We present a detailed analytical self-consistent theory based on wave kinetic equations that describes generation spectrum and output power of a Raman fiber laser (RFL). It is shown both theoretically and experimentally that the quasi-degenerate four-wave mixing (FWM) between different longitudinal modes is the main broadening mechanism in the one-stage RFL at high powers. The shape and power dependence of the intracavity Stokes wave spectrum are in excellent quantitative agreement with predictions of the theory. FWM-induced stochasticity of the amplitude and the phase of each of the longitudinal modes generated in the RFL cavity is an example of a light-wave turbulence in a fiber.
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