Large Petermann factor in chaotic cavities with many scattering channels
Abstract
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
Γ
of the lasing mode and the number of scattering channels N. We find for
N≫1
that for typical values of
Γ
the average Petermann factor
<K>∝
N
−
−
√
≫1
is parametrically larger than unity.