Considering noninstantaneous Kerr nonlinearity, the propagation of a partially coherent optical beam is theoretically investigated by using extensions of the nonlinear Schr?dinger equation (NLSE). In order to account for the partial coherence of the beam, a phase-diffusion model is used for the laser beam. To introduce the finite response time of the medium, a time-dependent nonlinear response is incorporated in the system of the NLSE using the Debye relaxation model. We analytically deduce the dispersion relation and numerically compute the gain spectra along with relevant second-order statistical quantities. A detailed study of how these statistical properties are influenced by the group velocity dispersion regime as well as by the delayed nonlinear response of the material is presented. The distinct features for slow and fast delayed nonlinear response are also emphasized.
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