Quantum limit of the laser line width in chaotic cavities and statistics of residues of scattering matrix poles
Abstract
The quantumlimited line width of a laser cavity is enhanced above the SchawlowTownes value by the Petermann factor K, due to the nonorthogonality of the cavity modes. We derive the relation between the Petermann factor and the residues of poles of the scattering matrix and investigate the statistical 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 nonanalytically on the area of the opening, and greatly exceeds the most probable value. For an arbitrary number N of scattering channels we calculate < K> as a function of the decay rate Γ of the lasing mode. We find for N≫1 that for typical values of Γ the average Petermann factor <K>∝ N≫1 is parametrically larger than unity.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 April 2000
 DOI:
 10.1016/S03784371(99)006020
 arXiv:
 arXiv:chaodyn/9911004
 Bibcode:
 2000PhyA..278..469S
 Keywords:

 Chaotic Dynamics;
 Condensed Matter;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 15 pages, 9 figures