回音壁式耦合光力学系统中的混沌现象  

Route to chaos in whispering gallery mode coupled opto-mechanical systems

作　　者：华志豪 郭琴[1] 樊碧璇 谢旻 Hua Zhi-Hao;Guo Qin;Fan Bi-Xuan;Xie Min(College of Physics and Communication Electronics,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]江西师范大学物理与通信电子学院,南昌330022

出　　处：《物理学报》2023年第14期101-108,共8页Acta Physica Sinica

基　　金：国家自然科学基金地区科学基金(批准号:12064018,11964014);江西省教育厅科学研究项目(批准号:GJJ191683);江西省主要学科学术和技术带头人培养计划——青年人才项目(批准号:20204BCJ23026)资助的课题。

摘　　要：在光力学系统中,辐射压力引起的非线性可导致系统产生混沌等多种丰富的动力学行为.从有序转变到混沌有各种各样的途径,本文研究了回音壁式耦合光力系统中两种不同途径通往混沌的现象——倍周期分岔道路和准周期道路.两个全同的光力学子系统通过光学倏逝波进行耦合,调控子系统间的耦合强度,可以有效地改变系统的动力学行为.采用分岔图、李雅普诺夫指数以及相空间轨迹的变化分析系统从有序到混沌的转变.研究表明,较强的耦合强度会迫使两个子系统的振荡产生完全同步,子系统间相互耦合的作用可等效于子系统光学模频率与外加控制场频率失谐量的增加,耦合光力学系统的动力学行为等效于单个光力学系统的动力学,可实现倍周期分岔道路通往混沌的转变.而对于相对较弱的耦合,耦合系统的动力学将在高维相空间展开,极限环发生Hopf分岔,形成环面吸引子.选取合适的失谐量,耦合系统可实现从准周期道路进入混沌的现象.In opto-mechanical systems,the nonlinearity caused by radiation pressure can lead to various abundant dynamical phenomena such as chaos.Chaos is an important branch of nonlinear dynamics,and researchers focus on understanding the transitions from order to chaos in different systems.In this paper,we investigate the chaotic dynamics in a system consisting of two evanescently coupled identical cavity opto-mechanical subsystems,where the optical fields are in whispering gallery modes.To thoroughly analyze the transition from order to chaos in our system,we utilize the bifurcation diagrams,the Lyapunov exponents,and phase space trajectories to characterize the system properties.It is found that the coupling strength between the two optomechanical subsystems plays a crucial role in determining the systemic dynamic behaviors.There are two routes to chaos in our system i.e.the period-doubling transition and the quasiperiodic transition.These routes correspond to strong coupling and weak coupling between the two opto-mechanical subsystems,respectively.Furthermore,the results show that the synchronization between the oscillations in the two opto-mechanical subsystems can occur under strong coupling.In this situation,the dynamic behaviors of the two optomechanical subsystems are exactly identical and the manipulation of the coupling strength is equivalent to the tuning of the frequency detuning between the cavity fields and their corresponding driving fields.Consequently,the coupled system behaves as a single opto-mechanical system,enabling a period-doubling transition to chaos through increasing the coupling strength.In the case of weak coupling,the dynamics of the two optomechanical subsystems are no longer synchronized,and the coupled system dynamic behaviors unfold in an eight-dimensional phase space.The limit cycles experience the Hopf bifurcation,resulting in the emergence of a toric attractor.Within a certain range of parameters,i.e.appropriate frequency detunings,the two-dimensional torus becomes unstable as couplin

关 键 词：耦合光力学系统 倍周期分岔 准周期运动 混沌 

分 类 号：O439[机械工程—光学工程]