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

## TL;DR

This paper introduces a finite element method to compute the regularized photon Green function in lossy materials, addressing divergence issues and validating results against analytical models for various structures.

## Contribution

A novel finite element approach for calculating the regularized photon Green function in lossy media, applicable to complex geometries and validated with analytical solutions.

## Key findings

- Excellent agreement with analytical results for homogeneous lossy materials.
- Accurate calculation of scattered Green function in metal nano-spheres.
- Method effectively regularizes divergence in photon Green function calculations.

## Abstract

Photon Green function (GF) is the vital and most decisive factor in the field of quantum light-matter interaction. It is divergent with two equal space arguments in arbitrary-shaped lossy structure and should be regularized. We introduce a finite element method for calculating the regularized GF. It is expressed by the averaged radiation electric field over the finite-size of the photon emitter. For emitter located in homogeneous lossy material, excellent agreement with the analytical results is found for both real cavity model and virtual cavity model. For 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.