Role of cross-phase modulation with the pump wave for the narrow generation regime of a random fiber laser

In present paper we discuss the role of interaction between the pump and generation waves in a fiber laser with randomly distributed feedback due to weak Rayleigh backscattering, operating in the ultra-narrow regime, observed just above the generation threshold. Spectrum in this case consists of narrow (less than 1 MHz) modes, having typical lifetime of 1 ms, decomposing through the nonlinear interaction processes. We demonstrate that cross-phase modulation between narrow mode and the pump wave can lead to demolition of the first if the walk-off length is big enough. Therefore, ultra-narrow regime is dependent on fiber dispersion, as it defines the walk-off parameter of the fiber. Comparison with the experiment proves our conclusion: in random lasers, based on fibers with low dispersion, no narrow generation occurs, while for fibers with larger dispersion coefficient it is steadily observed.