Large Petermann factor in chaotic cavities with many scattering channels

The quantum-limited linewidth of a laser cavity is enhanced above the Schaw low-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 cavit ies with chaotic scattering and broken time-reversal symmetry is calculated non-perturbatively using random-matrix theory and the supersymmetry techni que, as a function of the decay rate Gamma of the lasing: mode and the numb er of scattering channels N. We find for Ai much greater than 1 that for ty pical values of Gamma the average Petermann factor [K] proportional to root N much greater than 1 is parametrically larger than unity.