Polarization Switching Bistability and Dynamics in Vertical-Cavity Surface-Emitting Laser under Orthogonal Optical Injection

Bistability as well as dynamics associated to polarization switching in a vertical-cavity surface-emitting laser (VCSEL) submitted to orthogonal optical injection from an external master laser are investigated. Intensity-polarization switching bistability is studied by increasing and decreasing the intensity of the injected beam and for a fixed frequency detuning, i.e. the frequency offset between master and the free running VCSEL. Depending on the frequency detuning, bistable switching is experimentally found to occur with or without injection locking of the fundamental mode to the master laser frequency. For large positive detuning, injection locking of the first-order transverse mode with a strong depression of the fundamental mode has been observed. The case of frequency – polarization switching bistability, i.e. when the frequency detuning is first decreased and then increased for a fixed injected power, has also been theoretically analyzed. Qualitative comparison with previous experimental work is presented for the dependence of the width of the bistable switching region on the injection strength level. Finally we show an experimental result of complicated dynamics including period doubling route to chaos that accompany polarization switching and which motivates future theoretical investigations.     

光纤激光器自组织相干阵列的理论分析

 分析了光纤激光器自相干阵列最简单的情况——两个光纤激光器之间的相位锁定过程。建立了该过程的数学模型，并对它的时间特性和输出光束的模式进行了理论和数值分析，讨论了运行频率差和耦合系数对锁相过程的影响。对于运行频率相等的两个光纤激光器，当两个光纤激光器初始相位差不为0时，相位锁定后的激光器阵列输出模式为异相模；对于运行频率不等的情形，给出了锁相运行对两个光纤激光器运行频率差的要求，并分析了降低这种要求的几种方法。     

平坦宽带混沌激光的产生及同步

利用光纤环长外腔光反馈半导体激光器产生了频谱平坦的宽带混沌激光,其对应的激光频谱可有效地隐藏外腔的谐振频率,增加了系统的保密性.通过单向耦合方式,将产生的混沌激光注入到另一个参数相近的半导体激光器中,实现了平坦宽带混沌同步输出,两同步激光器输出的相关系数达到084.同时实验研究了注入强度和主从激光器的频率失谐对同步质量的影响,结果表明在强光注入锁定下,在很大频率失谐范围内均可实现同步,而且注入强度越大,主从激光器输出的相关系数越大,维持混沌同步所允许的频率失谐范围越大. 关键词： 混沌同步 单向光纤环 光反馈 半导体激光器     

Transient dynamics of a single-mode semiconductor laser subjected to both optical feedback and external light injection

The transient dynamics of a single-mode semiconductor laser subjected to both weak optical feedback and light injection is studied. Even at detuning values for which injection locking is not effective, turn-on jitter and frequency jitter can still be strongly reduced by adjusting either the length of the external cavity or the detuning.     

Experimental Injection Map of Semiconductor Laser Submitted to Filtered Feedback

Optical injection consists in the unidirectional coupling between a “slave” laser (SL) and a “Master” laser (ML). The injected SL may exhibit different behaviors, showing frequency locking, wave mixing, relaxation regimes, period doubling, and chaos. The different regimes may be mapped on a chart where the injected power and the detuning between the slave and the master frequencies are varied. In this paper, a detailed overview of the regimes are given when the SL is submitted to both optical injection and filtered optical feedback. This last coupling is realized thanks to an extended cavity, which includes a frequency filter. When the SL is operating far from threshold (4 I_th), typical regimes mentioned for feedback-free laser are observed for all the external-cavity modes. On the contrary, when the SL operates close to threshold (1.5 I_th), it is shown that the dynamics is wealthier. New regimes, as one for which simultaneously chaos and locking occur, can be identified, in comparison to the case of a single-frequency SL.     

外部光注入空间耦合半导体激光器高维混沌系统的增频与控制研究

提出外部光注入空间耦合半导体激光器系统,研究 外部光注入两激光器混沌振荡频率增强以及混沌控制等特点, 给出稳定频率失谐公式.研究表明,当单激光器注入时,注入激光器 呈现出三个混沌扩频区域;发现在强激光注入条件下,随着注入程度的 增加,注入激光器混沌振荡频率增强非常有效且可达到 3.5倍以上(尽管另一个激光器频率会缓慢下降); 随着注入光正频率失谐的增加,两激光器混沌振荡都能进一步增 强;发现混沌控制窗口,即在弱注入条件下两激光器可以被控制到单周 期、双周期、四周期、六周期等.当双激光器注入时,随着注入程度 的增加,两激光器混沌振荡频率 进一步增加, 且可达到3.5倍和2.65倍以上; 随着注入光正频率失谐增加, 两激光器混沌振荡频率增加.双激光器注 入控制混沌的一个窗口也被发现:即在强注入条件下两激光器可以被 控制到单周期、三周期、六周期等.最后详细给出了单激光注入系 统从单周期模式锁定到类周期再进入混沌增频的发展路径以及双 激光注入系统从混沌到类周期再进入单周期模式锁定的演化控制路径等.     

