H. Schomerus et al., Quantum limit of the laser line width in chaotic cavities and statistics of residues of scattering matrix poles, PHYSICA A, 278(3-4), 2000, pp. 469-496
The quantum-limited line width of a laser cavity is enhanced above the Scha
wlow-Townes value by the Petermann factor K, due to the non-orthogonality o
f the cavity modes. We derive the relation between the Petermann factor and
the residues of poles of the scattering matrix and investigate the statist
ical properties of the Petermann factor for cavities in which the radiation
is scattered chaotically. For a single scattering channel we determine the
complete probability distribution of K and find that the average Petermann
factor [K] depends non-analytically on the area of the opening, and greatl
y exceeds the most probable value. For an arbitrary number N of scattering
channels we calculate [K] as a function of the decay rate Gamma of the lasi
ng mode. We find for N >>1 that for typical values of Gamma the average Pet
ermann factor [K] proportional to root N >> 1 is parametrically larger than
unity. (C) 2000 Elsevier Science B.V. All rights reserved.