定义：在每个偏振方向上只传导一个模式的光纤。

单模光纤是在给定波长情况下，每个偏振方向上只支持一个传播模式的光纤。它通常具有相对较小的纤芯（直径只有几个微米），并且纤芯和包层之间的折射率差很小。模式半径通常也是几个微米。 
单模光纤的一个比较特殊的性质是在光纤输出端口的横向强度分布是固定的，与入射光的入射条件以及空间性质都没关系，这里假设了包层模式不会到达出射端口。入射条件只会影响入射光耦合到导模中的效率。 
模间色散不会发生在单模光纤中。这在光纤通信中数据传输速率很高时（Gbit/s）非常重要，尤其是长距离传输。由于以上原因，并且结合其非常低的传输损耗，单模光纤大量应用于长距离数据传输中，并且即使在较短距离内也经常用在户外应用中。室内短距离的应用中，多模光纤更加常见，主要是由于这样可以采用更便宜的基于发光二极管的多模数据发射器。 

目录

• 有效耦合光进入单模光纤的条件
• 单模条件
• 单模光纤ITU标准
• 大模式面积单模光纤和有效单模光纤
• 应用

有效耦合光进入单模光纤的条件 
将光有效耦合进的那抹光纤需要光纤入射端口处光的横向振幅分布于导模匹配。这需要 

• 光源具有很高的光束质量 (M2≈1) 
• 入射光在光纤入射端口具有一个焦点（与光纤模式的平面波前匹配） 
• 光束分布具有合适的尺寸和形状，并且与纤芯严格对准（位置和方向）。更加准确的说，位置误差需要小于光束半径，并且角向不匹配值需要比模式的光束发散角小。 

在非理想情况下的入射效率，或者说激光光束尺寸不合适和角度未对准的情况，可以根据词条光纤连接器中的公式进行计算。 
一般来说，将自由空间的激光光束长期稳定有效耦合进单模光纤中需要仔细设计一些机械部分，从而能够保证精确对准，并且固定聚焦透镜和光纤端口，不会产生附加的偏移。 
对于具有很大有效模式面积的单模光纤来说，考虑聚焦位置后再准确对准比较容易，但是角度对准比较困难。 

单模条件 
对于阶跃折射率光纤来说，单模条件可以用V值（归一化频率）来表示，它可以由波长、纤芯半径和数值孔径（NA）来计算：V值必须小于2.405。这需要纤芯半径非常小，尤其是光纤需要具有很大的数值孔径。 

图1：单模阶跃折射率光纤的模式方程。折射率差为0.002，纤芯半径为4μm。这样波长为1μm时，V值为1.91。

图2：多模阶跃折射率光纤的模式方程，这里折射率差与上图相同，但是纤芯半径为10μm。V值为4.77。不考虑偏振态的情况下，该光纤支持四个模式。
通常来讲，光纤的单模特性只在有限波长范围内（几百纳米）满足。即适用于小于单模截止波长的范围，大于该波长时就支持多个模式。这种变化可以通过调谐入射波长在截止波长附近变化看到：透射光束分布在多模区域变化剧烈，而在单模区域则不变。单模区域的长波极限通常由附加的弯曲损耗来决定，后者来自于材料的吸收或者泄露到包层。 

图3：光纤的模式半径随波长的变化曲线。单模截止波长为793nm，小于该波长时，还存在LP11 模式，该模式在x和y方向上的半径图中都给出了
  
图4给出了在光纤左端入射进入的光存在很小的不对准情况下光束的变化情况。开始一些光进入包层模式，然后被衰减掉。经过一段距离后，大部分导模中的光仍然在光纤中。 

图4：1500 nm的入射光在不理想入射条件下在单模光纤中传播的情况。经过一段时间后，只有导模中的光存在
  
如果波长更短（图5），光纤进入多模区域，除了 模式，还有两个 模式。由于模式之间的干涉可以看到场分布为周期性振荡的。 

图5：光在与上图相同的光纤中传播，但是波长更短为1000 nm

对于更短的波长500nm（图6），传播形式更加复杂，因为支持更多的模式。 

图6：光在与上图相同的光纤中传播，光的波长更短为500nm

需要注意的是，任何影响模式传播常数的效应都会影响模式干涉。例如，很小的光纤弯曲都会影响模式间的相位关系。并且，模式分布于波长密切相关。所有的这些现象在单模光纤中都不存在。 
光子晶体光纤可以得到更宽或者更窄波长范围的单模传输。例如，存在无截止单模光纤，它具有非常大的单模波长区域。另外，还有光子带隙光纤，具有很窄的单模区域，并且不能传导其它波长的光。 

