In this paper, we have derived the analytical formulae for the cross-spectral densities of partially coherent Gaussian vortex beams propagating in a gradient-index (GRIN) fiber. In numerical analysis, the variations of the intensity and the phase distributions are demonstrated to illustrate the change in singularities within a GRIN fiber. It turns out that the beam intensity and phase distribution change periodically in the propagation process. The partially coherent Gaussian vortex beams do not typically possess the center intensity zero in the focal plane, which usually called ‘hidden’ singularities in intensities detection. We demonstrated the phase singularities more clearly by the phase distribution, one finds that the phase vortex of a partially coherent beam will crack near the focus, and opposite topological charge will be generated, we attribute to the wave-front decomposition and reconstruction of the vortex beams by the GRIN fiber. Our results show that the change in phase singularities not only affected by the GRIN fiber, but also by the initial coherence of the beam source, and high initial coherence will be more conducive to maintaining the phase singularities in the propagation. Our results may find applications in singular optics, wave-front reconstruction and optical fiber communications.

Analytical formulas for a class of tunable random electromagnetic beams propagating in a turbulent atmosphere through a complex optical system are derived with the help of a tensor method. One finds that the far field intensity distribution is tunable by modulating the source correlation structure function. The on-axis spectral degree of polarization monotonically increases to the same value for different values of order M in free space while it returns to the initial value after propagating a sufficient distance in turbulence. Furthermore, it is revealed that the state of polarization is closely determined by the initial correlation structure rather than by the turbulence parameters.OCIS It is well known the spatial correlation structure of random beams significantly affects the propagation intensity distribution [1] . However, only a few correlation function models such as the Schell-model source, Bessel-correlated source, and the Lambertian source have been introduced over the past decades [1][2][3] . As a typical correlation source, the Schell-model source with a Gaussian correlation function has been extensively studied both in theory and in experiments over the past decades [4][5][6][7][8][9] . Since Gori proposed a sufficient condition for the generation of genuine correlation functions based on a non-negative definiteness [10] , a variety of correlation functions have been proposed, both theoretically and experimentally. Beams generated by non-uniform correlation sources have found various unique properties in terms of self-accelerating, selffocusing and special beam profiles in terms of dark hollow, flat-topped and rectangular frame, etc. [11][12][13][14][15][16][17][18][19] . Coherence and polarization are two fundamentals of light fields both in classical and quantum optics. They had been studied separately in literature until James first reported that the spectral degree of polarization (DOP) generally changes on propagation induced by the source correlation property, even in free space [20] . Since Wolf developed a unified theory of coherence and polarization for random electromagnetic beams, it is widely used to determine the statistical properties of random electromagnetic beams in free space as well as in various media [21][22][23][24][25][26][27][28] . Optical communication exhibits various advantages in terms of high speed, high bandwidth, and anti-interference as compared with microwave communication. However, refractive index fluctuations caused by a turbulent atmosphere significantly limit the transmission of optical signals. As a general extension of Kolmogorov turbulence, non-Kolmogorov turbulence has been studied widely both in theory and in experiment in the past decades [29][30][31][32][33][34][35][36][37] . It is verified that random beams are found as a suitable way for reducing the disadvantages induced by a turbulent atmosphere [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] . Recently, random electromagnetic beams have been reported as a better optimization of scalar r...

No abstract