Role of cubic–quintic–septic–nonic nonlinearity over the instability of solitons in conversely guided couplers with bi-negative index metamaterial transmission medium

Abstract

This paper aims to theoretically examine the phenomenon of modulation instability (MI) in the presence of a considerable nonlinear refractive index movement in a triad-core nonlinear coupler, including a bi-negative refractive material transmission medium. The formula for the instability gain is deduced with the help of the linear stability analysis. The significant role of cubic, quintic, septic, nonic, and stability of the front-to-reverse-transmitting wave nonlinearities in the phenomenon of MI in the nonlinear triad-core coupler is critically confirmed via MI gain spectra analysis. It is found that the cubic, quintic, septic, and nonic nonlinearities improve the MI in both dispersion regimes (normal and anomalous) by boosting the gain and width of the instability profile by taking account of reverse-to-front ratio power (f). On the other hand, quintic nonlinearity improves the MI in the cubic case by enhancing its width and gain in the normal and anomalous dispersion areas. Using 3D pictures, we analyze the dynamic behavior of the MI under an anomalous dispersion area and find that, in both normal and anomalous dispersion scenarios, the instability shape develops with septic and nonic nonlinearity. Furthermore, as the figures clearly show, neither the normal nor the anomalous dispersion scenario significantly changes due to septic and nonic nonlinearity alone. We aim to shed light on the role of contamination in saturation nonlinearity by examining soliton and MI, their production, and control in triad-core couplers, focusing on a Negative Index Meta Material (NIMM) transmission medium.