Quantum theory of radiative decay rate and frequency shift of surface plasmon modes

In this paper we study, in the time domain, the interaction between localized surface plasmons and photons in arbitrarily shaped metal nanoparticles, by using the Hopfield approach to quantize the plasmon modes, where the electron oscillations are represented by a harmonic matter field linearly coupled to the electromagnetic radiation. The plasmon-photon coupling gives rise to dressed plasmon modes. We have found that the radiation does not induce a significant coupling among the different quasielectrostatic plasmon modes for particles of size up to the plasma wavelength, but causes a frequency shift and an exponential decay in time of the modes. By solving the equations governing the expectation values of the plasmon creation and annihilation operators, we obtain a closed-form full-wave expression for the decay rate and for the frequency shift of the plasmon modes. It is nonperturbative and it only depends on the surface charge distribution of the quasielectrostatic plasmon modes. We validate the expression against the Mie theory for a nanosphere of radius comparable to the plasma wavelength. Eventually, we investigate the decay rate and the frequency shift of the plasmon modes in isolated and interacting nanoparticle of noncanonical shape, as their size increases up to the plasma wavelength.