Analysis of directive radiation from a line source in a metamaterial slab with low permittivity

In this paper an investigation is presented of metamaterial structures excited by a line source aimed at producing narrow directive beams. The structure under consideration is a grounded slab made of a homogeneous metamaterial medium with a plasma-like dispersive permittivity; for low values of the slab permittivity an extremely directive beam pointing at broadside can be obtained. Conditions for the maximization of radiation at broadside are given and the narrow-beam effect is shown to be related to the excitation of a leaky mode supported by the slab, with radiation maximization corresponding to small and equal values of the phase and attenuation constants. The frequency bandwidth and directivity are expressed in a simple closed form in terms of the attenuation constant of the leaky mode. By increasing the slab height for a fixed frequency, the leaky mode is analytically shown to give rise to a beam that is scanned from broadside to the critical angle for plane-wave refraction, thus being confined to a narrow angular region around broadside. Numerical results are given that illustrate these features, and full-wave simulations of a metamaterial structure made of an array of metallic cylinders are presented that confirm the results of the analytical study. The case of a line source inside a semi-infinite metamaterial region is also considered and its radiation characteristics compared with those of the metamaterial slab