Diffraction of a cylindrical wave by a perfectly conducting cylinder enclosed in a metamaterial shell with a negative refractive index

The problem of diffraction of a plane (cylindrical) wave by a perfectly conducting cylinder enclosed in a metamaterial shell is rigorously solved. The influence of the geometric dimensions of the shell, the value of the negative refractive index of the metamaterial medium, and the position of a cylindrical wave source on the field structure in the near zone of the scatterer is investigated. It is found that, in the quasi-optical range of the problem parameters, this structure does not exhibit ideal focusing. It is shown that, there are two types of caustics inside the shell. The first type is related with rays reflected by the surface of the interior cylinder and has one cusp point, and the second type is formed by the geometric-optics rays that are refracted by the outer boundary of the shell and do not fall on the surface of the interior perfectly conducting cylinder. The spatial distribution of the total field amplitude and of the equal-amplitude lines in the near zone of the scatterer is reported. The obtained numerical results are correctly interpreted from the physical viewpoint.