Incoherently pumped polarization modulation instability in optical fibers

Modulation instability has been one of the most common nonlinear phenomena when an intense coherent light source propagates along optical fibers. While it has been widely studied using highly coherent lasers as pump sources, recent studies have been exploring incoherent light sources as an alternative. Particularly, owing to the intriguing characteristics of incoherent light, of which the intensity fluctuations can only be accounted statistically, the newly generated spectral components through the modulation instability process will inherit this characteristic and behave according to the phase-matching condition between the incoherent pump and generated sidebands. When the so-called phase-locking condition is satisfied, the phase-locking sideband will absorb the pump intensity fluctuations and the convection sideband will simultaneously evolve into more coherent sidebands. This special phase-matching condition can typically be fulfilled through a higher-order dispersion profile in scalar modulation instability, and it becomes extremely challenging to realize such a dispersion profile in reality. To this end, we explore in this work using a vector modulation instability process to realize this phase-matching process. Our design is based on the polarization modulation instability process in which the pump and two sidebands in the orthogonally polarization modes can be parametrically phase-matched, while the phase-locking convention process is fulfilled by the fiber's third-order dispersion. These combined processes subsequently result in asymmetrical broadening of the parametric sidebands. We derive the phase-matching condition and numerically investigate the incoherent field statistics induced by the phase-locking convention process.