Synchronization properties and effects of parameter mismatches in unidirectionally coupled chaotic vertical-cavity surface-emitting lasers

We numerically investigate the effects of parameter mismatches on chaos synchronization in vertical-cavity surfaceemitting lasers (VCSELs). We assume injection-locked chaos synchronization in a unidirectionally coupled and openloop optical feedback system. The accuracy of chaos synchronization is greatly affected by the mismatches of the device parameters and operation conditions between the two lasers. In particular, the oscillation frequency of the laser is one of the important parameters in a system of injection-locked chaos synchronization. However, the variations of the device characteristics of VCSELs are very large compared with those of other types of semiconductor lasers. We study the effects of parameter mismatches related to the oscillation frequency of VCSELs on chaos synchronization. We proved that mismatches in terms of the birefringence and the injection current play crucial roles for the quality of chaos synchronization.     

Chaos synchronization and communication of the polarization modes for two unidirectionally coupled vertical-cavity surface-emitting lasers

We theoretically investigate the synchronization performance of the polarization modes of two unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs), where the master VCSEL subjects to polarization-preserved optical feedback and the slave VCSEL subjects to polarization-preserved optical injection. We demonstrate that high synchronization can be achieved between corresponding polarization components of the master laser and the slave laser. We also analyze the influence of the internal mismatched parameters on the synchronization performance. Furthermore, this system is used to dual-channel communication and the different transmitted digital information is respectively recovered at each polarization branch of the slaver laser successfully with the encryption scheme of chaos masking (CM). The results open an opportunity for multichannel chaotic communication by utilizing different polarization components in single-mode or multi-transverse-mode VCSELs.     

基于外光注入互耦合垂直腔面发射激光器的混沌随机特性研究

通过在互耦合垂直腔面发射激光器(VCSELs)系统中增加外光注入, 建立了一种基于偏振可调光反馈VCSEL驱动互耦合VCSELs混沌系统模型, 分析了增加外光驱动对互耦合激光器随机特性的影响. 以不可预测度作为随机特性的评价指标, 采用信息论中的排列熵作为相应量化工具, 对系统输出混沌信号的不可预测性进行定量分析.数值研究了光强度、时延、偏振旋转角度以及驱动激光器与耦合激光器间的频率失谐对输出信号随机特性的影响.结果表明: 外光注入能够增大互耦合VCSELs输出混沌信号的排列熵, 即外光注入能够有效提高耦合系统的随机特性; 驱动激光器可调偏振片偏转角度调节到45° 附近, 注入强度适中, 满足耦合强度大于驱动激光器自反馈强度条件, 系统输出信号的排列熵较大; 在耦合时延与驱动激光器反馈时延不相等的同时, 增加驱动激光器与耦合激光器频率失谐, 外光注入互耦合VCSELs的随机特性能够得到进一步提高.     

互注入垂直腔表面发射激光器的多次偏振转换特性研究

基于垂直腔表面发射激光器(VCSELs)的自旋反转模型, 研究了互注入VCSELs系统中参数连续变化所引起的多次偏振转换(PS)特性. 研究结果表明: 连续改变互注入强度ξ、两个互注入VCSELs中一个激光器的激射频率以及同时连续改变两个激光器的激射频率, 均可产生多次的PS. 详细分析了上述三种参数连续变化所引起的多次PS的特性, 并讨论了耦合延时时间对多次PS特性的影响.     

Influence of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers

We analyze theoretically the effect of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs). Chaos in the master laser is induced by delayed optical feedback, and the slave laser is subject to isotropic optical injection from the master VCSEL. We show that the synchronization quality can be enhanced when the chaotic regime in the master VCSEL involves both fundamental orthogonal linearly polarized modes.     