单模光纤ITU标准 
国际电信联盟（ITU）对于应用于光纤通信中各种类型的光纤制定了标准。其中对于单模光纤最重要一些标准在表1中给了出来。 

大模式面积单模光纤和有效单模光纤 


有时用到的单模光纤需要具有相对较大的纤芯直径，为几十微米（参阅大模式面积光纤）。这可以通过几种方法得到，例如，制造具有很小折射率差（小的数值孔径）、很大纤芯的光纤，或者采用光子晶体光纤。通常来讲，具有大模式面积的单模光纤对弯曲损耗更敏感，因为导波相对较弱。 
有时并不需要严格的单模导波，也可以采用有效单模光纤，包含很少的几个纵向模式，但是高阶模式具有相对较高的损耗，并且基模与高阶模式的模式耦合很弱。如果光纤具有更高的弯曲损耗，也可以用弯曲来有效抑制高阶模式。 

应用 
单模导波可以应用到很多方面。例如： 

• 如果光纤激光器和放大器是利用的稀土掺杂光纤，单模导波是实现高的输出光束质量的基础。 
• 在光纤通信系统中，单模导波避免了模间色散问题，后者会引起接收器接收到很多信号光的复制信号。 
• 单模光纤可以用于连接光纤光学装置中的不同器件，例如干涉仪中。它们可以熔接在一起或者利用光纤连接器连在一起。 
• 在测量装置中，主要是利用单模光纤的输出具有特定的空间分布，而与入射条件无关。因此单模光纤可作为一种模清洁器。 
• 也可以利用长的单模光纤中的非线性相互作用。例如，通过受激的拉曼散射放大信号，或者展宽光谱（超连续光产生）。 
• 典型的应用到光纤通信上的单模光纤在1300nm和1500nm波长区域，常见的为SMF-28 Corning光纤（或者SMF-28e）。它的纤芯直径为8.2 μm，数值孔径为1.4。模场直径在1310nm处约为9.2μm，在1550nm处为10.4μm.单模截止波长约为1260nm。 

Acronym: SMF

Definition: optical fibers supporting only a single guided mode per polarization direction

Alternative term: monomode fibers

More general term: optical fibers

Opposite term: multimode fibers

Single-mode fibers (also called monomode fibers) are optical fibers which are designed such that they support only a single propagation mode (LP₀₁) per polarization direction for a given wavelength. Higher-order modes like LP₁₁, LP₂₀ etc. then do not exist – only cladding modes, which are not localized around the fiber core. Single-mode fibers usually have a relatively small core (with a diameter of only a few micrometers) and a small refractive index difference between core and cladding; the mode radius is typically a few microns. However, there are also large mode area fibers with a relatively large mode area.

A peculiar property of single-mode fibers is that the transverse intensity profile at the fiber output has a fixed shape, which is independent of the launch conditions and the spatial properties of the injected light, assuming that no cladding modes can carry substantial power to the fiber end. The launch conditions only influence the efficiency with which light can be coupled into the guided mode.

Intermodal dispersion can of course not occur in single-mode fibers. This is an important advantage for the application in optical fiber communications at high data rates (multiple Gbit/s), particularly for long distances. Essentially for that reason, and partly because of their tentatively lower propagation losses, single-mode fibers are exclusively used for long-haul data transmission, and nearly always for outdoor applications even over shorter distances. For short-distance indoor use, multimode fibers are more common, mostly because that allows the use of cheaper multimode data transmitters based on light-emitting diodes instead of laser diodes.

As a standard single-mode fiber for use in optical fiber communications in the 1.3-μm or 1.5-μm wavelength region, the SMF-28 of Corning (or the enhanced version SMF-28e) is common. This has a core diameter of 8.2 μm and a numerical aperture of 0.14. The mode field diameter is ≈ 9.2 μm at 1310 nm, or 10.4 μm at 1550 nm. The single-mode cut-off is at ≈ 1260 nm.

Conditions for Single-mode Guidance

For step-index fibers, the condition for single-mode guidance can be formulated using the V number (normalized frequency), which can be calculated from the wavelength, the core radius, and the numerical aperture (NA): the V number must be below ≈ 2.405 [2]. This requires that the core radius is small, particularly for fibers with high NA.

