  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 S-matrix 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.
