Periodic properties of Laguerre-Gaussian correlated Schell-model beams in a gradient-index fiber

The explicit expressions of the cross-spectral density (CSD) and the propagation factor of Laguerre-Gaussian correlated Schell-model (LGCSM) beams propagation in a gradient-index (GRIN) fiber were derived. The statistical properties, such as the spectral intensity, the spectral degree of coherence (DOC) and the propagation factor of LGCSM beams in a GRIN fiber are illustrated numerically. Our results show that the beams spectral intensity and spectral DOC change periodically in a GRIN fiber. We can adjust the initial beam parameters of LGCSM beams, such as the beam order, the transverse beam width and the transverse coherence width, to control the distributions of the spectral intensity and the spectral DOC of the beams in the output plane of a GRIN fiber. Furthermore, the propagation factor of the beams remains invariant on propagation and it is determined only by the initial beam parameters. Our results may be useful in optical fiber communications.