Characteristics Of Super-regular Breather In Nonlinear Optical Systems

Dynamics of nonlinear waves is one of most important topics in nonlinear science.According to the distinction of physical properties,commonly nonlinear waves can be classified into three types: soliton,rogue wave and breather.Recent studies have shown that the generation of rogue wave and breathers stems from the widespread modulation instability(MI)in nonlinear physical systems.This is a fundamental property of many nonlinear dispersive systems,which is associated with the growth of small amplitude perturbations on a plane wave background.MI consists of two states,a linear growth state and a nonlinear evolution state.In general,the MI criterion and the growth rate of the initial linear state can be easily obtained by linear stability analysis.However,the precise description of the complete MI process is still an open question until now.Super-regular(SR)breather describes the complex evolution process of multiple quasiAkhmediev breathers developed from a localized small perturbation,the MI induced by localized perturbation.Recently,SR breather has been widely concerned because it can accurately describe the evolution of MI of local small amplitude perturbations.Based on the standard scalar nonlinear Schr¨odinger equation,the dynamical characteristics of SR breathers has been studied.On the other hand,experimentally SR has been confirmed in both optics and hydrodynamics.However,the study of SR breathers in the actual complex physical systems(beyond the standard nonlinear Schr¨odinger model)is still blank,and the essence of the corresponding relationship between SR breathers and MI is still unclear.In this paper,based on existing experimental facts and theoretical models namely in the actual optical physics system(considering high-order effects,multi-mode fiber interactions,and light-matter interaction by dopant atoms),we explore the characteristics of fundamental nonlinear waves and SR breathers,state transition and the relationship between growth rate of SR breathers and MI.These results extend,to some extent,our understanding of the characteristics of nonlinear wave and complete MI in actual optical systems.The details are given as follows:1.Characteristics,state transitions and dispersion management of femtosecond SR breathers in single-mode fibersFor the propagation of ultrashort pulses in optical fiber,third-order effects such as higherorder dispersion,self-steepening,and self-frequency shift impact strongly the properties of nonlinear waves.We study SR breathers in a complex modified Korteweg-de Vries(mKdV)equation and a non-autonomous higher-order nonlinear Schr¨odinger equation.By using Darboux transformation and Jukowsky transform,the the exact solution of general fundamental nonlinear waves and the the exact solution of SR breathers is given.We demonstrate that such SR waves can exhibit intriguing nonlinear structures,including the half-transition and full-suppression modes,there are no analogues in the standard nonlinear Schr¨odinger equation.Furthermore,we discuss the propagation behaviors of controllable SR breathers.These results provide a theoretical reference for the realization of SR experimentally.2.Characteristics of fundamental nonlinear wave in erbium-doped fiber systemsNonlinear waves propagating in an erbium-doped fiber have attracted special attention,since people find that the resonant absorption of the erbium-doped two-level system is a good solution to the optic signal attenuation problem in fiber.In general,the dynamics of nonlinear waves in the erbium-doped fibers is described by the coupled nonlinear Schr¨odinger and the Maxwell-Bloch models.We first study the characteristics and state transition of different types of nonlinear waves,including multi-peak soliton,periodic wave,anti-dark soliton,and W-shaped soliton.Then,considering the higher-order effects,by using the Darboux transformation,the general fundamental exact solution of nonlinear waves in a coupled Hirota and Maxwel-Bloch(H-MB)model is given.In particular,important characteristics of multi-peak solitons induced by the higher-order effects,such as the velocity changes,localization or periodic attenuation,and state transitions,are revealed in detail.3.Polariton Super-regular breathers in a resonant erbium-doped fiberWe study polariton SR breathers triggered by the resonant interaction of an optical field and two-level doping ions in an erbium-doped fiber.We demonstrate explicitly that the optical wave component always features a bright structure that describes the MI development from localized small perturbations,while the SR matter-wave breathers exhibit more complicated dynamical evolution.Despite it is complex,the exact link between these SR breathers and MI is established strictly by showing that the absolute difference of group velocities of SR breathers coincides exactly with the linear MI growth rate.In particular,we show how a small dip perturbation of the dark SR breather in the matter wave component induces an intriguing MI process of completely exponential decay.These results will enrich our understanding on the MI development in complex coupled light-matter interaction systems.4.Characteristics of fundamental and Super-regular modes in a multiple self-induced transparency systemWe study fundamental and SR nonlinear modes on a plane-wave background in a multiple self-induced transparency system,which is governed by the multi component coupled Maxwell-Bloch equations.Important characteristics of fundamental mode transitions and SR waves induced by the interaction between different components are revealed in detail.In particular,we demonstrate that the SR waves can exhibit some novel states,including the halftransition,full-transition and full-suppression modes,which are absent in the standard SR wave theory reported previously.It is shown that these different nonlinear states can evolve from an identical initial perturbation.Our results will enrich the understanding of MI of the nonlinear stage in a coupled multi component wave system.