用半导体环形激光器产生混沌信号

提出了一种由一个分布式反馈激光器为主激光器和一个半导体环形激光器为从激光器组成的主从式激光混沌系统方案,主激光器产生的光单向注入到从激光器中,通过调整注入系数、主从激光器的失谐频率和从激光器的偏置电流,使从激光器工作在混沌状态,输出混沌信号。从基于光注入条件下的环形激光器的速率方程组入手,数值模拟了主从激光器的失谐频率、注入系数和从激光器的偏置电流3个工作参量对从激光器输出动态的影响。研究表明:外光注入条件下,半导体环形激光器可以产生混沌信号。通过分析得出:当失谐频率为3.9 GHz、注入系数为0.07、偏置电流为81 mA时,环形激光器可以产生功率谱平坦、带宽较宽的高质量混沌信号。     

Numerical study of the spiking instability caused by modulation frequency detuning in an actively mode-locked solid-state laser

We have studied both analytically and numerically the transient active mode locking in the case of a modulation frequency detuning. Analytical results for pulse width and position, extending previous works, are obtained within the frame of the stationary theory by assuming that a short pulse restores its shape after each round trip. Numerical evaluation leads to relaxation oscillations and change of the short-pulse shape. The results of both approaches agree with each other only for small detunings, when laser is operated in the steady state. For larger detunings the laser dynamics change dramatically, and the three operation modes observed earlier in experiments were demonstrated numerically: sequences of damped relaxation oscillations, deep periodic spiking and chaotic spiking. The periodic spiking can be used to increase the intensity of mode-locked pulses.     

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.     

两种调制方式下主从激光器同步性能的理论研究

 以单周期信号为例，数值模拟并讨论了注入频率和注入光场波动强度对主从式半导体激光器同步性能的影响。分别通过直接调制和外部调制两种方式获得单周期信号，并采用改进的参数——相似指数评价系统的同步性能。研究结果表明：当注入强度足够大时，系统实现注入锁定同步，外部调制的相似指数大于内部调制；注入强度恒定时，同步品质几乎不受调制指数的影响，而受调制频率的影响；由于内部、外部调制引起主激光器的输出反相，两种调制方式下同步品质随调制频率的变化趋势也相反。     

Low-Frequency Fluctuation and Frequency-Locking in Semiconductor Lasers with Long External Cavity Feedback

The properties of low-frequency fluctuations in semiconductor lasers with optical feedback from a long external cavity are experimentally studied. Frequency-locking of the laser light output to the injection current modulation is observed when the modulation frequency approaches the external cavity mode. The modulation frequency for the successful frequency-locking is always less than the external cavity mode frequency and the locking domains as a function of the modulation amplitude is asymmetric with respect to the frequency detuning.     

Locking bandwidth and birefringence effects for polarized optical injection in vertical-cavity surface-emitting lasers

The aim of this paper is to investigate the effects of external optical injection taking account of polarization and electron spin properties in vertical-cavity surface-emitting lasers (VCSELs). Using external polarized injection we seek the locked phases and amplitudes of specific polarized fields in terms of injection level and frequency detuning, taking account of two kinds of distinguishable carrier density (spin-up and spin-down). For the conventional form of optical injection without taking account of spin-polarized fields there are three fundamental equations describing the carrier density, field amplitude and phase. However, by using the spin flip model (SFM), the combined effect of polarized fields along two perpendicular crystal axes and electron spin properties results in six equations. We analyse the conditions for stable locking and also the influence of birefringence effects on the stability map of detuning versus optical injection for both cases of injection polarized parallel and perpendicular to the lasing mode of the solitary VCSEL. For given values of pumping and spin relaxation rate there is a minimum birefringence rate for orthogonal injection. Above this value three regions of elliptical polarization are found in the stability map, namely “quasi-stability” (QS), “coupled limit cycle” (CLC) and “coupled chaos” (CC). The three regions of linear polarization, namely chaos, limit cycle and stability, are reduced in area compared to the case of parallel injection. For orthogonal injection it is found that increased birefringence or reduced spin relaxation rate causes the stable locking region to begin at higher injected power and frequency detuning.     

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.     

