A theoretical investigation is made of third-order nonlinear processes, including Raman scattering and the parametric process in optical fibers. The analytical expressions are obtained for the gain coefficient and the required index mismatch for maximum gain, with the contributions from both the real and the imaginary parts of the third-order nonlinear susceptibility taken into account. This study shows that, as a result of the simultaneous occurrence of these two processes, the Raman–Stokes wave, the signal, and the idler (resulting from the parametric process) are allocated specific amounts of power at the end of a long fiber and that the amount of power in each wave depends on the phase-matching state of the parametric process. Our results also show that the threshold for a Raman–Stokes wave is greatly enhanced when the index mismatch among the waves for the parametric process reaches its optimum value.
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