Finite-element method for obtaining the regularized photon Green function in lossy material

Abstract

The photon Green function (GF) is a vital and decisive factor in the field of quantum light-matter interaction. It is divergent with two equal space arguments in lossy structure and should be regularized. We introduce a finite-element method (FEM) for calculating the regularized GF in arbitrary-shaped lossy structure, which is expressed by the averaged radiation electric field over the finite size of a photon emitter. For an emitter located in a homogeneous lossy material, excellent agreement with the analytical results is found for both real and virtual cavity models. For an emitter located in a metal nano-sphere, the regularized scattered GF, which is the difference between the regularized GF and the analytical regularized one in homogeneous space, agrees well with the analytical scattered GF. Applying this method for an emitter located in a metal nano-rod where there is no analytical solution, we find that the scattering contribution to the enhancement of the spontaneous emission rate is nearly unrelated to the cavity radius while the homogeneous part depends heavily. Our results should be significant for novel photon sources within lossy structures.