定义：
激光器产生超短脉冲采用的技术。

锁模是一种激光器产生超短脉冲的方法（实际上是一组方法），然后这种激光器就被称为锁模激光器。其中，激光谐振腔中包含一种有源组件（光调制器）或者无源非线性器件（饱和吸收器），从而光能够在谐振腔中循环往复形成超短脉冲。在稳态情况下，影响循环脉冲的各种效应达到平衡，脉冲每循环一周后参数不会发生变化，或者几乎不发生变化。而每当脉冲入射到输出耦合器的反射镜上时，就会辐射一个可用的脉冲，其重复周期对应于谐振腔中循环一周所需的时间（通常为几个纳秒），脉冲长度非常短；通常在30fs到ps之间，极限情况下可以低至5fs。因此，锁模激光器的峰值功率会比其平均功率高几个数量级。 
本词条侧重于描述锁模的方法和一些基本原理，在锁模激光器词条中则包含各种锁模激光器更多的细节。 

图1：无源锁模激光器中产生脉冲列的过程。介质中的增益补偿损耗，饱和吸收反射镜会增强脉冲产生过程。每次脉冲入射到输出耦合反射镜，就会有一个脉冲产生。 

目录 

1. 主动和被动锁模
2. 连续光与同步泵浦对比
3. 高脉冲重复频率和低脉冲重复频率
4. 光谱：频率梳
5. “锁模”的起源
6. 锁模激光器的不稳定性和噪声

主动和被动锁模 
主动锁模需要周期性调制谐振腔损耗或者循环一周的相位变化，通常是由声光调制器、电光调制器、马赫-曾德尔集成光学调制器或者半导体电吸收调制器来实现。周期性调制结合谐振腔就可以得到超短脉冲，通常长度为皮秒。大多数情况下，得到的脉冲长度是由调制器引起的脉冲压缩和其它效应（例如有限的增益带宽）引起的脉冲展宽之间的平衡来决定的。 

图2：主动锁模激光器装置示意图。 
被动锁模（采用饱和吸收器）可以产生更短的脉冲（飞秒），主要是因为饱和吸收器本身是由短脉冲驱动的，比电子调制器调制谐振腔损耗更快：脉冲越短，损耗调制越快，前提是吸收器的恢复时间足够短。脉冲长度甚至会小于吸收器的恢复时间。有些情况下，并不能达到快速锁模。 

图3：被动锁模激光器示意图。 

在主动锁模和被动锁模词条中有更详细的介绍。 
在有些激光器中（尤其是锁模二极管激光器），需要同时采用主动和被动锁模。这种混合锁模激光器结合了一些关键的优势，例如外加控制脉冲重复频率和较短脉冲。 

连续光与同步泵浦对比 
大多数锁模激光器是连续光泵浦的，通常采用激光二极管。泵浦光源为增益介质提供连续的光源，而循环的脉冲以规律的时间间隔提取出能量。大多数情况下，与上能态寿命相比，脉冲间隔较短，因此在这一时间内增益介质可以非常容易的储存能量。那么采用相同的平均功率的连续光激光器，增益饱和情况相同。 
即使有些增益介质具有相对较短的上能态寿命，例如在染料激光器或者一些半导体激光器中，连续光泵浦时可能的，前提是脉冲重复频率不能太低。如果不能满足这一条件，单脉冲引起的增益饱和效应很强（脉冲形成过程就会不稳定），可以采用同步泵浦方法。但是，这就需要另外一个锁模激光器作为泵浦源。 

高脉冲重复频率和低脉冲重复频率 
高的脉冲重复频率通常是由谐波锁模得到的，其中多个脉冲以恒定的时间间隔在谐振腔中循环往复。这样即使采用光纤激光器也可以产生几个GHz的脉冲列，往返一周频率只有几十个MHz。 
采用基本锁模得到的高脉冲重复频率的情况下，即不采用谐波锁模，需要非常短的激光谐振腔。如果通过适当的设计，那么可以避免Q开关不稳定性，这种激光器就会非常简单，稳定且体积小。 
在脉冲重复频率很高时，锁模激光器得到的脉冲能量非常有限，通常为纳焦耳或者皮焦耳。采用倾斜腔锁模激光器和正反馈放大器，就能同时获得很高的脉冲能量和更低的重复频率。 

