Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics

Abstract

We describe a powerful and intuitive theoretical technique for modeling light-matter interactions in classical and quantum nanoplasmonics. Our approach uses a quasinormal mode (QNM) expansion of the photon Green function within a metal nanoresonator of arbitrary shape, together with a Dyson equation, to derive an expression for the spontaneous decay rate and far field propagator from dipole oscillators outside resonators. For a single QNM, at field positions outside the quasi-static coupling regime, we give a closed form solution for the Purcell factor and generalized effective mode volume. We augment this with an analytic expression for the divergent local density of optical states very near the metal surface, which allows us to derive a simple and highly accurate expression for the electric field outside the metal resonator at distances from a few nanometers to infinity. This intuitive formalism provides an enormous simplification over full numerical calculations and fixes several pending problems in QNM theory.