The cross-spectral density function of a multi-Gaussian Schell-model vortex (MGSMV) beam propagating through slanted atmospheric turbulence was derived, and the influences of the MGSMV beam parameter and slanted atmospheric turbulence on the spreading properties of a MGSMV beam are studied. One can find that a MGSMV beam propagating in slanted atmospheric turbulence can evolve into the flat-topped beam, and a MGSMV beam with larger index N and topological charge M propagating in slanted atmospheric turbulence will lose the dark hollow center and evolve into the Gaussian beam more slowly than the MGSMV beam with smaller index N and topological charge M. It is also found that a MGSMV beam propagating in slanted atmospheric turbulence with larger strucutre parameter C will evolve into Gaussian beam faster, but the influences of zenith angle α on the spreading properties of MGSMV beam in the far field can be ignored.
Based on the extended Huygens–Fresnel principle, the cross-spectral density function of a partially coherent anomalous hollow beam (AHB) propagating in underwater oceanic turbulence has been derived. The average intensity of partially coherent AHB propagating in underwater oceanic turbulence has been calculated. The influences of coherence length and the strength of underwater oceanic turbulence on the spreading properties of partially coherent AHB are illustrated and analyzed using numerical examples. It is found that the partially coherent AHB with smaller coherence length and the partially coherent AHB propagating in stronger underwater oceanic turbulence will lose the initial beam profile and evolve into the Gaussian beam faster. The results are useful in applications for underwater wireless optical communication.
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