A non-Lorentzian approach to exciton-plasmon systems at strong coupling

We develop a non-Lorentzian analytical model for quantum emitters (QE) resonantly coupled to localized surface plasmons (LSP) in metal-dielectric structures. Using the explicit form of LSP Green function, we derive non-Lorentzian version of semiclassical Maxwell-Bloch equations that describe LSPs directly in terms of metal complex dielectric function rather than via Lorentzian resonances. For a single QE resonantly coupled to an LSP, we obtain an analytical expression for effective optical polarizability of the hybrid system which, in the Lorentzian approximation, recovers the results of the classical coupled oscillators model. We demonstrate that non-Lorentzian effects originating from temporal dispersion of the metal dielectric function affect significantly the optical spectra as the hybrid system transitions to the strong coupling regime. In contrast to the results of Lorentzian models, the main spectral weight in the system scattering spectra is shifted toward the lower energy polaritonic band, consistent with the experiment.