Excitation of surface plasmon waves by 2D defects on metal surfaces: Analytical approach

Abstract

The excitation of surface plasmon polaritons (SPPs) by two-dimensional protrusions and depressions on a flat plasmonic metal surface illuminated by a normally incident plane wave is investigated. We employ an analytical approach treating SPPs as waveguide eigenmodes excited by a current source. A model is developed to describe the distribution of effective currents within Gaussian-profile protrusions and depressions responsible for SPP excitation. This approach extends beyond the classical Born approximation for the electromagnetic field intensity inside inhomogeneities by introducing corrections to account for polarization effects. This allows us to derive analytical expressions describing the dimensional (dependence on inhomogeneity size) and spectral (wavelength dependence) characteristics of the SPP response of such structures. The presented theory shows good agreement with the results of full-wave numerical simulations. The proposed approach also demonstrates the difference in SPP response between isolated protrusions/depressions and their arrays forming a periodic corrugation on the metal surface. It is shown that, in the case of sinusoidal gratings, polarization corrections—which are significant for individual inhomogeneities—are not required to quantify the resonant SPP response at the fundamental spatial frequency of the corrugation. The proposed analytical framework reduces computational costs and may serve as a useful tool for the design of nanophotonic devices and plasmonic metamaterials with desired optical properties.