Bandwidth of quantized surface plasmons: competition between radiative and nonradiative damping effects

We investigate the damping effects of coherent electron oscillations on the bandwidth of a quantized nanoparticle plasmon resonance. The nanoparticle (NP) is treated as a two-level quantum system, and the total relaxation time involves both the population relaxation time associated with radiative processes and the collisional relaxation time associated with nonradiative processes that result in dephasing/decoherence of electron oscillations. We describe the optical response of NPs to an external electromagnetic field by the optical Bloch equations employing the density matrix formalism to capture the quantum description nature of dipolar plasmon resonance and suggest a generalized criterion for the validity of dipole approximation. Then we explore the competition between the radiative and nonradiative damping in determining the plasmon bandwidth of two typical NP models; metallic nanospheres and dielectric core-metal shell NPs (nanoshells). We show that the frequency of plasmon resonance, in addition to the NP size, plays an important role in the competition between the damping mechanisms. Consequently, the damping processes are significantly influenced by the factors that determine the resonance frequency, such as the core size, the dielectric constant of the medium, and the shell thickness (for nanoshells). For both models of NPs, we identify the optimum parameters that achieve a narrower plasmon bandwidth (minimal damping), which is a prerequisite for advanced sensing and medical applications. We demonstrate excellent agreement of the simulated spectral features of the plasmon resonance with previously reported experimental results for a single NP where the inhomogeneous broadening of the plasmon line is excluded. For NP ensembles where inhomogeneous broadenings and interface chemical effects are significant, our theoretical approach successfully predicts the overall trend of size-dependent damping rates.