Noise amplification in dispersive nonlinear media

The propagation of a partially coherent optical beam through dispersive nonlinear media is investigated theoretically by using a phase-diffusion model for the laser beam. Changes in the second-order statis- tical properties during beam propagation depend on whether the nonlinear medium exhibits normal or anomalous group-velocity dispersion. In the case of normal dispersion, the coherence function and the corresponding optical spectrum remain unaffected. By contrast, modulation instability is found to be responsible for noise amplification in the anomalous dispersion regime, enhancing phase fluctuations and causing spectral distortion as well as coherence degradation. Under certain conditions, phase fluctuations exhibit temporal oscillations that lead to the characteristic spectral sidebands associated with modulation instability. The nonlinear Schr\"odinger equation is solved numerically to study the propagation regime in which the analytic theory becomes invalid.

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