Collimated laser beam in a turbulent atmosphere: Fractal structure and phase branch points

The statistics of the fractal dimension of the intensity image and the number of phase branch points in the light field of a collimated laser beam propagating through a turbulent atmosphere are evaluated for a series of numerically-generated field and intensity patterns. Some results are summarized as follows. The fractal dimension and the number of phase branch points increase with the fluctuation condition. The fractal dimension has definite relation with the pattern sharpness, but there is no relation between the number of phase branch points and the sharpness. In the situation considered here, no saturation phenomenon is found for the fractal dimension, and the number of phase branch points has a probability distribution instead of a definite value under a certain fluctuation condition