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

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.