With the paraxial approximation, we derive the analytical formulas for the propagation of a twisted rectangular multi-Gaussian Schell-model (TRMGSM) beam in free space and oceanic turbulence. The spectral density and degree of coherence of the TRMGSM beam both in free space and oceanic turbulence are investigated. We found that the oceanic turbulence barely had any influence on the rotation effect both of the spectral density and degree of coherence. In addition, we found that the spot could degenerate into a Gaussian profile caused by a turbulence medium. Furthermore, for stronger turbulence, the beam spot spreads more rapidly, and the coherence region decreases faster. In this paper, we also study the effect of the twisted factor on the propagating properties. (C) 2018 Optical Society of America
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