Reflection and Transmission at a Parabolic-Cylinder Interface

The two-dimensional problem of the reflection and transmission of a plane electromagnetic wave symmetrically incident from either the convex or the concave side on a parabolic-cylinder interface separating two different media is solved exactly and in closed form, in the phasor domain. The two media are linear, lossless and isotropic, are either isorefractive or anti-isorefractive to each other, and are characterized by different intrinsic impedances. In the anti-isorefractive case, the double-negative metamaterial on one side of the interface has real negative permittivity and real negative permeability; because of causality, its refractive index is negative and its intrinsic impedance is positive [1]. Thus, the two media have real propagation constants of opposite sign, and real positive intrinsic impedances.