Modulation instability solitons in oppositely double-doped directed couplers with two negative refractive index material channel and non-Kerr nonlinearity

In a three-core nonlinear contrarily directed coupler with two negative-index material channels, we theoretically explore the instability in the presence of a non-Kerr-like nonlinear refractive -index shift. Through the use of linear stability analysis, we determine an expression for the instability gain. It is discovered that the septic saturation, the ratio of the forward-to backward -propagating wave power, pump power, and nonlinearity all have a substantial impact on the MI in the nonlinear three-core contrarily directed coupler. The septic and saturation nonlinearity is found to improve the MI in the case of forward-to-backward ratio power (f) by boosting the width and gain of the instability profile in both normal and abnormal dispersion regimes. However, septic nonlinearity improves the MI in the case of pumps by boosting both its width gain and in the abnormal dispersion regime alone. Using 2D pictures, we could investigate the MI's dynamic behaviour during an anomalous dispersion regime. We discovered from the contour images that the gain of the instability profile grows as septic and saturation nonlinearity increases in both normal and abnormal dispersion regimes. So, with a focus on a negative refractive material channel in the existence of contamination and saturation nonlinearity, we report new techniques for producing and controlling MI and soliton in three-core contrarily directed couplers.