Dielectric Response of a Planar Periodic Array of Polarizable Wires Parallel to an Interface with a Nonlocal Dynamic Plasma-like Medium

We examine the spatially inhomogeneous polarizability and dielectric function of the combined Coulomb-coupled system of a periodic lateral lattice array of polarizable 1D wire plasmas and a semi-infinite bulk plasma nearby. Furthermore, we carry out an exact closed form analytic solution of the spatially inhomogeneous random phase approximation integral equation for the dynamic nonlocal screening function, K(r⃗,t;r⃗′,t′) which is the space-time matrix inverse of the inhomogeneous dielectric function ε(r⃗,t;r⃗′,t′) in the sense ∫d³xdτK(r⃗,t;x⃗,τ)ε(x⃗,τ;r⃗′,t′) = δ³(r⃗ - r⃗′)δ(t - t′). In this work we also determine the exact dispersion relation coupling the periodic wire lattice plasmons with the semi-infinite bulk plasmon, and the residues of the screening function at the coupled mode frequencies provide the relative excitation amplitudes (oscillator strengths) of the various plasmon roots that emerge.