光电耦合对InGaN/GaN量子阱光学性能的影响

围绕高性能GaN基垂直腔面发射激光器(VCSELs),设计了两种具有不同光电耦合强度的InGaN/GaN量子阱(QWs)样品,研究了它们的光学性质。样品A在腔模的两个波腹处各放置两个InGaN耦合量子阱,而样品B在腔模的一个波腹处放置5个InGaN耦合量子阱。计算表明样品A具有较大的相对光限制因子1.79,而样品B为1.47。光学测试发现样品A有着更高的内量子效率(IQE)和更高的辐射复合效率。使用两种样品制作了光泵VCSEL结构,在光激发下实现激射,其中基于样品A的VCSEL有着更低的激射阈值。结果表明有源区结构会显著影响量子阱与光场的耦合作用、外延片的内量子效率、辐射复合寿命和VCSEL激射阈值,同时也说明样品A的有源区结构更有利于制作低阈值的VCSEL器件。     

Stable anticipation synchronization in mutually coupled vertical-cavity surface-emitting lasers system

Two vertical-cavity surface-emitting lasers(VCSELs) are mutually coupled through a partially transparent mirror (PTM) placed in the pathway. The PTM plays the role of external mirror,which controls the feedback strength and coupling strength.We numerically simulate this system by establishing a visible SIMULINK model.The results demonstrate that the anticipation synchronization is achieved and it can tolerate some extent frequency detuning.Moreover,the system shows similar chaos-pass filtering effect on unidirectionally coupled system even both VCSELs are modulated.This system allows simultaneously bidirectional secure message transmission on public channels.     

Nonlinear dynamics and localized synchronization in mutually coupled VCSELs

Nonlinear dynamics of mutually coupled vertical-cavity surface-emitting lasers (VCSELs) are studied theoretically. We consider both identical and nonidentical cases, respectively. For identical cases, where the device parameters and the operating conditions are the same, both lasers show the same behaviors with an identical output, and some typical nonlinear states, including period-one, period-two, multi-period and chaos, are observed. However, for nonidentical cases, the symmetric behaviors are broken. Due to the mismatch of the bias current of these two lasers, the system nonlinearity is increased and the synchronization performance is degraded greatly. Nevertheless, it is found that the coupled VCSELs can still exhibit a form of localized synchronization when they operate under the periodic state introduced by either the weak coupling or the frequency detuning.     

光反馈诱发长波长垂直腔面发射激光器低功耗偏振开关

基于扩展的自旋反转模型,对光反馈诱发下长波长垂直腔面发射激光器中的低功耗偏振开关进行了理论研究.研究表明:长波长垂直腔面发射激光器在自由运行下未能获得的偏振开关现象,可以通过引入中等强度的偏振旋转光反馈来实现.对比强弱两种不同的线性色散效应,发现了一些有趣的现象:弱线性色散条件下更易于在低注入电流下获得偏振开关,并且产生偏振开关所需的反馈强度具有更大的调控范围;强色散效应中未能始终获得偏振开关,会出现两模共存区,并且偏振开关出现的注入电流值较高.同时,观察到的偏振模跳变和多偏振开关现象类似于短波长垂直腔面发射激光器,因而证实这两类激光器在偏振开关的本质规律上是相似的.此外,还对长波长垂直腔面发射激光器不易在低注入电流下获得偏振开关的原因进行了分析,并给出了合理的解释.     

Theoretical study on phase conjugation in weakly injected vertical-cavity surface-emitting lasers

This paper gives a detailed theoretical investigation on phase conjugation induced by nearly degenerate fourwave mixing in single mode vertical-cavity surface-emitting lasers （VCSELs） with weak optical injection. Considering VCSELs that can work in linearly polarized or elliptically polarized states, it derives the theoretical expression of the conjugated field by small signal analysis based on the vectoral rate equations-the spin-flip model. For linearly polarized state, VCSELs show similar conjugate spectra to edge-emitting semiconductor lasers. For the elliptically polarized state, dichroism and birefringence parameters as well as the spin-flip rate can change the conjugate spectra. Especially, when frequency detuning of the probe and pump waves is between the positive and negative relaxation oscillation frequency, changes are evident. For specific values of parameters, conjugate efficiency between 20 dB to 40 dB are obtained.     

