定义：
光放大器中存在谐振腔，于是光脉冲在耦合出去之前在腔内可以循环很多圈。

正反馈放大器是用来将光脉冲放大的装置，通常超短脉冲长度在皮秒或者飞秒量级（参阅超快放大器）。将增益介质放在谐振腔中，可以多次通过增益介质（通常是固态介质），再加上一个光开关，是采用电光调制器和偏振器实现的。可以通过光开关来控制在谐振腔中循环的圈数，可以非常大，这样总体的放大因子可以非常高。 
尽管脉冲在正反馈放大器中多次通过增益介质，但是多通放大器还是指具有确定通道数目的装置，根据光束路径的几何性质来得到的，而不是采用光开关。将正反馈放大器看做是一个多通放大器也是非常自然的。 

图1：皮秒正反馈放大器装置图。泡克尔斯盒，与四分之一玻片和薄膜偏振片起着光开关的作用。法拉第旋镜用来分来入射和出射脉冲。 

正反馈放大器的工作原理 
正反馈的工作原理可以从如下方面来理解： 

• 首先，增益介质先被泵浦一段时间，可以收集一些能量。 
• 然后，第一束脉冲通过由电光效应开关（或者声光效应）控制的短暂开放（小于脉冲在腔内循环一圈的时间）的端口进入谐振腔。 
• 这束脉冲在谐振腔中循环多次（可能上百次），被放大到一个很高的能量量级。 
• 最后，脉冲从谐振腔中释放出来。这可以通过采用第二个电光开关，或者可以采用将它耦合进去的开关。 

这一工作原理使采用中等大小的放大器就可以得到很高的增益，并且脉冲能量达到毫焦耳量级，采用更大的装置则能得到更高的能量。典型的脉冲重复速率在1kHz量级（也可能达到几百个kHz），在较低的重复速率时可以得到最高的脉冲能量。

注意种子激光器通常是锁模激光器，它的脉冲重复率非常高，例如几百个兆赫兹，只有非常少数的种子脉冲被用于放大器中。 

对于高重复率情形（几十kHz甚至更高），通常会持续对放大器增益介质进行泵浦。而对于低重复率情形（尤其是脉冲周期远大于上能级寿命），脉冲泵浦（例如，采用调Q激光器）更有利。一个常用的结构是采用倍频YAG激光器来泵浦正反馈钛蓝宝石放大器。 

其它问题 
由于放大器介质有限的增益带宽因此会减小脉冲宽度，于是被放大的脉冲长度可以变大。这被称为增益变窄效应，可以在放大器中加入合适的光谱滤波器减小这个效应，于是净增益谱变得更宽，更加平坦。 

在飞秒装置中，泡克尔斯盒引起的色散需要被补偿掉。也会存在非线性效应，需要采用啁啾脉冲放大或者分脉冲放大来有效抑制这些效应。如果不采取措施的话，得到的脉冲能量会被非线性效应限制，甚至产生光学损伤现象。 

正反馈放大器的功率效率因为腔内的损耗效应（尤其是电光开关中的）而大大降低。当单圈增益较低时，对这些损耗更加敏感，因为这样为了得到某一放大因子需要提高脉冲在环路中循环的圈数。 

正反馈放大器也会因为低能态寿命有限而降低其增益和泵浦效率，于是在放大脉冲时低能级的布居数很大，于是发生重吸收发生激光跃迁。这一问题主要出现在放大器放大超短脉冲时，但是啁啾放大过程中不会出现，因为这时放大器的脉冲长度相对较长。 

在一些应用中，需要将伴脉冲能量维持在一个比较低的水平，也就是得到高的脉冲对比。伴脉冲可以有几个途径产生，例如，泡克尔斯盒的不完美开关或者放大器中的寄生反射。需要采用额外的脉冲拾取器来抑制前面的或者后面的脉冲。 

当脉冲重复率高时，脉冲放大过程可能会有很强的涨落。倍周期分岔也会发生，也就是脉冲能量在两个值之间变化，之后则是四个值之间甚至八个值。脉冲重复率更高时，则会引起混沌效应。图2是一个数值模拟情况。 

图2：正反馈放大器的脉冲能量与谐振腔中循环圈数的关系，利用RP光纤功率软件得到模拟结果。 
正反馈放大器常用的增益介质是钛蓝宝石，它具有很宽的增益带宽和热传导性。其它的增益介质，例如掺镱或者掺钕的介质，适宜于采用二极管泵浦的情况，由于它们上能级寿命较长，因此储能能力强，但是由于较小的增益带宽，因此产生的脉冲更长（通常几百个fs或者更长）。 

