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 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. The study of resonant scattering goes back to the early work of Breit and Wigner [1], and was developed extensively in the context of nuclear physics [2]. The Breit-Wigner resonance is described by a frequency-dependent scattering matrix S(ω) with elements Snm = δnm + σnσ ′ m(ω − Ω+ iΓ/2) , (1) where Ω and Γ are, respectively, the center and the width of the resonance, and σn, σ ′ m are the complex coupling constants of the resonance to the scattering channels n, m. (In the presence of time-reversal symmetry the scattering matrix is symmetric, hence σn = σ ′ n.) The coupling constants of a Breit-Wigner resonance are related to its width by the sum rule [3]