Surface wave diffraction by a sloping ´left-handed´ region

An exact analytical solution to the problem of surface wave diffraction by a penetrable `left-handed` medium (LHM) ε = μ = -1 material slope of arbitrary angle (subject to valid physical constraints) is presented. Standard analysis involving discontinuous angular eigenfunctions resulted in a discrete spectrum leading to a series solution that exhibits the expected negative refraction phenomenology. Numerical results are presented, some of which seemed paradoxical, but are explainable by classical ray optics means. A new type of illusory edge radiation is observed and explained. Although the exact solution applies to the lossless case only, it compares very favourably with independent finite difference time-domain (FDTD) solutions involving causal Lorentzian materials with small but significant loss. Since exact solutions for penetrable materials are virtually non-existent, the author`s solution represents a significant addition to the theory of surface wave diffraction.