正反馈放大器的应用包括材料加工（例如用mJ脉冲能量切割金属）和科学实验，例如高能物理中用于产生高次谐波。 

替代品 
正反馈放大器的一个替代品就是多通放大器，多个通道是采用很多镜子排列来得到的（每一个通道的传播方向稍微不同）。这种方案无需采用快的调制器，但是穿过增益介质中的通道数目很多时会比较复杂（也很难排列）。根据经验法则，多通放大器更适宜于在增益被限制的情况下得到非常高的脉冲能量（因为入射脉冲能量已经相当高），而正反馈放大器则更适宜于非常高增益的情形。当然，这两个放大器可以结合在一起：正反馈放大器提供高的增益，终端的多通放大器提高脉冲能量（参阅放大器链，超快放大器）。 

另外一种技术也可以得到高的脉冲能量，尽管没有正反馈放大器中得到的那么高，这种技术就是锁模激光器采用倾斜腔。这种技术尤其适合得到高达几个兆赫兹的高脉冲重复率的情况。

Definition: optical amplifiers with a resonator in which a light pulse can do multiple round trips before being coupled out

More general term: optical amplifiers

A regenerative amplifier is a device which is used for strong amplification of light pulses, usually with ultrashort pulse durations in the picosecond or femtosecond domain (→ ultrafast amplifiers). Multiple passes through the laser gain medium (nearly always a solid-state medium) are achieved by placing the gain medium in an optical resonator, together with an optical switch, which is usually realized with an electro-optic modulator and a polarizer. The number of round trips in the resonator can be controlled with the optical switch, and it can be very large, so that a very high overall amplification factor (gain) is achieved.

Note that although a pulse makes multiple passes in a regenerative amplifier, the term multipass amplifier is often reserved for a device where a fixed number of passes is obtained – not with an optical switch, but just according to the geometric beam path. It would be more natural, though, to consider a regenerative amplifier as one type of multipass amplifier.

Figure 1: Setup of a regenerative amplifier for picosecond pulses. A Pockels cell, combined with a quarter-wave plate and a thin-film polarizer (TFP), acts as an optical switch. The Faraday rotator is used for separating input and output pulses.

Operating Principle of a Regenerative Amplifier

The principle of operation can be understood as follows:

• First, the gain medium is pumped for some time, so that it accumulates some energy.
• Then, the input light pulse is injected into the resonator through a port which is opened for a short time (shorter than the round-trip time) with an electro-optic (or sometimes acousto-optic) switch.
• After that, the pulse can undergo many (typically tens or hundreds) of resonator round trips, being amplified to a high energy level. Typically, one will let the pulse energy grow until a substantial part of the energy is extracted from the gain medium.
• Finally, the pulse is released from the resonator. That can be achieved either with a second electro-optic switch, or with the same one as used for coupling in.

One amplification cycle may be done in 1 ms or less.

This operation principle makes it possible to achieve very high gain and thus pulse energies in the millijoule range with amplifiers of moderate size, or even higher energies with larger devices. Typical pulse repetition rates are of the order of 1 kHz, although repetition rates of hundreds of kHz are sometimes possible. The highest pulse energies are achieved at lower repetition rates.

Note that the seed laser, normally a mode-locked laser, may have a much higher pulse repetition rate of e.g. 80 MHz; only a small number of the generated seed pulses is used by the amplifier. A separate pulse picker is in principle not required, since the regenerative amplifier itself can “pick” an input pulse when required, but one may want to improve the suppression of additional pulses.

A common gain medium for regenerative amplifiers is Ti:sapphire, which has a broad gain bandwidth and high thermal conductivity. Other gain media, e.g. doped with ytterbium or neodymium, are suitable for diode pumping and have a good energy storage capability due to their long upper-state lifetimes, but the generated pulses are longer (typically hundreds of femtoseconds or more) due to the smaller gain bandwidth.

Pumping can be continuous or pulsed.

For high repetition rates (e.g. tens of kilohertz or higher), the amplifier gain medium is usually pumped continuously. For lower repetition rates (particularly for pulse periods well above the upper-state lifetime), pulsed pumping (e.g. with a Q-switched laser) is preferable. A common configuration is to use a frequency-doubled YAG laser to pump a regenerative Ti:sapphire amplifier.

