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General linewidth formula for steady-state multimode lasing in arbitrary cavities

A formula for the laser linewidth of arbitrary cavities in the multimode non-linear regime is derived from a scattering analysis of the solutions to semiclassical laser theory. The theory generalizes previous treatments of the effects of gain and openness described by the Petermann factor. The linewidth is expressed using quantities based on the non-linear scattering matrix, which can be computed from steady-state ab initio laser theory; unlike previous treatments, no passive cavity or phenomenological parameters are involved. We find that low cavity quality factor, combined with significant dielectric dispersion, can cause substantial deviations from the Schawlow-Townes-Petermann theory.