Study Of Solitons And Extreme Waves In Optical Self-induced Transparency Media

The study of novel dynamics of solitons and rogue waves can be generally thought of as one of cutting-edge research topics in nonlinear science.The history of the soliton concept can date back to 1834,when Scottish scientist John Scot Russell made his first observation of shape-maintained water waves(which he called the translation wave)in a canal near Edinburgh.Since then,especially after the 1960 s,optical soliton science has developed rapidly,and has been widely used in such fields as long-haul optical communication,optical data storage,and all-optical switching,thanks to the advent of lasers,the maturity of material manufacturing technologies and the emergence of new ultrafast diagnostic technologies.In a broad sense,the rogue wave can be referred to as a doubly localized soliton built on a finite background,hence termed soliton on finite background(SFB).It was first proposed by Dr.Howell Peregrine in1983 when solving the fundamental rational solution of the integrable nonlinear Schr(?)dinger(NLS)equation.In the past decade,there has been a surge of intense research activities on rogue wave solutions in diverse areas such as fluid dynamics,nonlinear optics,plasma physics,and acoustics,given that these solutions can model well the extreme wave events occurring in real-world settings,e.g.,oceanic giant surface waves,optical modulation instability,and financial storms.On the other hand,it has been revealed that the interaction between optical pulses and two-level resonant media can give rise to the self-induced transparency(SIT)soliton phenomenon.However,the question whether such interaction can allow the generation of extreme waves still remains open,as far as we knew.In this thesis,after a brief overview of the related concepts and recent developments of soliton and rogue waves,we give a detailed study of the propagation dynamics of SIT solitons as well as their multi-soliton interaction in resonant optical media.Then we investigate the generation of optical extreme waves and the underlying mechanism responsible for it,under specific parameter conditions.Our work includes the following two aspects:1)With the help of the Darboux transformation method,we present different kinds of exact soliton solutions of the sine-Gordon(s G)equation,including the kink solutions,the cusp soliton solutions,the degenerate soliton solutions,and the breather solutions.The multi-soliton dynamics,especially the multiple cusp soliton dynamics,are discussed as well,in which the collision behaviors and the far-field propagation characteristics are highlighted.As the propagation of optical waves in two-level resonance media can be described by the s G model under the perfect resonant condition,these soliton solutions are therefore suitable for understanding the SIT phenomenon occurring in such resonant media.2)In terms of the multi-breather solutions of the s G equation,we explored in depth the collision characteristics of breathers using different sets of system parameters.As the solution of the s G model can be reduced to that of the SIT model by a simple differential operation,we found,from the above analytical solutions,that extreme wave phenomena can actually be allowed in the SIT medium under a certain parameter condition,in a sense that the peak amplitude can be significantly higher than the surrounding wave amplitude.Moreover,the more breathers involved in,the higher the central peak amplitude formed in the collision regime.We also confirmed our analytical prediction by numerical simulations.We expect that these results may help to understand or experimentally realize the extreme wave phenomena in optical two-level atomic media.