Dynamics and spectral analysis of optical rogue waves for a coupled nonlinear Schrödinger equation applicable to pulse propagation in isotropic media

Abstract

The nonlinear Schrödinger equation is the standard model in nonlinear optics. The pulse propagation in an isotropic medium can be described by this equation. This paper reports the dynamics of optical rogue waves that appear in the coupled nonlinear Schrödinger equation via several effective calculation methods. The approach is based on its Lax integrable nature, and subsequently, exact rogue wave solutions are obtained by a new matrix form Darboux transformation with computer software. These rogue waves show dark or ultrahigh peak rogue wave patterns, as well as many observable peaks and depressions in their structures. Numerical simulations show that such rogue waves have more stability than the standard eye-shaped ones. In addition, with modulation instability, a large number of rogue wave structures can be produced from perturbed continuous waves. Finally, the spectral analysis method can be used to obtain the mathematical properties of the observed rogue waves in a mode-locked fiber laser, allowing us to predict, regulate and control the rogue wave appearing in the field. These results in this paper can help understand ultrashort wave phenomena found in physics and engineering domains such as optics, plasma, alkali-atom Bose–Einstein condensates, etc.