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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.

An efficient and rigorous approach to analyze the radiation from an electric dipole placed in 3-D woodpile electromagnetic bandgap material (EBG) structures consisting of layered periodic arrays of circular cylinders is presented. The response in the spectral domain of the woodpile EBGs excited by a dipole source is calculated using one-dimensional lattice sums, the 3-D transition matrix of a circular cylinder, and the generalized reflection and transmission matrices of the layered system. The closed-form expression of the radiated field is rigorously obtained by a finite integral of the spectral response. Comparisons with the far fields calculated using reciprocity both with the present approach and with a fully independent commercial EM software package are presented showing excellent agreement with the proposed method and demonstrating the high computational efficiency of the semianalytical formalism.

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.

All-optical amplification of the light pulse in a weakly coupled nonlinear photonic crystal waveguides (PCWs) is proposed. We consider pillar-type PCWs, which consist of the periodically distributed circular rods made from a Kerr-type dielectric material. The operating frequency is properly chosen to be located at the edge of the dispersion diagram of the modes. In case of nonlinear medium when the amplitude of the injected signal is above some threshold value, solitons are formed and they are propagating inside the coupled nonlinear PCWs. Near field distributions of the light pulse and the output powers of the registered signals are studied in a detail. A good agreement between the numerical and theoretical studies is observed.