Rigorous expansion of electromagnetic Green's tensor of lossy resonators in open systems

We obtain an eigenmode expansion of the electromagnetic Green's tensor G(r,r') for lossy resonators in open systems, which is simple yet complete. This enables rapid simulations by providing the spatial variation of G⁰(r,r') over both r and r' in one simulation. Few eigenmodes are often necessary for nanostructures, facilitating both analytic calculations and unified insight into computationally intensive phenomena such as Purcell enhancement, radiative heat transfer, van der Waals forces, and Förster resonance energy transfer. We bypass all implementation and completeness issues associated with the alternative quasinormal eigenmode methods, by defining modes with permittivity rather than frequency as the eigenvalue. Thus, modes decay rather than diverge at infinity, and are defined by a linear eigenvalue problem, readily implemented using any numerical method. We demonstrate its general implementation in COMSOL Multiphysics, using the default in-built tools.