For the 2D cavity case, one needs to consider beyond the simple density of state argument. Note that the loss associated with the lifetime 𝜏 c only considers the loss in the 𝑘 ⊥ direction. What we have not explicitly considered before was the cavity loss along the 𝑘 ‖ direction due to the photon propagating outside the cavity. When 𝑘 ‖ ̸ = 0, the photon propagation along the in-plane direction will cause additional loss, due to the photon propagating outside the effective coupling area. Let 𝒟 be the diameter of the quantization area (along the 𝑘 ‖ direction in Fig. ) and ℒ be the mirror distance (along the 𝑘 ⊥ direction in Fig. ), so the effective cavity quantization volume 𝒱 = ℒ • 𝒟 2 . The mode lifetime can be estimated as