accounts for the effective photon lifetime due to propagation in the in-plane direction within a mode area with diameter D. Detailed derivations are provided in Supplementary Note 9. The cavity frequency at the normal incidence (k ∥ = 0), ω c implicitly shows up in the expressions of Γ 2D Q and R2D (see Eqs. 23a-23b) as the lower bound of the dω integral, due to the photonic DOS only has a finite value when ω k ≥ ω c (or |k ∥ | ≥ 0).