Probability distribution of laser beam intensity after propagating through turbulent media

Abstract

Laser beams experience random scattering when they are propagated in turbulent media. If the turbulences are strong and the propagation distance is long enough, the statistics of the laser beam intensity is expected to reach the saturation regime in which the intensity possesses a Gaussian probability distribution as a consequence of the central limit theorem. However, in many cases the condition for saturation is not reached, and K distributions, instead of Gaussian distributions, have been reported by experimentalists. To give interpretations for these distributions, although simple theoretical models were introduced, a more rigorous method is presented with more physical insight. The theory behind these K distributions includes the conceptions of double-scattering by large and small irregularities and narrow laser beamwidth. Statistical fourth moments of laser intensities are evaluated and discussed thoroughly to show different properties of K distribution from those of Gaussian distribution. In mathematical computations, the path integral technique is applied under the assumption of forward scattering.