In the example presented in Figure , both linewidths and resonance positions of plasmon and dye coincide. In that case, ∆ = 2Ω 0 . Note that for deviating resonance positions, the splitting would be smaller. We now use eq 3 instead of eq 2 in the Mie-Gans model to model the extinction of the Drude metal core-shell sphere. To do so, we determine Ω 0 from the peak splitting of the outer peaks of each classical spectrum presented in Figure and insert it into the the expression of the semi-classical permittivity of a two-level system, leaving all other parameters unchanged. The resulting extinction spectra are presented in Figure . We again see the splitting into upper and lower polariton resonance. However, in contrast to the classical model, no additional peak emerges between the two polariton peaks since this region is exactly the region where the power broadening weakens the transition between ground and excited state in the dye. Stronger coupling strengths (and thus higher Ω 0 ) are met by a stronger power broadening and consequently, the additional peak is suppressed effectively even for high oscillator strengths of the dye.