| Abstract: |
| A statistical properties of a laser beam propagating in a turbulent medium
are studied. It is proven that the intensity fluctuations at large
propagation distances possess a Gaussian probability density function and
establish quantitative criteria for realizing the Gaussian statistics
depending on the laser propagation distance, laser beam waist, laser
frequency, and turbulence strength. We calculate explicitly the laser
envelope pair correlation function and corrections to its higher-order
correlation functions breaking Gaussianity. At intermediate distances the
laser intensity fluctuations follows the Poisson distribution (i.e. the
amplitudes satisfies the Gaussian statistics) while the tail is strongly
non-Gaussian with square-root dependence on the intensity in the exponent.
The transition between the Poisson distribution and the non-Gaussian tail
occurs at the values of intensity which quickly increases with the
propagation distance. We find the explicit analytic expression for the
fourth order correlation function vs. propagation distance and the
turbulence strength which is determined by non-Gaussian tails. We finds
that this correlation function is in excellent agreement with the large
scale supercomputer simulations of laser wave propagation. We discuss also
statistical properties of the brightest spots in the speckle pattern and
find that the most intense speckle approximately preserves both the
Gaussian shape and the diameter of the initial collimated beam while
loosing energy during propagation. After propagating 7km through
typical atmospheric conditions, approximately one in one thousand of
atmospheric realizations produces an intense speckle with 20-30\% of the
initial power. Such optimal atmospheric realizations create an effective
lens which focuses the intense speckle beyond the diffraction limit of
the propagation in vacuum. |
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