定义：
一种光束合束的方式，需要合束的光束是相干的。

相干合束是一种通过光束合束进行功率放大的技术。目的是将多个高功率激光光束合在一起得到一束光束，不仅具有更高的光功率还保持光束质量，因此光束亮度提高。相干合束还保留了光谱宽度。另一种方法是光谱合束。 

并排合束与连续孔径技术比较 
相干合束技术可以分为以下几种： 

1. 并排合束技术，可以得到更大的光束尺寸，但是光束发散角减小 
2. 连续孔径技术，其中几个光束合成一个光束，具有相同的尺寸和发散角，采用了N*1光栅分束器。 

图1：相干合束技术。a)并排合束的例子，其中四个光纤放大器的输出光结合成一束具有更大的光束面积。b)连续孔径合束的例子，采用了一个衍射光栅。 
连续孔径合束的一个特殊的离子是相干偏振合束。其中，入射光束只能有两个。但是，由于输出光偏振态为线偏振，因此可以重复这一合束过程。 
并排合束技术的发展受益于早期在相控阵天线和微波发射器和接收器的应用。在光学领域，由于采用的波长更短，因此实现合束非常困难，这需要非常严格的机械允差。 

任意情况下，都需要合在一起的光束是相干的，且相对相移需要小于1 rad r.m.s. 这在之前给出的两个例子中都提到了，在实际情况下似乎并不理想，但是理论上比较简单： 

1. 作为并排合束技术的一个简单的例子，具有平顶光强、矩形横截面和平坦相位的四束光束合在一起得到一束光束，尺寸是原来的两倍，面积是四倍，功率也是原来的四倍。（实际中，光束间可能具有较小的间隙，但是原则上这种间隙可以非常小。）如果光束是相互相干的，并且相对相位经过仔细调整，在整个横截面都能得到非常平坦的波前，那么得到的光束发散角只有单个光束的一半。因此，光束质量不变，亮度是单个光束的四倍。实际上，很难简单的得到平顶光束，单个光束间的间隙也会降低光束质量和亮度。 
2. 为了理解连续孔径合束技术，考虑具有50%反射率的分束器。将两入射光束在分束器中叠加，一般能够得到两束光，但是，如果两束光相干并且调整使一束光发生相消干涉，那么就可以只得到一束光。这种技术可以更好的保持光束质量，并且不需要特殊的光束形状，但是当发射器数目较多时就不方便。 

除了相位相干，光束还需要具有稳定的线偏振态，幅值涨落也不能太大。 

得到相干光束的方法 
有很多种技术可以得到相干光束，总结如下： 

1. 将低功率单频激光器的输出光分束，然后再采用高功率光纤放大器进行放大可以得到相干的单频信号。由于放大器会引入放大器噪声，尤其是温度变化引起的低频相位漂移，需要采用主动反馈稳定机制，作用于每个放大器的泵浦功率或者才每个放大器入射端采用一个相位调制器。得到的相位相干光束可以在多光束分束器或者并排合束方案进行合束。后者低于光束数量多时更加方便。这种技术尤其可以用在光纤放大器阵列，激光二极管，和脊形波导放大器。 
2. 另外，多个高功率激光器的相位也可以采用光学耦合进行合成。一种方案是通过衰逝波进行耦合，可以激发波导结构的多个模式，具有很高的光束质量。这种技术尤其适用于激光二极管阵列，其中在一个芯片上包含多个波导，只需要将波导放置的足够近就能实现耦合。这种技术也可以应用于多芯光纤，或者分离光纤激光器。但是，一个问题就是不仅要实现耦合，同时波导的各个输出光束的相位是相等的。 
3. 上一问题可以采用普通谐振腔技术解决，采用普通的谐振腔但是不同子谐振腔的光程差别很大。对于特定光学频率，从不同子谐振腔的反射在输出耦合器叠加形成某些超级模式。这种方法称为自组织相位合成。它不需要干涉稳定光程，尤其适用于光纤激光器。 
4. 还可以采用非线性相互作用，例如受激布里渊或拉曼散射，来实现相位合成。这种技术还没有很好的发展。 

