High directivity in low-permittivity metamaterial slabs: Ray-optic vs. leaky-wave models

A study is presented on the directivity of grounded low-permittivity metamaterial slab structures that achieve highly directive broadside radiation. Two-dimensional (2D) configurations excited by electric line sources are considered, adopting a scalar plasma-like dispersive permittivity for the metamaterial medium that suitably models a wire medium in the presence of a 2D electromagnetic field, with the electric field directed along the wire axes. The role of leaky waves in producing the high directivity attainable with such structures is illustrated by comparing it with a simple ray-optic model for the radiation mechanism. We show how for increasing substrate heights, the leaky-wave effect (dominant for optimal thicknesses, and responsible for the very high directivity) evolves into a lensing effect purely explained with ray-optics, when losses are present. (c) 2006 Wiley Periodicals, Inc.