Resolving an inverse problem through a momentum flow within the framework of electromagnetic scattering

Although there have been many approaches to inverse problem in the classic theory of potential scattering, they are implicitly confined to the analysis of the scattered electric field, and thus the magnetic counterpart of the scattered wave is ignored, which limits the further application of those approaches to some extent. Here, we propose a new, to the best of our knowledge, technique for an inverse problem within the framework of electromagnetic scattering. This technique aims at reconstructing the correlation function of the scattering potential of a random medium through measuring the electromagnetic momentum flow of the scattered field in the far zone. As illustrative examples, we use the technique to determine the correlation functions of the scattering potentials of homogeneous, isotropic, and Gaussian-correlated spheres. Our new inversion approach works both microscopically and macroscopically.