with the real part corresponding to the eigenenergy and the imaginary part corresponding to the loss/broadening. For the model system investigated here, κ = 175 cm -1 (from directly fitting the numerical value of R (1) (ω), the black curve in Fig. to a gaussian), and for Γ = 100 meV (806 cm -1 ), the Rabi splitting is reduced (see Eq. 57), causing the peak of the upper and lower polariton to shift from ±456 cm -1 to ±428 cm -1 , which is in semiquantitative agreement with our numerical results. In fact, the agreement between the analytic answer from Eq. 57 and the simulated spectra are incredibly good, across all cavity loss Γ we explored.