Specific features of speckle structure formed by dispersed laser beams

The geometry of statistical average of intensity speckles formed by a broadband dispersed laser beam spatially coherent in initial plane z = 0 is studied theoretically. A computer simulation was used to obtain two-dimensional distributions of random intensity that provide a clear picture of the transformations experienced by the speckle structure upon laser beam propagation. Correlation functions and power spectra of random intensity are calculated in order to determine the characteristic size and shape of speckles as a function of longitudinal coordinate z , the width and shape of the frequency spectrum, and the degree of dispersion of the light beam. Analytical expressions that describe an increase in the speckle size along the beam axis and in the direction of beam dispersion as a function of distance from the initial plane are obtained. The ultimate (at z → ∞) width of speckles in the direction of beam dispersion is calculated.