Nonlinear gain coefficient experienced by non-paraxial perturbations under small signal approximation

Abstract

Starting from the nonlinear Shroedinger equation describing the evolution of non-paraxial perturbations co-propagating with a strong background inside a nonlinear Kerr medium, we have deduced the small signal gain coefficient of the non-paraxial perturbation superimposed on the strong background wave. The results indicate that both the cut-off frequency and the asymptotic value of the gain coefficient of the non-paraxial perturbation are smaller than that of the paraxial counterpart. In addition, it is also shown that the gain coefficient degenerates to the nonlinear gain coefficient of paraxial perturbations under the paraxial approach. Furthermore, under the condition that the perturbation travels far enough inside the nonlinear medium, the gain coefficient degenerates further to the asymptotic gain coefficient predicted by the Bespalov and Talanov theory. The gain coefficient obtained in this work provides a more general solution to the study of perturbations.