Parametric and Raman amplification in birefringent fibers

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Abstract
We derive the gain for mixed Stokes and anti-Stokes waves propagating in a birefringent fiber in the presence of an intense pump wave, under the combined action of parametric four-photon mixing and Raman scattering, for different types of phase matching. We discuss the conditions for the suppression or the enhancement of the Raman gain as a function of the linear mismatch and of the sideband detuning, owing to coupling between Stokes and anti-Stokes components of the growing wave. We confirm the analytical predictions of the linearized analysis with the numerical solution of the coupled nonlinear Schrödinger equations, including the contribution of the tensorial Raman response of the fiber.