Diffraction of plane and cylindrical waves by a cylindrical metamaterial shell with a negative refractive index

The problems of scattering of plane and cylindrical waves by a cylindrical metamaterial shell are solved rigorously. The influence of the geometric dimension of the shell, the value of the negative refractive index of the metamaterial medium, and the location of the cylindrical wave source on the near (far) field structure is investigated. It is shown that, in the quasi-opticl region, a caustic with one cusp is formed inside an electrically thick shell and whispering-gallery waves or standing waves are formed in between the facets of an electrically thin shell. It is found that, in the resonance region, reactive (surface) fields with substantial amplitudes are observed near the boundaries of a thin shell.