Synchronization of polarization mode of two unidirectionally coupled vertical-cavity surface-emitting laser and its application in communication

We theoretically investigate the synchronization performance of polarization mode of two unidirectionally coupled vertical-cavity surface-emitting laser (VCSEL) and propose an encryption scheme, where the phase of the polarization states of the master laser are modulated. It is demonstrated that high synchronization can be achieved between corresponding polarization components of the master laser and the slave laser. Moreover, two distinct synchronization regimes exist, complete synchronization and injection locking. The transmitted digital information is successfully recovered at each polarization branch of the slaver laser. The results open an opportunity for multichannel chaotic communication by utilizing different polarization components in single-mode or multi-transverse-mode VCSELs.     

Oscillation properties of matter-wave bright solitons in harmonic potentials

We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter- and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton (without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects.     

Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback

Time-delay (TD) signatures of chaotic outputs generated by vertical-cavity surface-emitting lasers (VCSELs) are investigated quantitatively by using two proposed estimators, the peak signal to mean ratio (PSMR) calculated based on the auto-correlation function, and the valley signal to mean ratio (VSMR) calculated based on an information-theory-based estimator, the permutation entropy (PE) function. The VCSELs subject to variable-polarization optical feedback (VPOF) are considered, and the effects of polarizer angle, feedback strength, feedback delay and injection current are discussed. When the feedback strength is small, the TD signatures for the fully developed chaotic outputs of VCSELs can be well concealed for all polarizer angles. While for large feedback strength, the TD signatures cannot be concealed for any polarizer angle. However, for moderate feedback strength, the TD signatures of VCSELs with VPOF at intermediate polarizer angles can be better concealed than those of VCSELs with conventional polarization-selected optical feedback. Thus, the VCSELs with VPOF are extremely interesting for the security-enhanced chaotic optical communication systems.     

基于两正交互耦1550nm垂直腔面发射激光器获取多路随机数

提出将正交互耦1550 nm垂直腔面发射激光器(1550 nm-VCSEL)在优化条件下输出的多路平均功率可比拟、延时特征(TDS)得到有效抑制的混沌信号作为混沌熵源,经8位模数转换器(ADC)量化和最低有效位(m-LSB)后续处理获取多路物理随机数的方案,并研究了系统参量对最终获取的比特序列随机性的影响.首先,基于VCSEL的自旋反转模型分析耦合强度和频率失谐对两个正交互耦合1550 nm-VCSEL输出动力学的影响,初步确定利用该系统产生四路平均功率可比拟、TDS得到抑制的混沌信号所需的耦合强度和频率失谐优化范围;在此基础上,选择一个耦合强度值,利用处于优化范围内的不同频率失谐下获取的四路混沌信号作为熵源,经8位ADC量化和m-LSB后续处理得到最终的比特序列;最后,采用NIST Special Publication800-22统计测试套件对获取的最终比特序列的随机性能进行测试,确定了同时获取四路高质量随机数所需的参数范围.     

Polarization switching and synchronization of mutually coupled vertical-cavity surface-emitting semiconductor lasers

Polarization switching (PS) dynamics and synchronization performances of two mutually coupled vertical-cavity surface-emitting lasers (VCSELs) are studied theoretically in this paper. A group of dimensionless rate equations is derived to describe our model. While analysing the PS characteristics, we focus on the effects of coupling rate and frequency detuning regarding different mutual injection types. The results indicate that the x-mode injection defers the occurrence of PS, while the y-mode injection leads the PS to occur at a lower current. Strong enough polarization-selective injection can suppress the PS. Moreover, if frequency detuning is considered, the effects of polarization-selective mutual injection will be weakened. To evaluate the synchronization performance, the correlation coefficients and output dynamics of VCSELs with both pure mode and mixed mode polarizations are given. It is found that performance of complete synchronization is sensitive to the frequency mismatch but it is little affected by mixed mode polarizations, which is opposite to the case of injection-locking synchronization.     

