We describe a powerful and intuitive technique for modeling light-matter interactions in classical and quantum nanoplasmonics. Our approach uses a quasinormal mode expansion of the Green function within a metal nanoresonator of arbitrary shape, toget
her 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 quasinormal mode, 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 LDOS 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 quasinormal mode theory.
We demonstrate tunable frequency-converted light mediated by a chi-(2) nonlinear photonic crystal nanocavity. The wavelength-scale InP-based cavity supports two closely-spaced localized modes near 1550 nm which are resonantly excited by a 130 fs lase
r pulse. The cavity is simultaneously irradiated with a non-resonant probe beam, giving rise to rich second-order scattering spectra reflecting nonlinear mixing of the different resonant and non-resonant components. In particular, we highlight the radiation at the sum frequencies of the probe beam and the respective cavity modes. This would be a useful, minimally-invasive monitor of the joint occupancy state of multiple cavities in an integrated optical circuit.
