Wave dynamics by a plane wave on a half-space metamaterial made of plasmonic nanospheres: a discrete Wiener–Hopf formulation

摘要

A rigorous analytical solution for the description of wave dynamics originated at the interface between a homogeneous\udhalf-space and a half-space metamaterial made by arrayed plasmonic nanospheres is presented. The solution\udis cast in terms of an exact analytical representation obtained via a discretized Wiener–Hopf (WH) technique\udassuming that each metallic nanosphere is described by the single dipole approximation. The solution analytically\udprovides and describes the wave species in the metamaterial half-space, their modal wavenumbers and launching\udcoefficients at the interface. It explicitly satisfies the generalized Ewald–Oseen extinction principle for periodic\udstructures, and it also provides a simple analytical solution for the reflection coefficient from the half-space. The\udpaper presents a new WH formulation for this class of problems for the first time, and describes the analytical\udsolution, which is also tested against a purely numerical technique. While only the case of orthogonal plane wave\udincidence and isotropic inclusions is considered here, the method can be easily generalized to the oblique incidence\udand anisotropic constituent (tensorial polarizability) cases.