Multi-state optical flip-flop memory based on ring lasers coupled through the same gain medium

We investigate a system consisting of multiple ring lasers coupled by a single gain medium. All the ring lasers share a common feedback arm. The output power of an individual laser shows periodic oscillations as a function of time. The periodicity of the oscillation is determined by the ratio of the roundtrip times of the feedback arm and the ring cavity. In the case that two of such ring lasers are coupled, either their oscillation periodicities are synchronized, or the system is bi-stable. In the latter operation regime, the system can act as an optical flip-flop memory whose state be switched by injection of external light. The concept can be extended to multi-state operations; an eight-state optical flip-flop memory is experimentally demonstrated.     

基于单向注入垂直腔面发射激光器系统的密钥分发

随机源对于信息理论安全的密钥分发至关重要,本文提出了一种基于单向注入垂直腔面发射激光器系统的密钥分发方案.首先基于单向注入的方式产生无时延特征的激光混沌信号,并通过单向注入驱动两个从激光器产生带宽增强的混沌同步信号.然后经过采样、量化以及异或等后处理,生成密钥流.数值仿真结果表明,在单阈值情况下,合法用户之间的误比特率低至1%左右,合法用户与窃听者之间的误比特率都高于10%;在双阈值情况下,误比特率可以低至10^-6.最后,对生成的密钥流进行了NIST随机性测试.该方案有效地增强了密钥分发的安全性.     

Oscillation death in a coupled van der Pol–Mathieu system

We report an investigation of the oscillation death (OD) of a parametrically excited coupled van der Pol–Mathieu (vdPM) system. The system can be considered as a pair of harmonically forced van der Pol oscillators under a double-well potential. The two oscillators are coupled with a cubic nonlinearity. We have shown that the system arrives at an OD regime when coupling strength crosses a threshold value at which the system undergoes saddle-node bifurcation and two limit cycles coalesce onto a fixed point of the system. We have further shown that this nonautonomous system possesses a centre manifold corresponding to the OD regime.     

模型化研究两细胞间基因、蛋白耦合振荡中的噪声效应

本文基于Hill动力学与Michaelis-Menten方程,建立理论模型研究两细胞间基因、蛋白耦合振荡中的噪声效应.研究发现,在Notch信号通路中,两细胞间基因、蛋白耦合振荡呈现了周期振荡特性,表明了细胞间信号传导的同步振荡特性.“内在”噪声和“外在”噪声对两细胞间基因、蛋白耦合振荡有着不同的作用.内噪声有利于细胞间Notch信号通路中各基因、蛋白表达再次提升.外噪声诱导通路中基因、蛋白的表达水平降低,周期振荡变得阻尼.内、外噪声共同作用不仅可使得基因表达适当并呈现出持续振荡模式,而且还可使得细胞间基因转录合成相应的蛋白过程呈现出持续振荡模式.从而表明了基因表达的内、外噪声共同作用有利于控制细胞间基因激活、蛋白合成保持周期节律性.本文理论结果揭示了内外噪声对细胞间Notch信号通路动力学的一种调控机制,确定了内外噪声各自的调控效应,澄清了内外噪声共同作用调控体系持续周期振荡的物理机制,理论结果符合实验,可为设计阻止Notch体系基因、蛋白变异导致的多种疾病和癌症的通路治疗方案提供理论依据.     

基于双光注入锁定1550 nm垂直腔表面发射半导体激光器产生可调谐毫米波

基于自旋反转模型, 对双光注入下1550 nm 垂直腔表面发射半导体激光器(1550 nm-VCSEL)的非线性动力学行为进行了理论分析和数值仿真研究. 结果表明: 当一个中心波长位于1550 nm 的副VCSEL(S-VCSEL)同时受到来自两个主VCSELs (M-VCSELs)的光注入时, 在适当的注入条件下, S-VCSEL可处于双光注入锁定态. 此时, S-VCSEL中的两偏振模式均呈现频率为两注入光频率之差的周期性振荡, 输出的光谱仅包含两个主频率部分, 即光谱具有单边带特征. 因此, 基于双光注入下S-VCSEL的周期性振荡可以获得两个相互正交的光毫米波. 通过调节两个M-VCSELs之间的频率差异可使毫米波频率在较大范围内连续可调, 通过调节系统参量可以控制毫米波功率以及调制深度. 关键词： 垂直腔表面发射激光器 双光注入 毫米波 调制深度