Evolution of the C-point dipole in oceanic turbulence

In order to find out performance of the C-point dipole nested in partially coherent stochastic vortex beam in oceanic turbulence, the Gaussian-Schell model vortex (GSMV) beam carrying a C-point dipole is constructed, which is used to research the evolution property of the C-point dipole in oceanic turbulence. According to the definition of the polarization singularities in partially coherent vector beams, the GSMV beam constructed was to realize a parting coherent beam carrying a pair of C-point dipoles with opposite topological charges. According to the extended Huygens–Fresnel principle, the formula of the cross-spectral density (CSD) for the GSMV beam propagating through oceanic turbulence is deduced by using of the integral formula. In accordance with the formula of the CSD derived above, the effects of propagation distance z, the off-axis parameter s and coherent length δ on the evolution behavior of the C-point dipole is illustrated and analyzed. The position of a C point can be determined by the contour lines of phase of Stokes field S₁₂ = S₁ + iS₂. The degree of polarization of a C point can be calculated by spectral Stokes parameters, while its topological charge can be judged by the sign principle which was proposed by Freund. It is shown that, the position and the degree of polarization of the C points may be changed with propagation of the GSMV beam. Though the creation and annihilation of C points may occur with variation of the propagation distance, the total of the topological charges of C points of the beam hold consistent. Besides, as the off-axis parameters are chosen as opposite numbers, the numbers of C points from the optical fields are equal. When the partially coherent vortex beam carrying a C-point dipole propagates in oceanic turbulence, the evolution behavior of the C-point dipole is affected by the propagation distance of the host beam, the off-axis parameter, turbulence intensity as well as the spatial coherent length.