非单色光相干合束 
相干合束大多数情况下采用的是单色光。但是，入射光也可以是非单色光，只要是相干的即可。例如，具有很宽光谱的超短脉冲可以相干合成。这需要光程严格匹配，这样入射光束的峰值与输出光的峰值在相同的时间达到。光波带宽越宽，对于时延匹配要求越严格。对于非常宽带的脉冲（不考虑其时间延伸与否），臂长差在几微米或者更短是可以接受的。

还有一种被动合束的技术，其中入射激光能够自动的相干振荡，即使它们不是单频激光器。但是，主动稳定激光器阵列通常需要单频工作。 

一般性说明 
总的来说，相干合束的技术并没有很广泛的应用，尽管很多方案都在进行研究。最大的困难是得到很高功率的足够稳定的相位相干的光束，不仅能够工作在实验室环境还可以在更噪杂的工业环境中应用。另一个问题是需要波前和偏振方向严格匹配和稳定。采用单频信号和高功率光纤放大器的方案需要采用额外的方式来抑制受激布里渊散射的产生的问题。在并排合束系统中，填充因子小于1也会降低光束质量，在远场光束中形成旁瓣。与之形成对比的是，采用光谱合束的系统对各种因子要求没有那么严格，但是如果需要窄的辐射光谱时需要相干合束。

Definition: a class of methods for beam combining, requiring mutual coherence of the combined beams

Alternative term: coherent beam addition

The term coherent beam combining (also called coherent beam addition) denotes one class of techniques within the more general technique of power scaling by beam combining. The goal is to combine several high-power laser beams so as to obtain a single beam not only with correspondingly higher power but also with more or less preserved beam quality and thus with increased radiance (brightness). Coherent combining also preserves the spectral bandwidth. An alternative class of techniques, discussed in a separate article, is spectral beam combining.

Side-by-side Combining Versus Filled-aperture Techniques

Techniques of coherent beam combining can be subdivided into

• side-by-side combining (tiled aperture) techniques, using a kind of phased array, leading to a larger beam size but reduced divergence
• filled-aperture techniques, where several beams are combined into a single beam with the same beam size and divergence, using e.g. some kind of N × 1 grating splitter.

Figure 1: Techniques for coherent beam combining. a) Example of tiled-aperture combining, where the outputs from four fiber amplifiers are combined into one beam with a large area. Due to the synchronized optical phases, the overall beam has a reduced beam divergence. b) Example for filled-aperture combining, using a diffraction grating.

A special case of a filled-aperture technique is coherent polarization beam combining [21]. Here, one can have only two input beams. However, as the output polarization is linear, one can repeat the combination as required.

Techniques for side-by-side combining can be implemented with fiber arrays, for example. They may have been inspired by the earlier implementation of phased-array antennas in radio frequency and microwave transmitters and receivers. In the optical domain, the realization is more difficult due to the much smaller wavelength, which introduces correspondingly tighter mechanical tolerances.

In any case, mutual coherence of the combined beams is essential; typically the relative phase deviations need to be well below 1 rad r.m.s. This is illustrated for both mentioned sub-classes with two examples, which may not be ideal in a practical sense but conceptually simple:

• As a simplified example of side-by-side combining, four beams with flat-top intensity profiles of rectangular cross-section and flat phase profiles may be arranged to obtain a single beam with just two times the dimensions, or four times the area, and of course four times the power. (In practice, there may small gaps of low intensity between the beams, but this gap can in principle be fairly small.) If the beams are all mutually coherent, and the relative phases are properly adjusted to obtain essentially plane wavefronts over the whole cross-section, the resulting beam has a beam divergence which is only half that of the single beams. As a result, the beam quality is preserved, and the brightness can be four times that of the single beams. In practice, flat-top beam profiles may not be easily obtained (especially not of rectangular shape), and the gaps between the individual beams (i.e. the limited fill factor) will somewhat reduce the beam quality and brightness.
• To understand the principle of filled-aperture techniques, consider a beam splitter with 50% reflectance. Overlapping two input beams at this beam splitter will in general lead to two outputs, but a single output can be obtained if the two beams are mutually coherent and adjusted such that there is destructive interference for one of the outputs. This technique makes it easier to preserve the beam quality and does not require special beam shapes, but it may be less convenient for large numbers of emitters.