Enhancement of chaotic carrier bandwidth in laser diode transmitter utilizing external light injection

Semiconductor laser with optical feedback emitting chaotic optical signal can be treated as chaotic carrier transmitter. Based on laser rate equations, we numerically study the effect of external injection light on the bandwidth of chaotic carrier transmitter. Our numerical simulation shows that the bandwidth of the chaotic carrier transmitter can be enhanced significantly by external photons injection. Compared with the 2 GHz relaxation oscillation frequency of a solitary laser diode without optical injection, the bandwidth of a chaotic carrier transmitter is expanded to 14.5 GHz with injection parameter at k_inj = 0.39. Simulation results also demonstrate that the enhanced bandwidth depends obviously on the frequency detuning between the external injection laser diode and the chaotic carrier transmitter. The maximum bandwidth of the chaotic transmitter can be obtained when the frequency of the injected light is higher than the central frequency of the carrier transmitter between 2 GHz and 4 GHz.     

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     

非即变相位共轭反馈对半导体激光器动态特性的影响

从四波混频产生相位共轭的物理原因出发,定义了相位共轭镜（PCM）的响应时间．建立起非即变相位共轭反馈条件下半导体激光器的外腔模型。以响应时间及频率失调为参变量,对其分岔及噪声等动态行为进行数值分析。结果表明,不考虑噪声影响时,增加相位共轭镜响应时间会使混沌带出现的次数和范围得到较大的抑制,当响应时间增大到1．5ns时,混沌带消失,半导体激光器保持稳定的单周期状态;考虑噪声影响后,随若响应时间的相对强度噪声（RIN）可减小几dB甚至十几dB,产生突变需要的反馈量也增大一个数量级以上,且其频谱的峰值向高频方向移动;另外,由于共轭反馈引起的频率失调低于半导体激光器激射频率3个数量级以上．它只对分岔特性有影响．对相对强度噪声的影响几乎为零。     

主副垂直腔面发射激光器动力学系统混沌输出的时延特征及带宽分析

基于垂直腔面发射激光器(VCSEL)的自旋反转模型, 数值研究了由一个光反馈VCSEL (定义为主VCSEL, M-VCSEL)输出的混沌光单向注入到另一个VCSEL (定义为副VCSLE, S-VCSEL)所构成的主副VCSELs系统的混沌动力学特性, 分析了注入强度、M-VCSEL与S-VCSEL之间的频率失谐以及M-VCSEL所受到的光反馈强度对系统混沌输出时延特征(包括强度时延特征(I-TDS) 和相位时延特征(P-TDS))以及输出带宽(BW)的影响. 结果显示: 通过调节注入强度和频率失谐, 该系统混沌输出的两个偏振分量(X-PC和Y-PC)的P-TDS和I-TDS可以同时得到抑制; 进一步分析注入强度和频率失谐对混沌BW的影响, 发现在较大负频率失谐区域, 系统可输出BW超过30 GHz 的X-PC和Y-PC混沌信号; 结合系统混沌输出信号的TDS与BW在注入强度和频率失谐参量空间下的演化特性, 可确定宽带宽、低时延特征混沌信号输出的参量空间区域. 此外, 通过合理调节M-VCSEL 所受到的光反馈强度, 可以显著优化系统的混沌输出信号质量.     

The influence of collective effects on quantum fluctuations of laser radiation

Quantum fluctuations in a laser with two different relaxation times are considered, i.e., transverse (polarization relaxation) and longitudinal (population relaxation) in the case in which the cavity transmission band half-width is much smaller than the transverse width and much larger than the longitudinal one. The lasing frequency detuning from the transition frequency of a two-level system is assumed to be arbitrary in this case, and it is necessary to take into account the contribution of two-particle correlators into the dispersion and laser linewidth. The results are considered as applied to a semiconductor laser.     

Observation of optical bistability in a GaAlAs semiconductor laser under intermodal injection locking

Experimental observation of optical bistability in a semiconductor laser under intermodal injection locking is reported for what is believed to be the first time. It is seen that a change in injection power of several microwatts or master laser frequency detuning of a few hundred megahertz can induce a change of as much as several hundred gigahertz in the lasing frequency of the slave laser. The results are in qualitative agreement with theoretical predictions.     

微米气室铯原子自旋噪声谱

利用自旋噪声谱技术研究了无缓冲气体133Cs原子气室的自旋动力学和展宽机制.在宏观原子气室中,自旋弛豫速率失谐频率谱的线型为高斯分布;在空间局域较强的微米气室中,自旋弛豫速率失谐频率谱的线型为洛伦兹分布.实验测量得到的自旋弛豫速率失谐频率谱的展宽约4 GHz,明显大于宏观原子气室中约度强烈依赖于激光相对于原子共振跃迁的频率失谐;在微米气室中,由于较强的均匀展宽,总噪声的失谐频率谱中心处出现明显的凹陷.通过建立简化的物理模型来计算微米气室的展宽机制,在实验与理论中解释了原子的均匀展宽特性.