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This paper presents an analytical and numerical investigation of the radiation features of an interesting class of electromagnetic bandgap (EBG) structures excited by an electric line source. The radiation from two-dimensional (2-D) lattices made with lossless dielectric cylinders, typically optimized by using the Bloch analysis of the corresponding 2-D photonic crystals, are originally investigated in terms of leaky waves. A thorough modal analysis of open waveguides, composed by a finite number of periodic chains of circular dielectric rods, is presented that shows a multiplicity of bound and leaky modes. Two radiation windows are identified and the relevant directive features are described in terms of properly excited dominant leaky modes. The possible excitation of higher order leaky modes and guided modes has been carefully considered, by also capturing the relevant residue contributions in a nonspectral representation of the excited fields. The final results on radiated fields by realistic truncated structures, obtained by ad-hoc software as well as full-wave EM simulators, are in excellent agreement with those predicted by the proposed leaky-wave approach.

A full-wave numerical approach for the analysis of bounded and leaky modes in periodic chain composed of both lossless and lossy 2-D cylindrical inclusions is proposed. An effective method based on the lattice sums technique is adapted to the analysis of modes with complex propagation wavenumbers, thus allowing for the appropriate choice of the spectral determination for each spatial harmonic. Periodic chains of both dielectric and silver nanocylinders are studied and the relevant modal phase and attenuation constants are rigorously calculated in all the different propagation regimes, including bound and radiative regions as well as plasmonic behaviors.

Electromagnetic Band-Gap (EBG) media, working right above the band-gap can shape the radiation of a simple emitter embedded in their periodic structures. In this region of the dispersion diagram, degenerate lattice modes can be selectively excited with a proper positioning of the primary sources. This paper presents the design of an antenna that exploits such physical mechanism, which is potentially attractive at mm-waves since it relies on dielectric structures. An antenna fed by two sources and based on a square lattice of dielectric cylinders is presented. For the first time, the dependences of radiation properties on some geometrical parameters are investigated before moving to a final realistic design.