Apart from phase coherence, the beams involved must have a stable linear polarization, and the amplitude fluctuations should also not be excessive.

Methods for Obtaining Mutual Coherence

There are a variety of techniques to obtain the mutual coherence, which are briefly summarized in the following:

• Mutually coherent single-frequency signals can be generated by splitting the output of a low-power single-frequency laser and amplifying the resulting beams e.g. in high-power fiber amplifiers. As the amplifiers may introduce amplifier noise, particularly in the form of low-frequency phase disturbances (drifts) caused e.g. by temperature changes, an active feedback stabilization scheme may be required, acting e.g. on the pump power of each amplifier or using a phase modulator at each amplifier input. The resulting phase-coherent beams can then be combined either at multiple beam splitters, or with a tiled-aperture approach. The latter is probably more convenient for a larger number of beams. Such techniques have been applied particularly to arrays of fiber amplifiers [11], laser diodes [7], and ridge waveguide amplifiers [5].
• Alternatively, the phases of multiple high-power lasers can be synchronized by some kind of optical coupling. One approach is coupling via evanescent waves (leaky-wave coupling) with the goal of exciting a suitable supermode of the structure, which exhibits a high beam quality. This technique is applied particularly to laser diode arrays [2, 6], containing multiple active waveguides on one chip, where coupling can be obtained simply by placing the waveguides sufficiently closely. The technique may also be applied to multi-core optical fibers [16], or to separate fiber lasers [15]. However, a difficult challenge is to obtain not only tight coupling, but also coupling so that the phases are equal (rather than e.g. opposite) at the outputs of the waveguides.
• The latter problem is avoided with common-resonator techniques, where the beams are fully combined at the output coupler, but split within the resonator (laser resonator) to be amplified in different gain elements.
• There is a variant of the latter approach, also using a common resonator but with the optical path length in the different sub-resonators being significantly different [9, 10, 13]. For certain optical frequencies, there are supermodes where the reflections from the different sub-resonators add in-phase at the output coupler. If such supermodes lie within the gain bandwidth, lasing may occur only on those, resulting in efficient coherent beam combination. This method has been called self-organizing phase synchronization [12]. It does not require interferometric stabilization of the optical path lengths, and appears to be particularly suitable for fiber lasers.
• There are also schemes where phase synchronization is achieved using a nonlinear interaction such as stimulated Brillouin or Raman scattering. Such techniques are not yet highly developed.

There are also techniques of passive beam combining where the input lasers automatically get into mutually coherent oscillation (via some feedback or nonlinear interactions) even though they not single-frequency lasers. However, single-frequency operation is typically required for actively stabilized laser arrays.

A special case is the non-collinear coherent superposition of ultrashort pulse beams [25]. Here, the term beam combining should actually not be used, since one only exploits the superposition of two clearly separate beams in the region around their foci. For some applications, that can be sufficient.

Coherent Beam Combining with Non-monochromatic Waves

Coherent beam combining is mostly done with monochromatic waves. However, it can also be applied to non-monochromatic input beams, as long as these are mutually coherent. For example, ultrashort pulses, having a broad optical spectrum, can be coherent combined [22]. It is then required that the path lengths are exactly matched such that the temporal peaks of the contributions of all input beams to the output occur at the same time. The broader the optical bandwidth, the more critical is that delay matching. For very broadband pulses (disregarding whether they are temporally stretched or not), arm length differences of only a few micrometers or even less are acceptable.

General Remarks

Overall, methods for coherent beam combining have not been very successfully applied, although many different approaches have been investigated. The main difficulty is to obtain phase coherence at high power levels in a sufficiently stable manner, working not only in a quiet laboratory environment but also in a mechanically more noisy industrial setting. Another challenge is the need to match precisely and stably wavefronts and polarization directions. Schemes using single-frequency signals and high-power fiber amplifiers may require additional measures to suppress problems with stimulated Brillouin scattering (SBS). In tiled-aperture systems, some degradation of beam quality is caused by a fill factor of less than unity, which leads to side lobes in the far-field beam pattern. In comparison, systems relying on spectral beam combining are more tolerant in various respects, but coherent combining may be used e.g. if a narrow emission spectrum is required.

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