Electromagnetic scattering by an elliptic DNG metamaterial cylinder

The geometry analyzed in this work consists of an infinite cylinder of elliptical cross section made of a DNG metamaterial whose permittivity and permeability are real and opposite to the corresponding parameters in the surrounding space. Under these conditions, it is known that causality requires that the refractive index of the DNG metamaterial be negative, whereas its intrinsic impedance must be positive. The primary field is a plane wave of arbitrary polarization propagating in a direction perpendicular to the axis of the cylinder. The electromagnetic fields inside and outside the cylinder are expressed in terms of infinite series of elliptic-cylinder wave functions, involving products of radial and angular Mathieu functions. The simple relations that exist between Mathieu functions with real parameters of opposite sign allows one to determine explicitly the modal expansion coefficients in the infinite series of eigenfunctions, thus yielding an exact analytical solution to the boundary-value problem. Numerical results are shown and discussed.