Scattering of light by a nanowire grating on a dielectric slab

Interaction of light with the metallic nanostructures gives rise to various novel effects in photonics and optoelectronics. Research of surface plasmons and their excitation by light is of particular interest in the studies of metamaterials, optical antennas, plasmonic sensors, and plasmonic crystals. The enhanced surface plasmon resonance in noble metallic systems at optical frequencies is expected to be a promising issue for realizing excellent scatterers and absorbers of the visible light. The surface plasmons characterize the unique response in collective motions of electrons on a metal-dielectric interface, which is allowed when the permittivity of the metal is negative for the wavelength of excitation. Recently, much attention has been paid to the light scattering from periodic nanowires coupled to a layered dielectric structure for their applications to optical sensors, imaging, and integrated devices. In this paper, we shall analyze the scattering of TE polarized plane wave by a nanowire grating supported on a dielectric slab by using a semi-analytical approach based on the recursive algorithm combined with the lattice sums technique. The nanowire grating consists of a periodic planar array of metal (Ag)-coated dielectric circular cylinders. In this approach, the reflection and transmission matrices of the planar array is firstly extracted and then a recursive formula is applied to derive the scattering matrix for the whole structure consisting of the grating and the dielectric slab. The method is straightforward and not time-consuming because the recursive relation is based on a simple matrix multiplication. The spectral responses in power reflection, transmission, absorption coefficients are numerically investigated. Numerical results demonstrate that there appear three types of resonant behaviors in the power transmission spectra of the nanowire grating supported on the dielectric slab. They are the Rayleigh anomalies characterized by the periodicity of the structure, the resonant interactions between the scattered fields and the guided waves propagating along the dielectric slab, and the localized surface plasmons resonances on the metal-coated dielectric cylinders. For these particular wavelengths, the power absorption resonantly increases and hence the power transmission is significantly decreased. Near field distributions are also calculated to show the localization of enhanced fields inside the dielectric slab or nanowires under the resonances. The accuracy of the numerical analyses is tested based on the principle of the energy conservation.