Stochastic noise amplification of partially coherent CW beam in the region of minimum GVD in lossless Kerr media with delayed response

Motivated by experimental evidences of spectral broadening of partial coherent pulses emitted by a P2O5-doped Raman fiber laser in a silica fiber, we theoretically study the propagation of a partially coherent optical beam through a noninstantaneous media by using extensions of the nonlinear Schrödinger equation (NLSE) including a phase-diffusion model for the partially coherent beam. The finite response time of the medium is incorporated by means of the Debye relaxation model. The dispersion relation is analytically calculated, and the gain spectra together with relevant second-order statistical quantities are numerically computed. Moreover, we provide a complete description of how these statistical properties vary as a function of the delayed nonlinear response of the medium; specifically in the regime of fast nonlinear response in which modulation instability is not expected to occur for genuine incoherent pulses.