Consider the evolution of the wander and M2-factor of Mathieu Gaussian-Schell beam in turbulent ocean. We develop models for wander and M2-factor of this beam based the theory of wigner distribution function. The influences of the oceanic parameters on the wander and M2-factor are discussed in detail. It is found that as the propagation distance, the dissipation rate of temperature variance, the eddy diffusivity ratio and ratio of temperature and salinity contributions to the refractive-index spectrum increases, both M2-factor and beam wander increase; but M2-factor and beam wander increase with the decreasing of initial beam width, the kinetic energy per unit mass of fluid. However, as the variation of ellipticity factor and OAM quantum number increase, the evolution of M2-factor and beam wander are some complexes. The influences of coherent width of light source and wavelength on the M2-factor and beam wander are negligible. Our results are helpful in the design of an optical communication system in an oceanic environment.
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