Combining isolated scatterers into a dimer by strong optical coupling

Abstract

We analyze the transition between different coupling regimes of two dielectric rods, which occurs at a critical distance between them. The hallmark of a strong-coupling regime is the peak splitting effect observed in the spectra. Here, we comprehensively evaluate the critical distance as a function of the rod permittivity using a number of different approaches. The scattering spectra of the two rods in dependence on the distance demonstrate a weak-to-strong coupling transition. We start the analysis by introducing a region of a tidal energy flux around a single isolated rod (the region is related to the near field) and demonstrate that its effective radius corresponds to the critical distance obtained from the scattering spectra. Next, we study the eigenfrequencies of the dimer as functions of distance by ``diagonalizing'' the coupled multipole matrix. In order to find an analytical formula for the critical distance, we consider the problem under several approximations, which yield similar results.