Applications of regenerative amplifiers include laser material processing (e.g. cutting of metals with millijoule pulse energies) and scientific experiments e.g. in high-intensity physics, such as high harmonic generation.

Various Issues

Fast and Accurate Switching

Pulse injection and ejection require the use of a Pockels cell and a Pockels cell driver with a short switching time (well below the resonator round-trip time) and precision. These requirements are substantially more challenging than those for simple Q switching of a laser, for example.

Limited Repetition Rates

The possible output pulse repetition rate may be limited by different factors:

• Frequently, one requires an output pulse energy as high as possible, and needs to have a long pumping time between the application cycles – often of the order of the inverse upper-state lifetime of the gain medium. In extreme cases (with intense pulsed pumping), the repetition rate needs to be further decreased because cooling of the gain medium would otherwise be difficult.
• If low pulse energies are sufficient, one can realize far higher pulse repetition rates. A possible limit then arises from the time for the required number of resonator round trips. However, the round-trip time can be limited to a couple of nanoseconds, so that hundreds of round trips can be done within a microsecond, allowing for a repetition rate of the order of 1 MHz, or more with fewer round trips.

Gain Narrowing

The duration of the amplified pulses may be increased due to the limited gain bandwidth of the amplifier medium, which reduces the pulse bandwidth. This so-called gain narrowing effect may be reduced by inserting a properly designed spectral filter in the amplifier, which makes the net gain spectrum wider and more flat, but reduces the power conversion efficiency.

Chromatic Dispersion and Nonlinearities

At least in femtosecond devices, the chromatic dispersion introduced by the Pockels cell (in addition to that from the gain medium and other components) has to be carefully compensated. Nonlinear effects may also occur; these can be effectively suppressed with the methods of chirped-pulse amplification or divided-pulse amplification. If this is not done, the obtainable pulse energy may be limited by nonlinear effects or even optical damage phenomena.

Influences of Losses

The power conversion efficiency of a regenerative amplifier can be severely reduced by the effect of intracavity losses (particularly in the electro-optic switch). Note that the sensitivity to such losses is particularly high in cases with low round-trip gain, because this increases the number of resonator round trips required to achieve a certain overall amplification factor.

Finite Lower-state Lifetime

Regenerative amplifiers can also have a reduced gain and power efficiency due to a finite lower-state lifetime, leading to a significant population of the lower laser level during amplification of a pulse, and thus to reabsorption on the laser transition. That problem occurs primarily in amplifiers for very short pulses, but not with chirped-pulse amplification, where the pulse duration within the amplifier is relatively large.

Satellite Pulses

For some applications, it is important to keep the energy of any satellite pulses very low, i.e. to achieve a high pulse contrast. Such satellite pulses can occur in various ways, e.g. via imperfect switching of the Pockels cell or parasitic reflections in the amplifier. An additional pulse picker may be used to suppress pre- and post-pulses.

Bifurcations

For high pulse repetition rates, it can happen that the pulse amplification process exhibits strong fluctuations. Bifurcations with period doubling can also occur, where the pulse energy first alternates between two values, later four or even eight values. For further increased repetition rates, this can lead into deterministic chaos [8, 9, 12]. Fig 2 shows a numerical example case.

Figure 2: Pulse energy from a regenerative amplifier versus the number of resonator round-trips per amplification cycle, from a simulation with the software RP Fiber Power. Bifurcation occurs for the highest numbers of round trips and leads to an oscillating output pulse energy.

Alternatives to Regenerative Amplifiers

A possible alternative to a regenerative amplifier is a multipass amplifier, where multiple passes (each time with a slightly different propagation direction) are arranged with a set of mirrors. That approach does not require a fast modulator, but becomes complicated (also in terms of alignment) if the number of passes through the gain medium is high.

As a rule of thumb, a multipass amplifier may be more appropriate for very high pulse energies if a limited gain is required (because the input pulse energy is already relatively high), whereas a regenerative amplifier is more suitable for very high gains.

It is common to combine both approaches: a regenerative amplifier provides the high gain, and a final multipass amplifier stage boosts the energy (→ amplifier chains, ultrafast amplifiers).

Another technique for reaching high pulse energies, although not nearly as high as with regenerative amplifiers, is cavity dumping of a mode-locked laser. That technique is particularly suitable for very high pulse repetition rates of several megahertz.

Bibliography