The problem of recovering the permittivity coefficient from the modulus of the scattered electromagnetic field (Q1675186)

The paper is about the problem of recovering the permittivity coefficient \(\varepsilon\) from given intensities of the scattering electromagnetic field. The information of the corresponding direct problem on the whole boundary of some compact domain \(\Omega\) is used to recover \(\varepsilon\) in \(\Omega\). The author studied the asymptotics of the solution to the direct problem with large frequency and showed that the recovering problem for the permittivity coefficient in the electrodynamic equations are reduced to the recovering problem for the refraction index from kinematic data, which is the inverse kinematic problem. In this paper, the uniqueness of the solution is established and a new method to construct the solution is provided.