Under the strong coupling condition (Eq. 23), the polaron decoupling limit is reached around the resonance condition, where the mixing angle Θ N → π/4. As a result, the polariton linewidth will become much narrower than systems outside the cavities . Under the fast limit, the polariton lineshape is described by Lorentzian (Eq. 30). Further consider the cavity loss with Γ c as the (homogeneous) cavity loss rate, so that the bare photon spectral lineshape is also described by a Lorentzian. As a result, the overall LP linewidth is additive, reading as