Changes of skewness and sharpness of partially coherent decentered annular beams on propagation

Changes of skewness and sharpness of partially coherent decentered annular beams (PCDA beams) on propagation both in free space and in oceanic turbulence are studied. Based on the Wigner distribution function, the analytical expressions for the skewness parameter A and the kurtosis parameter K of PCDA beams are derived. The analytical expression for the oceanic turbulence parameter T′ related to K is also derived, and characteristics of T′ are examined. It is found that the behaviors of A and K in oceanic turbulence are quite different from those in free space. In free space, the mass of the intensity distribution may move from one side of the centroid position axis yc to another side at a certain propagation distance z0, and z0 is independent of the correlation parameter τ. The mass of the intensity distribution is concentrated on one side of yc on propagation only for a poorly coherent beam in free space, but it is always this situation for different value of τ when oceanic turbulence is not weak. In free space, it takes a leptokurtic profile in the far field, and a Gaussian profile appears only for a poorly coherent beam. However, in oceanic turbulence it always reaches a Gaussian profile for different value of τ in the far field.