摘要
量子级联激光器(Quantum Cascade Laser, QCL)是依赖电子在量子阱子带间跃迁辐射出光子而发生激射的单极型半导体激光器。大量的理论与实验研究已经证明轻微的外部扰动(如光反馈、光注入)或内部足够强的非线性模式耦合能够引起半导体激光器的非线性输出。QCL作为新型半导体器件,具有腔内强度高、子带间光学非线性强以及电子弛豫时间快等特点,激发了学者研究其非线性动力学的兴趣。本文详细综述了QCL的非线性动态特性研究进展情况,探究了QCL非线性动力学性质的产生机理,总结了QCL非线性特性的应用场景。
关于非线性问题的认识可追溯到1673年Huygens对单摆的研究。1913年,Poincaré提出用几何方法解决动力学系统问题,并且预测非线性系统中存在对初始条件的敏感依赖性。同时,Lyapunov用代数方法系统探讨了非线性动力学的稳定性问题,两者开拓了非线性科学的新研究方法。1963年,Lorenz研究了大气流动的模型,指出由三个变量描述的非线性系统可以表现出包括混沌运动等的复杂动力学行为。现代混沌研究便始于Lorenz对大气流动的非线性系统复杂动力学的研究。对于激光领域研究人员来说,一个关键事件是1975年哈肯证明激光动力学方程与Lorenz方程同构。这一观察刺激了对各种激光系统中混沌路径的重要实验和理论分
量子级联激光器(Quantum Cascade Laser, QCL)是一种单极型半导体激光器,根据能带工程设计,可以工作于中红外和太赫兹波段,是重要的中红外和太赫兹激光光
即使没有引入额外的光电调制、注入或反馈,足够强的非线性模式耦合也可能导致QCL的不稳定性。20世纪60年代,Risken等预测了可能破坏单模激光器稳定性的基本相干机制,被称为Risken-Nummedal-Graham-Haken(RNGH)不稳定
Wang

图1 (a) 在300 K下,用3 μm宽的埋藏式异质结构激光器在8.47 μm处发射,获得了高于阈值的光学光谱与泵浦比()。对于 ,光谱与相同,(b) 光谱分裂和两倍拉比频率与单个激光面收集的输出功率的平方根相比。虚线是数据的最小平方线性拟
Fig. 1 (a) Optical spectra vs. pumping ratio () above threshold obtained in cw at 300 K with a 3-μm-wide buried heterostructure laser emitting at 8.47 μm. For the spectra are identical to , (b) spectral splitting and twice the Rabi frequency vs. square root of output power collected from a single laser facet. The dashed line is a least-square linear fit of the dat
2008年, Gordon
2012年,Bai
外部光反馈是半导体激光器产生非线性输出的典型调控模型之一。在QCL的激光腔前面放置一个外镜,激光从外镜反射并反馈到激光腔。根据反馈光的强度,可以观察到不同的非线性输出,其输出强烈依赖反馈光的强
2013年,Mezzapeas
2018年, Spitz

图2 (a) 77 K光反馈下QCL的时间演化,偏振器允许实现0到0.089之间的反馈比f的值,a) f = 0,b) f = 0.000 3,c) f = 0.000 8,d) f = 0.004 6,e) f = 0.014 1,f) f = 0.021 3,g) f = 0.029 8,h) f = 0.039 3,i) f = 0.089,左侧显示了在三种温度下出现LFF所需的关键反馈:290 K、170 K和77 K,蓝色虚线是为读者提供视觉指导,(b) QCL上能级载流子寿命随温度演化
Fig. 2 (a) Experimental time traces of the QCL under the optical feedback at 77 K. The polarizer allows achieving the value of feedback ratio f between 0 and 0.089, a) f = 0, b) f = 0.000 3, c) f = 0.000 8, d) f = 0.004 6, e) f = 0.014 1, f) f = 0.021 3, g) f = 0.029 8, h) f = 0.039 3, i) f = 0.089, (b) simulation of the upper state lifetime evolution with temperature for the QCL under stud
2020年,Spitz

图3 极端脉冲的时间序列
Fig. 3 Time series of extreme pulse
近期,Wang
目前,关于光反馈下激光动力学的研究大多集中在MIR QCL上。为了充分发挥太赫兹源的应用潜力,对于THz QCL的非线性动力学研究是有必要的。尚未解决的关键问题之一是双光反馈下THz QCL的输出性能。我们课题组通过数值模拟,计算了双光反馈下THz QCL的动态特性。

图4 固定其中一个外腔长度为0.75 m,反馈强度为0.22,(a) 另一外腔的长度为0.45 m,反馈强度为0.022的时间序列,(b) 与(a)对应的傅里叶频谱,(c)另一外腔的长度为0.6 m,反馈强度为0.022的时间序列,(d)与(c)对应的傅里叶频谱
Fig. 4 Fix one of the external cavities with the length 0.75 m and the feedback strength 0.22, (a) another external cavity with the length 0.45 m and the feedback strength 0.022, (b) Fourier spectrum corresponding to (a), (c) another external cavity with the length 0.6 m and the feedback strength 0.022, (d) Fourier spectrum corresponding to (c)
理论和实验都表明QCL对光反馈很敏感,但它们比带间激光二极管更具抵抗力。根据反馈比的不同,MIR QCL会出现五种反馈状
光注入也能对半导体激光器的稳定性产生影响。在大频率失谐或强注入的情况下,注入的激光通过不同的分岔机制失稳为混
Taubman

