Finite-difference time-domain technique as an efficient tool for obtaining the regularized Green function: applications to the local field problem in quantum optics for inhomogeneous lossy materials

TL;DR

This paper demonstrates that the finite-difference time-domain (FDTD) method effectively computes the regularized local density of states in lossy, inhomogeneous materials, resolving longstanding issues with divergence in Green function calculations in quantum optics.

Contribution

It shows that FDTD can accurately address the local field problem and compute the regularized Green function in arbitrary lossy inhomogeneous structures, including nanoplasmonic systems.

Findings

FDTD provides non-divergent LDOS calculations in lossy materials.

Excellent agreement with analytical results for nanoparticle cases.

FDTD is validated as an efficient tool for local field problems in quantum optics.

Abstract

The calculation of the local density of states (LDOS) in lossy materials has long been disputed due to the divergence of the homogeneous Green function with equal space arguments. For arbitrary shaped lossy structures, such as those of interest in nanoplasmonics, this problem is particular challenging. A non-divergent LDOS obtained in numerical methods like the finite-difference time-domain (FDTD), at first sight, appears to be wrong. Here we show that FDTD is not only an ideal choice for obtaining the regularized LDOS, but it can address the local field problem for any lossy inhomogeneous material. We exemplify the case of a finite-size photon emitter embedded within and outside a lossy metal nanoparticle, and show excellent agreement with analytical results.