非线性光学系统中呼吸子前沿发展现状(特邀)

Frontier Progress of Breathers in Nonlinear Optical Systems(Invited)

呼吸子泛指一类具有周期演化或周期分布结构的非线性波,它已成为非线性光学系统的研究热点之一。介绍了多种呼吸子在时域和频域空间中的动力学特性,讨论了其历史发展与实际物理意义。通过分析调制不稳定性与呼吸子之间的关系,讨论了呼吸子的激发机制及不同呼吸子之间的定量转换关系。由于呼吸子间存在多种相互作用形式,还讨论了由呼吸子碰撞诱发的高振幅波、Superregular呼吸子等过程。这些结果有助于读者对非线性系统中呼吸子动力学的理解,并进一步探究和实现光学呼吸子的实际应用与可控激发。

Breathers,nonlinear waves with periodic evolution or periodic distribution,whose shapes undergo periodic oscillations during propagation,can be localized in time or space with a finite background.Such breathers are widely found in physical systems such as nonlinear optics,fluid mechanics,Bose-Einstein condensates and PT-symmetric systems.Usually,according to the different excitation background,it can be divided into zero background and plane wave background.Among them,breathers on zero background are essentially“multi-soliton bound states”,and there are extensive experimental reports in ultrafast fiber lasers.Here we emphasize the importance of the breathers on the plane wave background of the latter case.Indeed,these breathers exhibit periodic energy exchanges with the plane wave background.Common breathers are mainly classified by their properties into Kuznetsov-Ma breather,Akhmediev breather,Tajiri-Watanabe breather,and Super-regular breather.Quite remarkably,the Akhmediev breather can be used to describe the well-known Fermi-Pasta-Ulam recurrence and higher-order modulation instability,showing the dynamic processes with doubly periodic characteristics such as regular or shifted recurrence and pulse splitting.In addition,the study of breathers is helpful to understand the phenomena including the generation of supercontinuum and turbulence in nonlinear systems.Moreover,the interactions of the breather have been shown to be useful for high-power pulse preparation and to reveal the nonlinear evolution of modulation instability.Generally,the study of the breather dynamics is mainly based on the integrable(1+1)dimensional nonlinear Schrödinger equation.In brief,the existence and excitation conditions of different kinds of breathers are obtained theoretically by exact solution in the integrable system,and the different breather structures are obtained by using the simple initial states for evolution.On the other hand,the formation conditions of breathers can be analyzed through the excitation mechanism of different breathers,and the dynamic properties and experimental realization of breathers can be explored.At present,the theoretical and experimental results of breathers are mainly discussed from the following aspects:1)the existence conditions of breathers in different nonlinear physical systems;2)theoretical method for accurate solution of breathers;3)structure and properties of breathers;4)excitation mechanism and production conditions of breathers;5)evolution characteristics of different breathers;6)interaction characteristics of breathers;7)applications of breathers in supercontinuum generation,high-power pulse preparation,etc.For nonlinear physical system,nonlinear fiber is a mature nonlinear experimental platform in experimental science.Therefore,based on nonlinear optical systems,this paper briefly discuss the experimental and theoretical research progress of several typical breathers on continue wave background.Based on the analytical expressions of fundamental breathers,the dynamical properties of Kuznetsov-Ma breather,Akhmediev breather,and Peregrine rogue waves in time and frequency domains are enumerated in detail.The historical development and practical physical significance of breathers is also discussed.The excitation mechanism and generation conditions of the fundamental breathers are discussed based on the modulation instability in nonlinear systems.The results show that Kuznetsov-Ma breather and Akhmediev breather can be excited by localized perturbation with zero modulation frequency and periodic perturbation with non-zero modulation frequency,respectively.Furthermore,the quantitative conversion relationship between different breathers is analyzed by combining effective energy and modulation instability.Finally,we show the dynamics of breathers interaction on a plane wave background.The phase sensitive collision of two breather is reported to form three different localized structures,that is super-high peak rogue waves,quasi-annihilation super-regular breathers,and ghost structures without any change.These important breather structures have been confirmed and discussed in detail in theoretical and optical experiments.Actually,understanding the physical significance of fundamental breathers and their interactions is expected to play an important role in the study of rogue wave events generation,integrable turbulence,modulation instability,Fermi-Pasta-Ulam recurrence and other phenomena in nonlinear systems.