Modulation instability gain and wave patterns in birefringent fibers induced by coupled nonlinear Schrödinger equation

Abstract

In this work, we studied the behavior of the modulation instability (MI) growth rate and modulated wave (MW) bright and dark-soliton in nonlinear optical fibers (OFs) where both birefringence and four-wave mixing (4WM) terms are employed. We have shown the effects of the 4WM and the group velocity dispersion (GVD) on the MI gain and MI bands as well as on the MWs patterns. For certain conditions on the coupled nonlinear Schrödinger equation (CNLSE) parameters, we exhibited stable and unstable zones of the MI. More precisely, in a normal dispersion regime, we shown how the variation of 4WM can generate additional sides lobes and consequently the formation of new MI bands. Furthermore, it is observed that when the coupling coefficient (CC) increases, its effects could reduce the stability zones by increasing strongly the number of sides lobes in a normal dispersion regime. To seek the behavior of the MWs patterns, we used numerical investigation (NI). From these results, it has been observed the propagation of the MW bright-soliton and dark-soliton with the effects of the 4WM. We noticed that the MWs patterns can preserve high energy on the peak and keep constant its shapes in birefringent OFs. These results show that the 4WM and the GVD behave as being energy sources for MI and MWs. Our finding can help to manufacture OF tools and could open the way for the use of the 4WM and cross-phase modulation (XPM) to generate MI bands and long-live temporal MWs patterns.