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Comparison of the beam-shaping effect of a field radiated by a line source, when an ideal infinite structure constituted by two photonic crystals and an actual finite one are considered, has been carried out by means of two different methods. The lattice sums technique combined with the generalized reflection matrix method is used to rigorously investigate the radiation from the infinite photonic crystals, whereas radiation from crystals composed of a finite number of rods along the layers is analyzed using the cylindrical-wave approach. A directive radiation is observed with the line source embedded in the structure. With an increased separation distance between the crystals, a significant edge diffraction appears that provides the main radiation mechanism in the finite layout. Suitable absorbers are implemented to reduce the above-mentioned diffraction and the reflections at the boundaries, thus obtaining good agreement between radiation patterns of a localized line source coupled to finite and infinite photonic crystals, when the number of periods of the finite structure is properly chosen.

Light scattering by a grating of the metal (Ag)-coated nanocylinders supported on the dielectric substrate is investigated using an accurate and rigorous formulation based on the recursive algorithm combined with the lattice sums technique. The proposed approach could be applied easily to the various configurations of the grating composed of the metal or metal-coated nanocylinders with different types and locations of the excitation sources. Special attention is paid to the three types of resonances: (a) surface plasmon resonances associated with the metal nanocylinders, (b) Rayleigh anomalies related with the periodic nature of the grating, and (c) resonances due to the coupling between the grating and the dielectric substrate. Near-field distribution of the magnetic field, which is parallel to the axis of the nanocylinders, is investigated numerically. Physical insight is given to the localization of the field along the interfaces of the metal nanocylinders, formation of the strong reflected field by the grating, and the field enhancement at the surface of the dielectric substrate. The accuracy of the numerical analyses has been tested based on the principle of the energy conservation. All these features are technologically important and have wide practical application from the viewpoint of the flexible design and fabrication of the plasmonic optical devices.

A self-contained coupled-mode theory for the coupled two asymmetric photonic crystal waveguides (PCWs) is presented. The first-order coupled-mode equations are derived under a weak coupling assumption. The coupling coefficients are obtained systematically by a matrix calculus using the modal solutions of each PCW in isolation. The coupled-mode equations are solved for contra-directional coupling between two asymmetric PCWs formed by a hexagonal lattice of circular air holes in a dielectric medium. The power transmission spectra at different output ports of the coupled PCWs are investigated. It is shown that the self-contained coupled-mode analysis is useful to characterize a peculiar feature of the contra-directionally coupled PCWs as a drop filter.

A self-contained coupled-mode formulation for coupled two-dimensional photonic-crystal waveguides (PCWs) is discussed. Using a perturbation theory, the first-order coupled-mode equations are systematically derived, which govern the evolution of the modal amplitude of individual PCWs in isolation. The coupled-mode equations are used to analyze the coupled symmetric PCWs consisting of a square lattice of circular dielectric rods or air holes. It is shown that the results are in good agreement with those obtained by the rigorous direct analysis of the coupled waveguide system.