A point radiator parallel to a plane layer with negative refractive index

Focusing of an electromagnetic wave radiated by a point source and transmitted through a plane layer filled with a medium with negative refractive index is considered. An elementary electric Hertzian dipole located in the air (or vacuum) parallel to the boundaries of the layer is considered as a point source of radiation. It is rigorously shown that, after transmitting through a layer with negative refractive index, the electromagnetic wave of the dipole is focused into a certain domain. The dimensions of the focusing region are investigated. The results of the investigation show that the use of homogeneous materials with negative refraction does not allow one to overcome the diffraction limit.