Quantum Theory of Radiative Decay Rate and Frequency Shift of Surface Plasmon Modes

Abstract

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 quasi-electrostatic 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 new closed-form full-wave expression for the decay rate and for the frequency shift of the plasmon modes. It is non-perturbative and it only depends on the surface charge distribution of the quasi-electrostatic plasmon modes. We validate the expression against the Mie theory for a nano-sphere 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 non-canonical shape, as their size increases up to the plasma wavelength.

References in corpus (10)

• Quantum Plasmonics
• Light interaction with photonic and plasmonic resonances
• Plasmon-assisted Quantum Entanglement
• Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics
• Strong coupling between a metallic nanoparticle and a single molecule
• Damping rates of surface plasmons for particles of size from nano- to micrometers; reduction of the nonradiative decay
• Demonstration of Quadrature Squeezed Surface-Plasmons in a Gold Waveguide
• Coherent Control of Floquet-Mode Dressed Plasmon Polaritons
• Quantum Antennas
• Quantum Light from a Metal Nanoparticle

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• Time-Domain Formulation of Electromagnetic Scattering Based on a Polarization Mode Expansion and the Principle of Least Action
• Static surface mode expansion for the full-wave scattering from penetrable objects
• Damped oscillators within the general theory of Casimir and van der Waals forces