Effect of nonlinear saturation on tunable instability gain spectra in meta materials with higher-order nonlinearities

This work studies the development of windows of harmonious instability in negative refractive material. After taking into account the fundamental need to monitor instability, such as self-phase modulation and group velocity spreading, we first examine the effects on the gain spectrum of fourth and third-order dispersals, cubic–quintic nonlinearity, higher-order nonlinear dispersions, self-steepening, and detuning parameter. Furthermore, in metamaterials with the aforementioned nonlinear effects, we investigate the influence of an adjustable nonlinear saturation effect over the modulational instability. Tunable modulation instability (MI) gain spectrum formation results from the tunable material parameters made possible by the engineering freedom offered by metamaterials. As a structure is operated at high incident power, generally exceeding the medium’s saturation inception, the SNL becomes a robust case. The nonlinear saturation window with negative index material can also produce adjustable instability gain spectrum formation. More methods for forming solitons and ultrashort pulses with desired parameters can be achieved with this tunable gain spectrum. The numerical approach validates the analytical prediction that came from the linear stability study.