光谱：频率梳 
锁模激光器产生脉冲列的光谱并不是平滑的，而是包含等间距的分离的线，间距与脉冲重复速率相等（参阅频率梳）。尽管谐振腔模式的谐振频率并不总是等间距的也会得到频率梳，因为增益介质中的色散效应的存在：锁模机制使激光器产生光的频率域谐振腔模式的频率不相等。这种频率差值可能非常高，只有当谐振腔色散非常小时才能够得到宽谱，这样谐振腔模式的频率近似是相等的。在时间域，可以理解为色散造成时间谱展宽，需要采用锁模机制进行补偿。然而需要注意的是，光学非线性效应也可能比较强，因此考虑“冷腔模式”会忽略很重要的一部分物理机制。 

“锁模”的起源 
锁模的名称来自于频域的一种描述：当激光谐振腔中的纵模之间具有固定相位关系时形成超短脉冲，更准确的说，是激光输出光谱的线之间。然而，锁模的基本机制在时间域上更容易理解。并且，在强的光学非线性效应影响下，谐振腔模式的概念就存在疑问。严格说来，不建议把锁模激光器光谱中的线称为模式，尽管光谱中分立的线与谐振腔模式是有关系的。 
可以将周期性脉冲列的合成看做一系列叠加等频率间隔的正弦振荡（图4）（对应于锁模激光器不同的轴向谐振腔模式）的叠加。采用的频率组分越多，产生脉冲的长度越短。 

图4：通过叠加七个不同模式的正弦波（蓝色曲线）合成的周期性脉冲列（红色曲线）。竖直线表示所有同相位的振荡对应的时间点。 
一个很重要的因素在于这些谐振腔模式需要具有固定的相位关系。如图5所示：蓝色曲线表示脉冲列具有固定的相位关系，因此在某个时间点，各频率组分的电场叠加得到总的场强度为最大值。红色曲线表示具有相同强度的各频率组分的电场，但是具有随机的相对相位。 

图5：激光腔内电场的时间演化曲线，蓝色曲线是模式间具有固定的相位关系，红色曲线对应模式的相位差是随机的。 

锁模激光器的不稳定性和噪声 
锁模激光器采用的不同机制会产生各种不稳定性。例如，激光器可能产生不稳定间隔的多个脉冲，不稳定能量的脉冲，或者具有本地噪声的脉冲。在追溯这些问题起因时采用的不同的模型非常重要，然后再寻找合适的解决方法。 
即使不存在常规的不稳定性因素，锁模激光器的输出也包含各种噪声；通常需要特别注意的是时间抖动（脉冲位置的随机涨落）。其它的噪声包括相位噪声，强度噪声，以及脉冲长度，啁啾和中心频率的涨落。相位噪声导致产生的频率梳的有限展宽。锁模激光器中的不同类型的噪声具有很多联系。 
需要注意的是，锁模激光器词条中包含更多不同锁模激光器的细节描述，在主动锁模和被动锁模词条中则对锁模技术有很详细的描述。

Definition: a group of techniques for generating ultrashort pulses in lasers

More general term: pulse generation

More specific terms: active mode locking, passive mode locking, fundamental mode locking, harmonic mode locking, self-starting mode locking, additive-pulse mode locking, Kerr lens mode locking, hard/soft aperture mode locking, soliton mode locking, nonlinear mirror mode locking, regenerative mode locking

Mode locking [1] (sometimes written as modelocking) is a method (or actually a group of methods) to obtain ultrashort pulses from lasers, which are then called mode-locked lasers. Here, the laser resonator contains some kind of mode locking device (mode locker) – either an active element (an optical modulator) or a nonlinear passive element (a saturable absorber), which causes the formation of an ultrashort pulse circulating in the laser resonator.

