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We theoretically investigate modulation instability (MI) in a two-core nonlinear oppositely directed coupler with a negative-index material channel in the presence of a non-kerr-like nonlinear refractive-index change. Using linear stability analysis, we obtain an expression for the instability gain. It is found that the MI in the nonlinear two-core oppositely directed coupler is significantly influenced by the ratio of the forward- to backward-propagating wave power, nonlinearity, power and saturation. In the normal dispersion regime, the septic nonlinearity is found to suppress the MI by reducing both the gain and width of the instability nonlinearity. But in anomalous dispersion regime, the situation is different because septic nonlinearity enhances the MI by increasing both the gain and width of MI. The increase of septic nonlinearity both in normal and anomalous dispersion regimes increases the gain of the instability nonlinearity. Thus, we report new ways to generate and manipulate the MI and solitons in two-core oppositely directed couplers with a particular emphasis on a negative-index material (NIM) channel in presence of septic nonlinearity.

We consider a nonlinear oppositely direct coupler with a negative-index metamaterial channel and a modified Kerr-type saturable nonlinearity (MSN). We presented an analytical expression for MI gain. Special attention is paid to investigation of the influence of system parameters such as the forward to backward-propagating wave's, the power, nonlinear parameters and nonlinear saturable parameter on the MI. The MSN behaves in a perceptible manner such that the gain and the unstable region inherently decrease. In the normal and anomalous dispersion region, the gain of the instability spectrum increases (decreases) monotonously with increases (decreases) of saturable nonlinearity. In other term, when the saturable parameter or the input power increases, the MI peak gain and the gain band-width may increase and then decrease.

We are motivated by recent studies in medium formed by two tunnel-coupled waveguides. One of the waveguides is manufactured from an ordinary dielectric, while the second has negative refraction. We present an investigation of the gain spectrum permitting modulation instability in the nonlinear optical coupler with a negative-index metamaterial channel whose non-linear response includes third- and fifth-order terms. The principal motivation for our analysis stems from the impact of the inevitable presence of the effective cubic–quintic nonlinearity. We emphasize the influence of higher order nonlinear terms, over the MI phenomena, and the outcome of its development achieved by using linear stability analysis. Gain spectrum investigation has been carried out for both anomalous and normal dispersion regime in the focusing and defocusing cases of nonlinearity and near-zero dispersion regime where higher order linear dispersive effects emerge. Our results show that the MI gain spectra consist of multiple spect...

We have investigated the modulation instability (MI) in a nonlinear optical coupler using a generalized model describing the pulse propagation of a waveguiding structure composed of two adjacent waveguides. The model consists of a nonlinear tunnel-coupled structure consisting of right- and left-handed media. The optical coupler considered here includes a local saturable nonlinear refractive index. In particular, we discuss the impact of the saturable nonlinearity for the MI of plane waves and formation of spatial solitons. The results show that MI can exist not only in the normal group velocity dispersion (GVD) regime but also in the normal GVD regime in the nonlinear positive-negative index coupler in the presence of saturable nonlinearity. The saturable nonlinearity can increase/decrease the number of sidebands or shift the existing sidebands. The maximum value of the MI gain, as well as its bandwidth, has been also affected by the saturable nonlinearity. Moreover, the saturable nonlinearity may influence considerably the number of wave trains induced by MI.