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

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. Introduction and background . When small metallic particles with dimensions much less than a wavelength (MNP) are illuminated with a beam of light, typically from a laser, the electric field strength at certain locations just outside of the metal surface can be enhanced by many orders of magnitude in comparison to the strength of the electric field from the laser beam that excites the particle. Many fields of science and sensor engineering have taken advantage of this property to boost the effective coupling strength of light to molecules or artificial atoms located near the MNP. Main result(s) . The largest field enhancements occur when the exciting radiation resonantly excites collective plasmon oscillations of the free electrons in the MNP. The resonant frequencies of the plasmon modes and the degree of field enhancement depend critically on the shape of the MNP, but analytic solutions are only available for spheres. Accurate numerical models needed for non-spherical geometries are extremely computational-time-intensive. The main result of this paper is a prescription for dramatically reducing the time required to numerically model the electromagnetic response of arbitrarily shaped MNP, assuming that only one or a small number of plasmon modes are involved in the problem. The approach described in the manuscript also offers considerable insight into the underlying mechanisms, that are typically obscured in brute force numerical simulations. As an example application, we study the enhanced spontaneous emission rate of a dipole emitter over a wide range of spatial positions and frequencies, and show excellent agreement with full numerical solutions. Wider implications . There is a rapidly growing "industry" of nanoplasmonic engineering, for both scientific and technological applications. The results of this work should benefit that community by offering intuitive insights that will help in the design of MNP shape and size for a particular application, and also greatly reduce the time required to obtain accurate numerical simulations of the systems response. Our quasianalytical approach can be applied to a wide range of problems in classical and quantum nanoplasmonics.

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