Optical Spectra of Plasmon--Exciton Core--Shell Nanoparticles: A Heuristic Quantum Approach

Light--matter coupling in plasmonic nanocavities has been widely studied in the past years. Yet, for core--shell particles, popular electromagnetic models that use the classical Lorentz oscillator to describe the shell predict extinction spectra with three maxima, if the plasmon and the shell absorption are in resonance. In contrast, experiments exhibit only two peaks as also expected from simple quantum models of hybrid states. In order to reconcile the convenient and widely used classical electromagnetic description with experimental data, we connect it to the quantum world by conceiving a heuristic quantum model. Our model is based on the permittivity of a two-level system in a classical electric field derived from the optical Bloch equations. The light--matter coupling is included via the collective vacuum Rabi frequency $\Omega_0$. Using our model, we obtain excellent agreement with a series of experimental extinction spectra of particles with various coupling strengths due to a systematic size variation. The suppression of the third maximum, which mainly stems from the absorption in the shell, can be interpreted as a vacuum induced power broadening, which may occur in lossy (plasmonic) cavities below the strong-coupling regime.