图5 线宽增强因子(LEF)值为0、0.5、1.0和2.5时,注入锁定QCL的局部分岔图。实线是鞍节点(SN)分叉,虚线是霍普夫分叉。超临界分叉用粗线表示,亚临界分叉用细线表示。稳定的锁定系统是由超临界分叉限定的。所研究的激光器工作在分岔图的稳定锁定区域,LEF为0.5,其中垂直虚线表示注入比为5.
Fig. 5 Local bifurcation diagram of an injection-locked QC laser for linewidth enhancement factor (LEF) values of 0, 0.5, 1.0, and 2.5. The solid line is the saddle node (SN) bifurcation and the dashed line is the Hopf bifurcation. The supercritical bifurcation is denoted by the thick lines while the subcritical bifurcation by the thin lines. The stable locking regime is bounded by the supercritical bifurcations. The investigated laser is operating in the stable locked region of the bifurcation diagram with an LEF of 0.5, where the vertical dotted line indicates an injection ratio of 5.
近期,Zhao
所有这些研究都得出,光注入QCL中无混沌现象可归因于其超快载流子寿命导致的小线宽加宽因子。在锁定范围内,预期会产生窄线宽、噪声降低或调制带宽增加的现象。然而,由于锁定范围相对较窄,应仔细选择主QCL和从QCL。此外,在极低的偏置电流下,一些P1振荡出现在正失谐的锁定范围之外。由于这些振荡发生在失谐频率处,光注入QCL可以用作可调谐光子振荡器,进一步的研究将确定光注入下QCL中是否存在对失谐频率不敏感的微波振荡
半导体激光器的独特之处在于泵浦电流的直接调制。注入电流本身为QCL引入了额外的自由度,导致输出的不稳定性跟混沌。注入电流的调制将会导致相位调制,因为激光振荡频率为注入电流的函数。注入电流的调制引起了载流子密度的扰动,然后载流子密度的变化引起光子数和相位的变化。因此,QCL作为一个耦合的非线性系统其本质就是存在不稳定性。
在QCL的非线性动力学研究中,通常把电流调制和光反馈相结合。应用外部光反馈和电流调制可以使LFF的峰值和频率同步,即夹带现

图6 (a) 正弦波信号调制的时间序列,(b) 与(a)对应的RF频谱,(c) 方波信号调制的时间序列,(d) 与(c)对应的RF频谱。I: 连续泵电流,A:调制振幅,F:调制的频
Fig. 6 (a) Time series under sine wave signal modulation, (b) RF spectrum under sine wave signal modulation, (c) time series under square wave signal modulation, (d) RF spectrum under square wave signal modulation. I: continuous pump current, A: peak-to-peak amplitude of the modulation, F: frequency of the modulatio
Chen
Spitz
激光谐振腔中光学损耗的调制也会导致动力学不稳定性,通常通过将增益部分与作为可饱和吸收体的反向偏置部分相结合来实现的。可饱和吸收体是实现超快脉冲的关键器件,是一种非线性光学器件。可饱和吸收体在调Q和锁模技术中起着至关重要的作用,由它所构成的被动调Q和被动锁模激光器具有结构简单、激光状态稳定、成本低等优点。激光器中的调Q和锁模技术是产生超短脉冲的主要方式。因此,可饱和吸收体的发展可等同于激光器本身的发展。
目前关于使用可饱和吸收体调制损耗导致QCL输出非线性动力学的研究较少,对于在QCL中集成可饱和吸收体的研究工作还处于探索阶段。QCL锁模是一个备受关注的研究领域。由于QCL的子带间跃迁弛豫时间较短(在太赫兹范围内为数十皮秒,在中红外范围内为1皮秒),导致被动锁模难以实
2015年,Bianco
QCL的混沌输出特性为人们提供了新型激光源,可以有效地用于光学对抗等领域。对于中红外频段的加密通信应用,MIR QCL的混沌输出可以提供随机比特生成或使用混沌调制进行信息加密的安全通信,并为信息传输提供同步混沌。THz QCL拥有更快的载流子寿命和更低的线宽增强因子,导致其动力学行为不同于中红外QCL中观察到的动力学状态。目前对于THz QCL非线性动力学的研究还不多,我们还需进一步探索与突破,更好地理解这些激光器各种参数范围内不稳定性的相互作用,实现对QCL输出特性的调控,并运用于合适的场合。QCL非线性动力学研究仍在进一步发展中,我们可以期待其在基础物理和实际应用方面取得丰硕成果。
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