Figure 1: Generation of a pulse train in a passively mode-locked laser. The gain medium compensates for losses, and the saturable absorber mirror (SA) enforces pulse generation. Each time the circulating pulse hits the output coupler mirror (OC), a pulse is emitted in the output.

In the steady state, the various effects influencing the circulating pulse are in a balance so that the pulse parameters are unchanged after each completed round trip, or often even nearly constant throughout each round trip. Each time the pulse hits the output coupler mirror, a usable pulse is emitted, so that a regular pulse train leaves the laser (Figure 1). Assuming a single circulating pulse, the pulse repetition period corresponds to the resonator round-trip time (typically several nanoseconds), whereas the pulse duration is much lower: typically between 30 fs and 30 ps, in extreme cases down to ≈ 5 fs. For that reason, the peak power of a mode-locked laser can be orders of magnitude higher than the average power.

This article focuses more on the methods of mode locking and on some fundamental aspects, whereas the article on mode-locked lasers contains more details on different kinds of mode-locked lasers.

Active and Passive Mode Locking

Active Mode Locking

Active mode locking involves the periodic modulation of the resonator losses or of the round-trip phase change, achieved e.g. with an acousto-optic or electro-optic modulator, a Mach–Zehnder integrated-optic modulator, or a semiconductor electroabsorption modulator. If the modulation is synchronized with the resonator round trips, this can lead to the generation of ultrashort pulses, usually with picosecond pulse durations. In most but not all cases, the pulse duration achieved is governed by a balance of pulse shortening through the modulator and pulse broadening via other effects, such as the limited gain bandwidth.

Figure 2: Schematic setup of an actively mode-locked laser.

More details can be found in the articles on active mode locking.

Passive Mode Locking

Passive mode locking (with a saturable absorber) allows the generation of much shorter (femtosecond) pulses, basically because a saturable absorber, driven by already short pulses, can modulate the resonator losses much faster than an electronic modulator: the shorter the pulse becomes, the faster the loss modulation, provided that the absorber has a sufficiently short recovery time. The pulse duration can be even well below the recovery time of the absorber. In some cases, reliable self-starting mode locking is not achieved.

Figure 3: Schematic setup of a passively mode-locked laser.

More details can be found in the articles on passive mode locking.

Hybrid Mode Locking

In some lasers (particularly in mode-locked diode lasers), active and passive mode locking are simultaneously applied. Such hybrid mode-locked lasers combine some key advantages, such as an externally controlled pulse repetition rate and fairly short pulses.

Continuous Versus Synchronous Pumping

Most mode-locked lasers are continuously pumped, often with a laser diode. The pump source then continuously supplies energy to the gain medium, while the circulating pulse extracts energy in regular time intervals. In most cases, the pulse spacing is very short compared with the upper-state lifetime, and the intracavity pulse energy is far below the saturation energy, so that there is negligible gain saturation during one round-trip; only the combined effect of many pulses is substantial. During one round trip (and during each pulse), the laser gain remains nearly constant.

Even for some gain media with a fairly short upper-state lifetime, e.g. in dye lasers or some semiconductor lasers (e.g. VECSELs), continuous pumping is possible, provided that the pulse repetition rate is not too low. If this condition can not be fulfilled, so that gain saturation by a single pulse becomes strong (which can make the pulse formation unstable), synchronous pumping can be a solution. This, however, requires another mode-locked laser as the pump source.

High and Low Pulse Repetition Rates

High repetition rate pulse trains are sometimes obtained with harmonic mode locking, where multiple pulses are circulating in the laser resonator with a constant temporal spacing. This allows the generation of multi-gigahertz pulse trains even with fiber lasers, which typically have fundamental round-trip frequencies of only some tens of megahertz.

For high pulse repetition rates with fundamental mode locking, i.e., without harmonic mode locking, very short laser resonators are required. If Q-switching instabilities are avoided with a proper design, such lasers can be very simple, stable and compact.

Due to the high pulse repetition rate, the pulse energies obtained from mode-locked lasers are fairly limited – normally nanojoules or picojoules. Higher pulse energies combined with lower repetition rates can be obtained with cavity-dumped mode-locked lasers and particularly with regenerative amplifiers.

