electromagnetic scattering problem with known superposition of incident electric dipoles

Abstract

In this paper, we consider the uniqueness of the phaseless inverse electromagnetic scattering problems. The phaseless data are the modulus of the tangential component of the far‐field pattern measured on the unit sphere and generated by the scatterer as well as the electric dipoles. Based on the superpositions of two electric dipoles with different positions and polarization vectors as the incident fields, the translation invariance property of the phaseless far‐field pattern corresponding to a single incident wave can be broken. A rigorous argument is given to illustrate that the location, shape, and boundary conditions of the obstacle or the refractive index of the medium can be uniquely determined by the phaseless far‐field data. Different from the existing method, we do not need to introduce an additional reference sphere. Thus our method makes the argument of uniqueness much simpler and clearer.