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.
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