Robustness of rogue waves: the route to improve the ultrafast propagation of pulses in wave guide structures

Abstract

In this work, an adaptive control of instability is used to improve the ultrafast propagation of pulses in wave guide structures. One focuses on robust wave profiles with ideal shape and amplitude that can be useful for the ultrafast propagation without severe perturbations. The few perturbations observed are managed to catch up the stability of pulses and pick up the ultrafast propagation. To achieve this aim, a rich generalized model of nonparaxial nonlinear Schrödinger equation that improves the description of spontaneous waves in higher nonlinear and chiral media is derived, based on the theory of Beltrami-Maxwell formalism. The type of rogue wave ideal for the fast propagation is constructed with the modified Darboux transformation (mDT) method and its robustness to nonlinear effects is shown numerically through the pseudo-spectral method. This paper provides a framework to appreciate the efficiency of rogue waves in the improvement of ultrafast propagation of pulses in wave guides, biological systems and life-science.