Size scaling law for radiation losses of modes in photonic crystal surface emitting devices

Photonic-crystal surface-emitting lasers (PCSELs) have garnered significant attention due to their ability to generate laser beams with ultra-high power and low divergence. This is because they support high-power single-mode lasing with volumes orders of magnitude larger than those of conventional semiconductor lasers. The finite lateral size in a PCSEL is a primary factor limiting its lasing mode volume and, consequently, its output power. We demonstrate that the scaling relation between the total cavity loss α=α_⊥+α_∥ and the device size L is such that the surface radiation loss scales as α_⊥ ∼ O(L^-2), while the edge radiation loss α_∥∼O(L^-3). Both scaling relations can be explained by the second-order expansions of the complex frequency ω(k) of the band diagram. Our results provide a guideline for estimating the size effect when designing large-area PCSEL-like devices.