Effects of higher-order nonlinear dispersions on modulational instability in a three-core coupler with negative index material channel and saturable nonlinearity

A theoretical investigation on the impact of high-order nonlinear dispersions of the modulation instability (MI) spectra in the three core triangular oppositely directed coupler with negative index material channel is carried out. A keen attention was paid to find out the influence of self-steepening (SS), intrapulse Raman scattering (TR), second-order nonlinear dispersion (SOND) as well as saturable nonlinearity (SNL) on the MI spectra. Gain spectra has been investigated for both anomalous group velocity dispersion (GVD) and normal GVD regime. Particularly, our results show that in the normal GVD regime, the instability gain exists even if the perturbation frequency (Ω) is zero; and the instability gain at Ω = 0 is nil when the dispersion is anomalous. We also find that the magnitude and sign of SOND exert strong influences on MI sideband. Furthermore, by adjusting various parameters such as SS, intrapulse Raman scattering, and SOND, we observe the occurrence of new instability regions. The MI sidelobes, as well as its bandwidth, have also been affected by the SNL. Finally, the SNL may influence considerably the number of wave trains induced by MI. These results can help to understand the generation of soliton-like excitation in nonlinear three-core oppositely directed couplers with a particular attention on a negative-index material channel.