Rapid simulation of lossy resonators via a robust spatial map of Green's tensor

摘要

We obtain the spatial variation of Green's tensor of lossy resonators in both source and detector positions and orientations without repeated simulation. We construct a simple yet rigorous eigenmode expansion of Green's tensor, bypassing all implementation and interpretation issues associated with the alternative quasinormal eigenmode methods. Modes are defined by a linear eigenvalue problem with permittivity rather than frequency as the eigenvalue. Our simple general implemention using default in-built tools on COMSOL enables simulation of arbitrarily-shaped structures, such as bow-tie antennas. Few eigenmodes are necessary for nanostructures, facilitating both analytic calculations and unified insight into phenomena such as Purcell enhancement, radiative heat transfer, and van der Waals forces.