We show that the threshold of a photonic crystal surface-emitting laser can be calculated from first-principles by the method of rigorous coupled wave analysis (RCWA), which has been widely used to simulate the response spectra of passive periodic structures. Here, the scattering matrix (S-matrix) of a surface-emitting laser structure with added gain is calculated on the complex frequency plane using RCWA, and the lasing threshold is determined by the value of gain for which the pole of the

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... trix reaches the real axis. This approach can be used for surface emitting laser struc tures in general, and is particularly useful for the surface emitting laser systems with complex in-plane structures.