A UTD for the Radiation by Sources near Thin Planar Metamaterial Structures with a Discontinuity

The development of asymptotic high-frequency, uniform geometrical theory of diffraction (UTD) solutions, which will identify and quantify all the pertinent ray mechanisms for predicting, in a relatively simple closed form, the high frequency radiation characteristics of practical, planar, metamaterial (MTM) antenna structures is presented in this paper. In particular, the present analytical UTD development can, in a physically appealing manner, characterize the diffraction of incident ray fields, and especially the launching and diffraction of backward surface waves (BSWs), respectively, from the ends (or the truncation) of finite size MTM slabs, with or without a perfect electric conductor (PEC) or ground plane backing. The ansatz for the proposed solution is based on the Wiener-Hopf (W-H) solution to a problem of the plane wave diffraction by a two part impedance surface. The present solutions are simpler to use because they do not contain the complicated split functions of the W-H solutions nor the complex Maliuzhinets functions. The present solutions recover the proper local plane wave Fresnel reflection and transmission coefficients and surface wave constants for the MTM. Besides being asymptotic solutions of the wave equation, the present UTD solutions, which are developed via a partially heuristic spectral synthesis approach, satisfy reciprocity, PEC boundary conditions, and the Karp-Karal lemma which dictates that the first order UTD space waves vanish on the material interface.