Large Petermann factor in chaotic cavities with many scattering channels

The quantum-limited linewidth of a laser cavity is enhanced above the Schawlow-Townes value by the Petermann factor K, due to the non-orthogonality of the cavity modes. The average Petermann factor [K] in an ensemble of cavities with chaotic scattering and broken time-reversal symmetry is calculated non-perturbatively using random-matrix theory and the supersymmetry technique, as a function of the decay rate Gamma of the lasing: mode and the number of scattering channels N. We find for Ai much greater than 1 that for typical values of Gamma the average Petermann factor [K] proportional to root N much greater than 1 is parametrically larger than unity.