Nonlinear dynamics of long mirrorless fiber raman laser

Numerical model of long fiber Raman laser is proposed. The model based on the equations, describing the propagation of pump and Stokes waves, linear coupling of oppositely running waves due to scattering and its nonlinear interaction. The derivation of equations for slowly varying pulse envelopes uses the field decomposition in terms of spatial harmonics rather then commonly used temporal harmonics, which allows to avoid the two-point boundary conditions, and to employ the numerical scheme of Courant- Isaakson-Rees. This scheme was used for numerical simulations of space-temporal dynamics in long fiber Raman laser in the absence of the reflection at output fiber ends. It was shown that the dynamical regimes is connected with the instabilities of Stokes waves which move in the direction of pump waves against generation of oppositely running Stokes waves, and superluminal propagation of oppositely running pulses having the velocities which are higher than group velocity in the optical fiber.