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We show that the threshold of a photonic crystal surface-emitting laser canbe calculated from first-principles by the method of rigorous coupled waveanalysis (RCWA), which has been widely used to simulate the response spectra ofpassive periodic structures. Here, the scattering matrix (S-matrix) of asurface-emitting laser structure with added gain is calculated on the complexfrequency plane using RCWA, and the lasing threshold is determined by the valueof gain for which the pole of the S-matrix reaches the real axis. This approachcan be used for surface emitting laser struc tures in general, and isparticularly useful for the surface emitting laser systems with complexin-plane structures.

First-Principles Threshold Calculation of Photonic Crystal Surface-Emitting Lasers Using Rigorous Coupled Wave Analysis