Comparative features of electromagnetic scattering by an invisible spherically symmetric lens with a negative refractive index

A spherically symmetric lens with a negative refractive index, which can be invisible from the point of view of geometrical optics, is considered. Expressions describing the profile of the refractive index and ray trajectories in the lens, as well as some results of numerical modeling of plane wave scattering by the lens in the rigorous statement of the problem, are presented. It is detected that, unlike in the case of an invisible lens with a positive refractive index, the minima of the radar cross section in the forward direction corresponding to invisibility for the lens with a negative index occur at integer, rather than semi-integer, values of the electric radius, and that their depth is smaller because of the astigmatism associated with focusing of rays on the axis. Some results characterizing influence of losses in the lens on the level of the radar cross-section minima are also presented.