Theory of stability and bifurcation in a multi-quantum well laser with opto-electronic delayed feedback

This paper presents an opto-electronic feedback multi-quantum well laser system and outlines our study of the dynamics and bifurcation in a multi-quantum well laser due to the opto-electronic delayed feedback effect. We point out theoretically the conditions of stability and Hopf bifurcation of the laser. The relaxation oscillation frequency of the system is educed to be the function of the feedback level, delayed time and in-current. The route from stability to bifurcation is numerically simulated via varying the delayed time, feedback strength and in-current. The results show that the induced dynamics can be grouped into four distinct types or modes (stable, periodic pulsed, undamped oscillating or beating, and chaos), where the frequency and intensity varying with the delayed time in the two periodic regions are analyzed detailedly to find that the pulsing frequency is reduced with the long delayed time while the pulsing intensity is added with the long delayed time. And the chaotic pulsing frequency is increased with the large in-current. In addition, the carrier transport between the barrier region and the active region can characterize the dynamics in the laser to produce stable, periodic pulsed, beating and chaotic states by altering the carriers transport or escape rate value.     

Bifurcation and locking in an multi-quantum-well laser subjected to external injection

Bifurcation and dynamic stability as well as locking in an external light injection multi-quantum-well (MQW) laser are studied. Different dynamic regimes in locking diagram are analyzed with the injection level and frequency detuning. Bifurcate behavior is numerically simulated via the external injection light intensity, frequency detuning, current, linewidth enhance factor, photon loss rate and carrier loss rate, respectively. And the route to chaos from bifurcation, period-doubling and quasi-period are described by numerical analysis. A perturbation equation of four-dimension model and the bifurcation condition are demonstrated. Dynamic stability of the laser is theoretically and numerically analyzed. The bifurcate expression is theoretically given while the maximum locking frequency domain is given. The variational characteristic of the oscillation frequency in the self-pulse regimes versus the injection and detuning are numerically analyzed to find that the relaxation frequency is reduced with adding the detuning in the smaller detuning or with adding the injection in the smaller injection while the relaxation frequency will be increased with adding the detuning in the larger detuning or with adding the injection in the larger injection. We find also that the chaotic spectra are broadened with adding the detuning or narrowed with adding the injection or the current.     

Experimental control of a chaotic semiconductor laser

We have experimentally controlled the chaotic output of a single-mode semiconductor laser pumped near threshold and subject to optical feedback. We used a novel technique called dynamic targeting, which was theoretically proposed by Wieland et al. [Opt. Lett. 22, 469 (1997)]. Optical feedback causes the semiconductor laser to undergo a bifurcation cascade that exhibits regions of stability, periodicity, chaos, and coherence collapse. By adjusting the feedback phase simultaneously as the feedback strength was varied we steered the laser into the stable maximum gain mode, and thus we stabilized the system at maximum intensity.     

Control of instability in a semiconductor laser using a functional pump current generator with a dynamical parameter

In this paper, an electric circuit to control the dynamic output of a semiconductor laser is introduced. The circuit controls chaos and instability of the laser output by changing its pumping current. The change of the current is also introduced by a nonlinear map. The most important element of this nonlinear map is a dynamical variable parameter. We have studied the dynamic behavior of the laser before and after applying the control using bifurcation curves and time series. We have shown that the laser output, in the intervals of the feedback phase and strength where it is chaotic, can be totally inverted to the quasi periodic (QP) and period one (P1) oscillation modes, by control method.     

短外腔偏振旋转光反馈下1550nm垂直腔面发射激光器的动力学特性研究

基于扩展的自旋反转模型,对短外腔偏振旋转光反馈下1550 nm垂直腔面发射激光器的动力学特性进行了数值仿真和理论分析.研究结果表明:增加反馈强度会导致多个偏振开关现象出现,中等反馈强度下呈现丰富的动力学状态,譬如单周期、倍周期、准周期及混沌态,增加注入电流使Y方向线偏振模的工作区域被压缩;随着反馈延迟时间的增加,在弱光反馈时,偏振模跳变现象将会以特定的频率发生,施加中等的反馈强度将会导致模式跳变的频率增加,并且出现各种新的动力学状态,包括拍频单周期、拍频脉冲包络、拍频准周期和拍频混沌态.新动力学行为的出现是由于短外腔区激光器的动力学特性对相位变化非常敏感,从而使外腔模式间的拍频效应发挥了关键作用.此外还发现各种动力学状态之间会伴随模式间的跳变而发生相互跳变.     

一类准周期参激非线性相对转动动力系统的稳定性与时滞反馈控制

建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程. 采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性. 在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响. 采用时滞反馈控制的方法对系统分岔和极限环(域)进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环(域)的幅值和稳定性. 关键词： 相对转动 准周期参激 时滞反馈 极限环     

Enhancing the relaxation oscillation frequency of a chaotic semiconductor laser transmitter using optical dual-feedback light

A method to enhance the relaxation oscillation frequency and carrier bandwidth of a delayed feedback semiconductor laser transmitter is presented using additive optical feedback light. A formula for frequency detuning of the optical dual-feedback is developed to demonstrate that frequency detuning is added with the additive optical feedback light level. The function of the relaxation oscillation frequency of the chaotic laser is theoretically determined to show that it can be broadened by including the delay time and feedback level. Numerical results demonstrate that the bandwidth with the additive optical feedback light can be enhanced 1.7 times more than the bandwidth without it and the relaxation oscillation frequency of the chaotic laser is increased to 1.8 times more than that of the laser without it. The current can enhance the relaxation oscillation frequency and bandwidth of the transmitter more efficiently.     

