定义：光纤端口间永久性的或者可移除的连接接头。

在光纤光学的很多应用中，将光纤端口处的光从一根光纤进入另一根光纤中时需要采取某一器件，保证在这过程中不会损失很多能量。例如光纤激光器和光纤通信系统中。 
有几种不同的技术连接光纤： 

• 永久性稳定的连接，通过熔接得到很低的跃迁损耗。通常是采用热处理将光纤端熔接在一起。 
• 半永久性连接可以采用机械接头实现，是一种相对简单的装置。通常需要采用折射率匹配的胶或粘合剂来降低反射损耗。与熔接接头相比，机械接头制作很快，并且使用后可以去掉。成本更低，但是单位接头的成本更高。接头损耗和反射损耗在0.5 dB量级，比熔接接头高很多。 
• 光纤连接器适用于需要重复插拔的情况。常见的连接器类型为FC，SC和LC用于单模光纤以及ST用于多模光纤，但是还有几百种其它的类型，具有其它性质，例如双工连接器，具有尺寸很小内置的快门来提高激光安全等。大多数情况下，采用一些粘合剂将光纤粘到连接器中，然后抛光光纤端。连接器的损耗与机械接头类似，但是稳定性更低。 

图1：光子晶体光纤（PCF，左侧）与普通光纤（右侧）熔接过程的微观图像。可以看到PCF中的孔状结构。 
在任何情况下，光纤端口在连接之前都需要仔细的处理。很多情况下需要垂直切割的端面。这种做法的好处在于辐射光的光轴与光纤轴在一条线上，因此很容易对准。有些情况则需要切割角度不等于90°。这种倾斜切面的优点在于当倾斜角度足够大的情况下，光在空气玻璃界面处的反射光不会重新进入光纤模式中。 
也可以利用自由空间光学将光从一根光纤传到另一根光纤中。典型的装置包含一个或者两个透镜。这种方法的优势是光纤端口间可以保持一个安全的距离，不太容易被损坏。另外，也可以有效耦合具有不同有效模式面积的光纤中的光，当然需要根据具体条件设计光路。还可以加入一些其它光学元件，例如光学滤波器或者法拉第隔离器。但是，自由空间光学需要很稳定的装置位置，并且对杂质很敏感。菲涅尔反射引起的损耗也不能避免。 

低损耗光纤接头的允差 
多模光纤 
两多模光纤接头的对准允差相对较低，尤其是具有很大纤芯面积的光纤。如果两光纤参数差别很大时也可以得到很高的耦合效率。第二根光纤（接收光）的纤芯直径和数值孔径等于或者比第一根光纤高就可以了。因为当第二根光纤的参数更大时，该光纤中的光强与第一根差不多相同，但是亮度低很多，因为从第二根光纤中出来的光会产生很大的耦合损耗。 
如果两个光纤纤芯横向不匹配或者角度不匹配，当光均匀分布在整个纤芯面积和角度区域，这时产生的耦合损耗可以根据几何关系来估计。需要注意的是，耦合损耗与光强在不同光纤模式中的分配有关。 

单模光纤 
单模光纤耦合与多模光纤有很大的不同。这里，耦合损耗与偏振方向无关。只有当以下条件满足的情况下才能得到较低的损耗： 

• 模式形状，尤其是有效模式面积类似。 
• 模式横向和角度都严格对准。 

横向位移Δx和模式面积w1和w2的不匹配对耦合效率的影响可根据下式计算： 

其中假设模场可通过高斯方程近似得到。该方程忽略了光纤端面的菲涅尔反射产生的效应，例如，熔接过程这种近似很合理。 
如果光纤端口不是严格垂直切割，就引起角度不匹配 Δθ。它对耦合效率的影响可以通过下式计算： 

从上式可以看出，大模式面积光纤中角度不匹配问题更严重。 
下面的图是根据以上方程得到的。 

图2：采用机械接头的单模光纤由于模式半径不匹配产生的插入损耗。 

图3：采用机械接头的单模光纤由于纤芯偏移引起的插入损耗。 

图4：采用机械接头的单模光纤，由于角度差（非垂直切割引起）引起的插入损耗。其中计算了不同模式半径比值得到的结果。

Definition: permanent or removable connections between fiber ends

In many applications of fiber optics, it is necessary to connect fiber ends (terminations) in some way such that light from one fiber can get into the other fiber without losing too much of its optical power. Examples are fiber lasers and systems for optical fiber communications.

