Reciprocity theorem for nonlocal optics: completion of proof and application to spectroscopic analysis

The problem of optical reciprocity in the long wavelength limit is considered in terms of the symmetry for the scalar Green’s function under the Neumann boundary conditions, for materials with nonlocal and anisotropic dielectric responses. This extends the previous works in the literature which were limited either to the Dirichlet conditions or to cases of perfect conductor and local dielectric response. Application of this symmetry principle to the analysis of surface-enhanced spectroscopy for a molecule near a metallic nanoparticle is demonstrated, accounting for the nonlocal response of the particle.