Abstract
We study the output emission statistics of a random continuous-wave Raman fiber laser. The signal evolution is governed by a generalized nonlinear Schrödinger equation (NLSE) with inserted gain. The statistics are close to the Rayleigh one, and the deviations are caused by the Kerr nonlinearity. To characterize the deviations, we analytically find the mean of the squared output signal intensity, based on the kinetic theory. We show qualitative agreement with available experimental data and supplement the results with numerical calculations. With the limit of small gain, the kinetic theory gives a finite answer for the mean of squared intensity in the first and the second order with respect to small nonlinearity. The result is consistent with the fact that the NLSE is integrable in the case of zero gain and is applicable to any generalized NLSE if the inserted terms are effectively small.
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