The Optical Spectrum: Frequency Combs

The optical spectrum of a pulse train, as generated in a mode-locked laser, is not smooth (as for a single pulse), but rather consists of discrete lines with an exactly constant spacing which equals the pulse repetition rate (→ frequency combs). This is true although the resonance frequencies of the resonator modes are usually not exactly equidistant due to the effect of chromatic dispersion, e.g. in the gain medium: the mode-locking mechanism forces the laser to emit frequencies which can to some extent deviate from the frequencies of the resonator modes. These frequency deviations may not be arbitrarily high, and therefore the generation of broadband spectra is usually possible only if the resonator dispersion is sufficiently small, so that the resonator mode frequencies are approximately equidistant. In the time domain, that condition can be understood via the temporal broadening of pulses caused by dispersion, which must be compensated by the mode-locking mechanism. Note, however, that optical nonlinearities often also play an important role, so that considering the “cold cavity modes” misses an important part of the physical mechanisms.

Origin of the Term “Mode Locking”

The term mode locking originates from a description in the frequency domain: a short pulse is formed in the laser resonator when a fixed phase relationship is achieved between its longitudinal modes, or more precisely, between the lines in the spectrum of the laser output. However, the basic mechanisms leading to mode locking can usually be much more easily understood in the time domain. Also, the concept of resonator modes becomes questionable under the influence of strong optical nonlinearities. Strictly speaking, it is not even advisable to use the term modes for the lines in the spectrum of a mode-locked laser, even though these lines are related to the resonator modes.

It is instructive to consider the synthesis of a periodic pulse train by superposition of sinusoidal oscillations (Figure 4) with equally spaced frequencies, corresponding to different axial resonator modes in a mode-locked laser. The larger the number of frequency components involved, the shorter can be the duration of the generated pulses.

Figure 4: Synthesis of a periodic pulse train (red curve) by adding seven oscillations with slightly different but equidistant frequencies (blue curves). The vertical lines indicate points in time where all the oscillations add up in phase.

An important aspect is that there must be a fixed phase relationship between these modes. This is illustrated in Figure 5: the blue curve shows a pulse train with a fixed phase relationship, so that at regular temporal positions (e.g. at t = 0) the electric fields of all frequency components add up to a maximum of the total field strength. The red curve shows the electric field for the same strength of all frequency components, but with random relative phases.

Figure 5: Temporal evolution of the intracavity field in a laser, once with a fixed phase relationship between the modes (mode-locked state), once with random phases.

The explanations and diagrams above are actually simplified in an important detail: it has been assumed that all involved optical frequencies are integer multiples of the pulse repetition frequency. In reality, it is generally such that every frequency is in addition shifted by a certain amount, called the carrier–envelope offset frequency. One then still gets a periodic pulse train in terms of intensity, but a change of the optical phase at the pulse maximum which evolves continuously. See the article on carrier–envelope offset for more details.

Instabilities and Noise of Mode-locked Lasers

The various mechanisms for mode locking can exhibit various kinds of instabilities. For example, a laser may generate bunches of pulses (instead of single pulses), pulses with unstable energy (→ Q-switching instabilities), pulses which fall apart after some time and are later replaced with new pulses, or pulses which are accompanied by a noise background. Different kinds of modeling can be very helpful in tracking down such problems and to find appropriate remedies.

Even without particular instabilities, the output of a mode-locked laser contains various kinds of noise; the timing jitter (random fluctuations of the pulse positions) is often of special interest. Other types of noise include phase noise, intensity noise, and fluctuations of other parameters such as the pulse duration, chirp, and optical center frequency. The phase noise results in a finite width of the lines in the generated frequency comb. There are interesting relations between different types of noise in mode-locked lasers [17].

Note that the article on mode-locked lasers contains some more details on different kinds of mode-locked lasers, and more details concerning mode-locking techniques can be found in the articles on active and passive mode locking.

Mode Locking Devices

Optimum mode-locked performance depends on a well worked-out laser design, including the choice of a suitable mode locking device, be it some kind of modulator or a saturable absorber. The article on mode locking devices gives more details.

Bibliography