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

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