Moment and kurtosis parameter of partially coherent cosh-Gaussian beam in turbulent atmosphere

An analytical expression for arbitrary moments of the cosh-Gaussian-Shell beam in turbulent atmosphere is derived. As a special case, kurtosis parameters of collimated and focused cosh-Gaussian beam with and without turbulent atmosphere are studied in detail. It can be seen from the study that the kurtosis parameters of Gaussian beam do not remain constant in turbulent atmosphere. Similar to the kurtosis parameters of a cosh-Gaussian beam at source plane, the kurtosis parameters at focal plane without turbulent atmosphere are independent of the propagation distance and vary with the parameters of the beam. But the variation of the kurtosis parameters at focal plane is different from that at source plane. However, the kurtosis parameters of collimated and focused cosh-Gaussian beam both vary with the propagation distance and gradually converge to 3 along the z-axis in turbulent atmosphere. Compared with a collimated beam, the kurtosis parameters of a focused beam converge more quickly.