Theoretical modeling of the dynamics of a semiconductor laser subject to double-reflector optical feedback

We theoretically model the dynamics of semiconductor lasers subject to the double-reflector feedback. The proposed model is a new modification of the time-delay rate equations of semiconductor lasers under the optical feedback to account for this type of the double-reflector feedback. We examine the influence of adding the second reflector to dynamical states induced by the single-reflector feedback: periodic oscillations, period doubling, and chaos. Regimes of both short and long external cavities are considered. The present analyses are done using the bifurcation diagram, temporal trajectory, phase portrait, and fast Fourier transform of the laser intensity. We show that adding the second reflector attracts the periodic and perioddoubling oscillations, and chaos induced by the first reflector to a route-to-continuous-wave operation. During this operation, the periodic-oscillation frequency increases with strengthening the optical feedback. We show that the chaos induced by the double-reflector feedback is more irregular than that induced by the single-reflector feedback. The power spectrum of this chaos state does not reflect information on the geometry of the optical system, which then has potential for use in chaotic (secure) optical data encryption.     

Period-one characteristic in an optoelectronic delayed feedback semiconductor laser and its application in sensing

Nonlinear dynamics in an optoelectronic delayed feedback semiconductor laser and its application in sensing are studied. We analyze the theories of stability and period of the laser. A route to quasi-periodic bifurcation or a stochastic state from stability is numerically analyzed by shifting the feedback level. The induced dynamics are found to be in one of four distributions(stable, periodic pulsed, period-three pulsed, and undamping oscillating).An external injection into the laser results in the process being more or less the opposite with the conventional optical injection cases. Based on this process or the dynamic regimes, we present a modeling of the incoherent detection sensor using the nonlinear period-one characteristic of the laser. The sensor discriminates the injection light variation as a sensing signal via detecting the behaviors from the period-one laser.     

双环掺铒光纤激光器混沌控制产生周期脉冲及多周期现象研究

研究了双环掺铒光纤激光器混沌控制产生周期脉冲以及多周期现象,并提出了光调制器调制泵浦控制、外部光注入控制、光衰减器控制、光延时时间控制器控制以及相位控制器控制和连续键控反馈光等多种双环掺铒光纤激光器的混沌控制方法.结果表明:用光调制器调制泵浦光能控制激光到周期态及多周期态;用外部光注入能控制激光到单周期态、双周期态、三周期态、四周期态、五周期态以及多种高周期态等,能形成多种形式相空间图样,产生双环掺铒光纤激光器独特的激光单锁模拟和双锁模拟现象;用外部光路反馈控制时,在负反馈条件下,用时间控制器控制反馈光的延时时间能控制激光到不同的周期态和双周期态,用光衰减器控制光的强度能控制激光到稳定态及周期态,用相位调制器控制反馈光的相位进行负反馈和正反馈转换时能有效地控制激光进入到稳定态及周期态;连续键控反馈光相位能控制激光到多周期态等.整个控制系统能动态、有效地控制产生周期光脉冲以及多种新颖的多周期态等.     

延迟光反馈VCSEL的混沌动力学特性

根据延迟光反馈垂直腔面发射半导体激光器动力学模型,数值模拟了激光器的混沌动力学特性,分析了外腔长度和光反馈强度对激光器混沌动力学特性的影响.结果表明:外腔较短的激光器,经过混沌区后仍会回到锁频状态|外腔较长的激光器,经过混沌区后不是进入锁频状态而是回到周期1.取定激光器外腔长度为3.0 cm,使反馈强度由小增大,得到激光器由倍周期分岔进入混沌的过程,并在混沌区中出现周期12窗口.本文对混沌保密通信的实际应用具有一定的理论参考价值.     

大幅度增加弛豫振荡频率来实现毫米级外腔半导体激光器的外腔机制转换

混沌外腔半导体激光器输出明显存在弛豫振荡特征,弛豫振荡频率小于外腔振荡频率时,外腔半导体激光器输出态是短腔机制;反之,外腔半导体激光器输出态是长腔机制.首先对比分析了弛豫振荡频率为5.6 GHz,腔长对频谱有效带宽的影响.然后同时调节注入电流和载流子寿命来大幅度地增加弛豫振荡频率.最后在弛豫振荡频率为40 GHz、腔长为毫米级(4—20 mm)时,实现由短腔机制到长腔机制的转换,进而分析了外腔反馈率和外腔长对外腔半导体激光器频谱带宽的影响.分析结果表明:短腔机制下,输出混沌态不稳定,0.1 mm的偏差就会导致混沌态与非混沌态之间的转化;长腔机制下,输出混沌态稳定,输出混沌区域较大,证明长腔机制下更有益于获得宽带连续的混沌区域.在弛豫振荡频率为40 GHz、外腔长度为毫米级时,实现了外腔半导体激光器的长腔机制,从而增大了高带宽混沌的参数空间.     

