Statistical properties of rectangular cusped random beams propagating in oceanic turbulence

The analytical formula for the cross-spectral density function of the rectangular cusped random beams, also known as fractional multi-Gaussian Schell-model beams, propagating in oceanic turbulence, is derived. The statistical properties incorporating the spectral density and the spectral degree of coherence of the beams on propagation are investigated. It is found that the beams maintain a rectangular-shaped cusped profile in weak turbulence just as in free space, whereas in strong turbulence or at sufficiently long propagation distances, the beams profile would be destroyed little by little, turning out to be Gaussian profile eventually. Moreover, the beams with smaller coherence length exhibit a more obvious rectangular outline. In addition, the spectral density and the spectral degree of coherence are both affected by various turbulence parameters.