In this paper, radiation at broadside is studied for a general class of leaky-wave antennas (LWAs) comprised of a grounded slab covered with a partially reflecting surface, on the basis of a simple transverse equivalent network model of the structure. The analysis of the one-dimensional (1-D) version of such a LWA excited by a line source shows that a central role in establishing the features of broadside radiation is played by the condition that the phase and attenuation constants of the leaky mode responsible for radiation are equal. When this happens, a beam with a single peak at broadside is on the verge of splitting into two distinct peaks, and maximum power density is radiated at broadside. Design formulas to achieve such an optimized condition, as well as approximate expressions for the frequency bandwidth and pattern beamwidth of the antenna and for the leaky-wave phase and attenuation constants are derived, both in the absence and in the presence of losses; in addition, an optimal-beamwidth condition (which gives the narrowest broadside beam) is derived. Finally, all the results are extended to the practical case of a 2-D LWA excited by a horizontal dipole

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

This review paper summarizes various aspects of directive beaming and explains these aspects in terms of leaky waves. Directive beaming occurs in antenna design where a narrow beam is obtainable by using fairly simple planar structures excited by a single source. These structures include Fabry-Pérot cavity structures as well as metamaterial structures made from artificial low-permittivity media. Directive beaming also occurs in the optical area where it has been observed that highly directive beams can be produced from small apertures in a metal film when an appropriate periodic patterning is placed on the film. One aspect that these phenomena all have in common is that they are due to the excitation of one or more weakly attenuated leaky waves, the radiation from which forms the directive beam. This is established in each case by examining the role of the leaky waves in determining the near-field on the aperture of the structure and the far-field radiation pattern of the structure.

Analytical expressions are presented for the intraband conductivity tensor of graphene that includes spatial dispersion for arbitrarily wave-vector values and the presence of a nonzero Fermi energy. The conductivity tensor elements are derived from the semiclassical Boltzmann transport equation under both the relaxation-time approximation and the Bhatnagar-Gross-Krook model (which allows for an extra degree of freedom to enforce number conservation). The derived expressions are based on linear electron dispersion near the Dirac points, and extend previous results that assumed small wave-vector values; these are shown to be inadequate for the very slow waves expected on graphene nanoribbons. The new expressions are also compared to results obtained by numerical integration over the first Brillouin zone using the exact (tight-binding) electron dispersion relation. Very good agreement is found between the new analytical expressions and the exact numerical results. Furthermore, a comparison with the longitudinal random-phase conductivity is also made. It is shown analytically that these new expressions lead to the correct value of the quantum capacitance of a graphene sheet and that ignoring spatial dispersion leads to serious errors in the propagation properties of fundamental modes on graphene nanoribbons.

The problem of accelerating the calculation of the periodic Green's function is addressed here for both 3-D and 2-D free-space configurations. In the 3-D case, periodicity is considered both along one axis and along two, generally skew, axes. A comprehensive review of the existing methods is first presented and some extensions are developed. The possibility of treating the case of complex phase shifts between unit cells, necessary for the study of complex modes in periodic structures, is also investigated. Comparisons among the various acceleration methods are performed, thus providing fundamental information on their actual efficiency in typical problems.