We consider the statistical properties of the fluctuations
in the orientation ofthe vector laser field for a nearly
isotropic laser, addressing the competition between the randomizing
influence of noise and the preference for linearly or circularly
polarized emission induced by saturation in the laser medium
and/or cavity anisotropies. We describe, through a nonpertubative
analysis, a crossover regime from diffusion-induced
polarization-isotropic emission to emission of nearly fixed
polarization characteristics. In this crossover the linewidth
of intensity fluctuations associated with one of the circularly
polarized components of the vector field amplitude
changes from decreasing to increasing with output power.
This behavior can be expressed in terms of a single parameter
which measures the pump or the total output intensity in
terms of the ratio of the noise amplitude to the degree of
cross-saturation of the amplitudes of the circularly
polarized components of the vector field amplitude. Analytical
results are given for the linewidth of the intensity fluctuations.
When the laser has preference for linearly polarized emission,
there is a weakly non-Lorentzian spectrum in the crossover
region. When the laser has preference for circularly polarized
emission the crossover regime is characterized by a non-Lorentzian
spectrum due to fast hopping between two circularly polarized
eigenstates. We also describe ellipticity fluctuations induced
by the diffusion of the direction of the main axis of the
polarization ellipse in the presence of cavity birefringence.
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