with the polariton frequency ω α = (Re[E α ] -E G )/ℏ taken from the real part of Eq. 57, and the width σ α = Im[E α ] = (κ + Γ)/4 taken from the imaginary part of Eq. 57. For a large cavity loss rate Γ, the term inside the square root becomes negative so that the real solution no longer exists and the two polariton peaks merge into one. Also, the width of the polariton peak, based on Eq. 57, is (κ + Γ)/4. As the cavity loss rate Γ increases, the width of the polariton peak will also increase. Under the Γ = 0 limit, the polariton peak has a width of κ/4, two times smaller than the original exciton width κ/2, indicating the polaron decoupling effect from the light-matter interaction (see Eq. 46 and discussions).