There are different techniques for joining fiber ends:

• Permanent and stable connections with very low transition losses can be obtained by fusion splicing. Essentially, the fiber ends are fused together with a heat treatment.
• Semi-permanent connections can be made with mechanical splices, which are relatively simple alignment devices holding the fiber ends together. Typically, some index matching gel or an epoxy is used for reducing reflection losses. Compared with fusion splices, mechanical splices are faster to make and can be removed after use. The initial cost is much lower, but the cost per splice is higher. The splice losses and reflection loss are of the order of 0.5 dB, i.e., significantly higher than for fusion splices.
• Fiber connectors are convenient for connections which need to be released more often. Common connector types are named FC, SC and LC for single-mode applications and ST for multimode, but there are also dozens of other types, with special qualities such as duplex connections, particularly small size, built-in shutter for improved laser safety, etc. In most cases, the fiber is glued into the connector with some epoxy, and then the fiber end is polished. The transition losses of connectors are similar to those of mechanical splices, although the stability is generally lower.

Figure 1: Microscope imagine of a fusion splice between a photonic crystal fiber (PCF, left side) and a conventional fiber (right side). The hole pattern of the PCF can be seen. The photograph has been kindly provided by NKT Photonics.

In any case, it is essential that the fiber ends are carefully prepared before joining them. In many cases, fiber ends with perpendicularly cut surfaces are needed. This has the advantage that the axis of the emitted light is in line with the fiber axis, and the alignment is comparatively simple. In other cases, the cleave angle has to have some deviation from 90°. Such angle cleaves have the advantage that light reflected at the air–glass interface will not get back into the fiber mode, provided that the cleave angle is sufficiently large.

It is also possible to use free-space optics for launching light from one fiber into the other. Typical configurations contain a single lens or two lenses. An advantage of that approach is that the fiber ends can be kept at a safe distance, making it less likely to damage them. Also, it is possible to efficiently couple light between fibers with different effective mode areas if the optics are designed accordingly. Furthermore, it is possible to insert other optical elements, such as an optical filter or a Faraday isolator. On the other hand, free-space optics have to be kept in stable alignment and are sensitive to dust. In addition, losses arising from the Fresnel reflections at the fiber ends cannot be avoided.

Tolerances for Low-loss Fiber Joints

Multimode Fibers

The alignment tolerances for connections between fibers are relatively low for multimode fibers, particularly for those with a large core area. A high coupling efficiency is possible if the parameters of the two fibers differ substantially. It is sufficient that the second fiber (receiving the light) has values of the core diameter and numerical aperture which are equal or higher than those of the first fiber. If these parameters are higher for the second fiber, the light in that fiber will in general have nearly the same power but a lower brightness, whereas a substantial coupling loss can occur for light coming from the second fiber.

If there is a transverse mismatch or an angular mismatch of the two fiber cores, this can lead to a coupling loss which may be estimated with geometrical considerations, if the light uniformly fills the whole core area and angular range. Note that the coupling loss generally depends on how the optical power is distributed over the fiber modes. For this and other reasons, reliably estimating coupling losses for multimode fibers is hard to achieve.

The wave nature of light can lead to surprising behavior in multimode fiber coupling. For example, if the output fiber has a somewhat larger core than the input fiber and the same numerical aperture, one may expect to have zero coupling losses. This is not the case, however, because the larger core changes the shapes of the mode profiles, so that the modes of the input fiber cannot fully be transformed into guided modes of the output fiber; some of the light gets into the cladding – but strongly depending on the considered mode of the input fiber, and often sensitively depending on the magnitude of core size mismatch (with complicated non-monotonic dependencies). For such reasons, reliable estimations of coupling losses for multimode fibers require numerical software, not just some simple equations.

Single-mode Fibers

The situation is rather different for coupling of single-mode fibers. Here, the coupling loss can not depend on the direction of propagation. It can be low only if the following conditions are fulfilled:

• The modal shapes and particularly the effective mode areas are similar.
• The transverse and angular alignment of the modes is rather precise.

The effects of a transverse offset Δx and a mismatch of mode radii w₁ and w₂ on the coupling efficiency can be calculated with the following formula:

It is assumed that the mode fields can be well approximated by Gaussian functions. The equation ignores possible effects from Fresnel reflections at the fiber ends, which is perfectly reasonable for fusion splices, for example.

If the fiber ends are not exactly perpendicularly cut, this can lead to an angular mismatch Δθ. Its effect on the coupling efficiency can also be calculated:

This shows that the angular alignment becomes more critical for large mode area fibers.

Note that for large angles, where the coupling loss becomes very large, the results become quite sensitive to the mode shape. This means that the mentioned formula, which depends on the approximation of a Gaussian mode shape, may no longer produce accurate results.

The following figures are based on the equations above.

Figure 2: Insertion loss at a mechanical splice for single-mode fibers due to a mismatch of mode radii.

Figure 3: Insertion loss at a mechanical splice for single-mode fibers due to a parallel offset of the cores.

Figure 4: Insertion loss at a mechanical splice for single-mode fibers due to an error of the angle, as might result from a non-perpendicular cleave. This has been calculated for different ratios of the mode radius to the wavelength.

Bibliography