Directive radiation from a line source in a metamaterial slab with low permittivity

An investigation is made into the directive radiation patterns produced by an electric line source inside of a low-permittivity metamaterial slab over a ground plane. The metamaterial slab is modeled as a homogeneous slab with a plasma-like dispersive permittivity. For low values of the slab permittivity, a very directive beam pointing at broadside can be obtained. Conditions for the maximization of the power density radiated at broadside are given, and it is shown that the directive radiation effect at broadside is due to a leaky mode supported by the slab with small and nearly equal values of the phase and attenuation constants. The frequency bandwidth and the directivity at broadside are also expressed in a simple closed form in terms of the attenuation constant of this leaky wave. Finally, numerical results are obtained for an actual metamaterial slab composed of metallic rods