单模激光混沌特性的理论研究

在光学中，激光是产生双稳态、振荡、混沌等多种自组织现象的典型例子。本文采用非线性理论分析了单模激光的混沌特性，对描述单模激光的非线性动力学方程进行了稳定性分析，从而确定了系统失稳后进入混沌态的分歧点，并利用计算机进行了数值计算，给出了系统呈现混沌态的模拟结果。计算机数值模拟的结果与理论分析的结果相吻合。     

激光局域网络的混沌控制及并行队列同步

本文提出并研究了"单队列-双参数"光电延时反馈控制条件下的激光局域网络的混沌控制及串联的动力学行为的并行队列"交叉驱动-反馈"网络同步实现,建立了该光学局域网络的数学物理控制模型.通过含时延超越方程理论的分析,预言了该光学局域网络是可以实现混沌控制的,且网络两路结点队列是可以实现实时引导控制到多个类周期状态上的,并通过并行队列同步方程理论证明并行串联队列同步是可以获得的.结果发现在可控的激光局域网络两个并行串联队列光路上,分别实现了网络队列结点的混沌控制并能够实现多个类周期的网络结点的并行串联队列同步,实现了络网结点激光器的2周期、3周期、4周期等状态的并行队列同步,以及其他多个类周期的队列并行同步和动态同步.还发现了两个类周期并行队列网络同步控制区域.本文还给出了激光局域网络"并行多点混沌载波同步发射及其在光学超宽带通信中应用"的一个案例并成功实现.这是一种新型的激光混沌局域网络控制系统,具有光局域网络光传送与光联接核心控制技术要素,具有复杂动力学系统与网络的多变量、多空间维度及并行两路不同队列混沌控制技术特点,还具有光网络超宽带通信功能等.其研究结果对局域网络、光网络的控制与同步、激光技术以及混沌的研究具有重要的参考价值.     

Direct observation of dynamical bifurcation in a superfluid Josephson junction

We report a direct observation of dynamical bifurcation between two plasma oscillation states of a superfluid Josephson junction. We excite the superfluid plasma resonance into a nonlinear regime by driving below the natural plasma frequency and observe a clear transition between two dynamical states. We also demonstrate bifurcation by changing the potential well with temperature variations.     

Mixed external cavity mode dynamics in a semiconductor laser

We observe experimentally and numerically novel mixed-mode dynamic states of a diode laser subject to two delayed optical feedbacks. These states have been proposed and analyzed within the framework of the Lang-Kobayashi single-feedback model. Such states are combinations of two distinct external cavity modes and can be identified through a characteristic sequence of a Hopf bifurcation followed by a secondary quasi-periodic bifurcation. We present experimental and numerical results that demonstrate such sequences.     

电光双稳态系统的混沌特性分析

从理论上分析了电光双稳态系统的稳定性,通过图解方式研究了各不动点的稳定性.用数值求解的方法,确定了分岔点的具体位置,分析了该系统是经过倍周期分岔和阵发混沌途径产生混沌.数值模拟由系统状态随参量变化的分岔图和最大李雅普诺夫指数随参量的变化关系,表明本文的理论分析结果是完全自洽的.     

Chaotic dynamic behavior analysis and control for a financial risk system

According to the risk management process of financial markets,a financial risk dynamic system is constructed in this paper.Through analyzing the basic dynamic properties,we obtain the conditions for stability and bifurcation of the system based on Hopf bifurcation theory of nonlinear dynamic systems.In order to make the system’s chaos disappear,we select the feedback gain matrix to design a class of chaotic controller.Numerical simulations are performed to reveal the change process of financial market risk.It is shown that,when the parameter of risk transmission rate changes,the system gradually comes into chaos from the asymptotically stable state through bifurcation.The controller can then control the chaos effectively.     

电光双稳态系统的混沌特性分析

从理论上分析了电光双稳态系统的稳定性,通过图解方式研究了各不动点的稳定性.用数值求解的方法,确定了分岔点的具体位置,分析了该系统是经过倍周期分岔和阵发混沌途径产生混沌.数值模拟由系统状态随参量变化的分岔图和最大李雅普诺夫指数随参量的变化关系,表明本文的理论分析结果是完全自洽的.     

环形腔中激光振荡输出的横向斑图及向光学湍流的转变

在研究环形腔中激光振荡输出的分岔与混沌的基础上,采用耦合映象格子模型研究了其空间扩展系统的横向效应.数值模拟表明,随着参数的改变,空间扩展系统由均匀稳态、行波解向时空混沌演化.在一定的参数条件下,空间扩展系统从光场取入射平面波(均匀分布)开始,经对称破缺向光学湍流转变. 关键词： 横向斑图 时空混沌 湍流 数值模拟