Statistics of laser intensity amplified by a slightly saturated optical amplifier with a random gain medium

Abstract

Recently, attention has been paid to the laser noise caused by the turbulence in the gain cell of a gas or liquid laser. In such a gain medium, the spatial and/or temporal variations of resonance molecules are supposed to be stochastic. Therefore, the gain coefficient and propagation constant in this medium become random. In this research, the statistics of a linearly polarized monochromatic plane wave are evaluated after the wave is propagated through an optical amplifier with a random gain medium. A partially homogeneously broadened slightly saturated laser amplifier is considered. To deal with nonlinear propagation, the perturbation method is used in which the slight saturation is regarded as the perturbative factor. As for the random molecule distributions, the relative fluctuation of molecule number density is assumed to follow a Gaussian probability distribution. Also, a Gaussian correlation function is used for describing the random structure. The average laser intensity and the contrast of intensity fluctuation are to be evaluated. The couplings among the random gain, random propagation constant, and nonlinear effect are discussed. Here only weak turbulences are considered. Numerical examples are presented.