The statistical properties of a Hermite-Gaussian correlated Schell-model beam in a gradient-index fiber

With the help of the extended Huygens-Fresnel principle, we derived analytical expressions for the cross-spectral density(CSD) and the second-order moments of a Hermite-Gaussian correlated Schell-model (HGCSM) beam propagating in a gradient-index (GRIN) fiber. The statistical properties, such as the spectral intensity, the spectral degree of coherence and the propagation factor of a HGCSM beam in the GRIN fiber are illustrated numerically. It can be found that the distribution of the spectral intensity and the degree of coherence exhibit periodicity and the propagation factor of a HGCSM beam does not depend on the parameters of the GRIN fiber and propagation distance. As a result, we can modulate the state of the spectral intensity of the output beam in GRIN fiber by varying the length of fiber and the initial beam parameters of a HGCSM beam.