Exact radiation by a line source located inside a confocal elliptic layer of DNG metamaterial

The two-dimensional problem of radiation from a line source encased inside an elliptic-cylinder confocal sheath of DNG metamaterial is solved exactly by separation of variables, utilizing series expansions of Mathieu functions. The radiation pattern is studied as a function of frequency, location of the line source along the major axis of the elliptical cavity, and thickness of the confocal sheath. A comparison of the exact solution with the geometrical optics solution of the problem is performed.