Figure 1: Mode function of a single-mode step-index fiber. The refractive index change is 0.002 in that case, and the core radius is 4 μm. This leads to a V number of 1.91 at a wavelength of 1 μm.

Figure 2: Mode functions of a multimode step-index fiber, having the same index contrast as above, but a larger core radius of 10 μm. The V number is 4.77. This fiber supports four modes, disregarding different polarization states.

Typically, a fiber has single-mode characteristics only over a limited wavelength range with a width of a few hundred nanometers. The limit towards smaller wavelengths is given by the single-mode cut-off wavelength, beyond which the fiber supports multiple modes. This transition is very sharp and can easily be seen e.g. when tuning the launched wavelength around the cut-off wavelength: the shape of the transmitted beam varies rapidly in the multimode regime but remains constant in the single-mode regime. The long-wavelength limit of the useful single-mode region is usually given by excessive bend losses, by absorption of the material or (for certain fiber designs, e.g. with index-depressed cladding) by leakage into the cladding.

Figure 3: Mode radii of a fiber as functions of the wavelength, calculated with the software RP Fiber Power. The single-mode cut-off is at 793 nm; below that wavelength, there is also the LP₁₁ mode, for which the mode radii in the x and y directions have been shown.

Figure 4 shows how light evolves when it is launched into the left end of a single-mode fiber with a slightly misaligned laser beam. Initially, some of the light gets into cladding modes, which however are attenuated substantially. After some length, mostly light in the guided mode remains.

Figure 4: Light propagation at 1.5 μm wavelength in a single-mode fiber with imperfect launch conditions. After some length, only light in the guided mode remains. The numerical simulation has been done with the software RP Fiber Power.

For a shorter wavelength (Figure 5]), the fiber gets into the slightly multimode regime: in addition to the LP₀₁ mode, there are now two LP₁₁ modes. Here, one obtains a periodic oscillation of the field profile due to mode interference.

Figure 5: Light propagation in the same fiber as above, but for a shorter wavelength of 1 μm.

For a still shorter wavelength of 0.5 μm (see Figure 6), the propagation gets more complicated, since the fiber supports more modes.

Figure 6: Light propagation in the same fiber as above, but for a still shorter wavelength of 0.5 μm.

Note that mode interferences can be affected by any effects acting on the propagation constants of the modes. For example, even slight bending would affect the phase relationship of the modes. Also, the beam profiles are strongly wavelength-dependent. All these effects are not observed in single-mode fibers.

Photonic crystal fibers can have substantially broader or narrower wavelength regions with single-mode propagation. For example, there are endlessly single-mode fibers with a very wide single-mode wavelength region. On the other hand, there are also photonic bandgap fibers, based on an entirely different operation principle, with narrow single-mode regions and no guidance at other wavelengths. Besides, there are hollow-core fibers, which can offer single-mode guidance in combination with very high power levels [7]. This is because in such fibers the light has very little spatial overlap with the glass, in contrast to the situation in a standard solid-glass single-mode fiber, where the average power level is usually limited to a couple of watts.

Conditions for Efficiently Launching Light into a Single-mode Fiber

Efficiently launching light into a single-mode fiber requires that the transverse complex amplitude profile of that light at the fiber's input end matches that of the guided mode. This implies

• that the light source has a high beam quality (with M² ≈ 1)
• that the light has a focus at the fiber's input end (for matching the plane wavefronts of the fiber mode)
• that the beam profile has the correct size and shape and is precisely aligned (concerning position and direction) to the core. More precisely, the error in position must be well below the beam radius, and the angular misalignment must be small compared with the beam divergence of the mode.

In practice, it is not always easy to align the optics for efficient launching into a single-mode fiber. One may even have difficulties finding the position of the often rather small fiber core to which the input beam must be focused. (For large mode area fibers, that task is simpler, but on the other hand the angular tolerances are tighter.) One usually does the alignment while watching the optical power throughput of the fiber with a photodetector at the output fiber end, assuming that only light launched into the fiber core can reach that detector (which may not be true when the fiber is rather short). It is helpful to have a high-quality fiber launch system for such purposes.

Generally, a long-term stable efficient launch of a free-space laser beam into a single-mode fiber requires well designed mechanical parts, which allow to precisely align and keep fixed the focusing lens and the fiber end while not exhibiting excessive thermal drifts.

The launch efficiency under non-ideal conditions, namely with a wrong laser beam size or wrong angular alignment, can be calculated with equations as given in the article on fiber joints.

ITU Standards for Single-mode Fibers

The International Telecommunications Union (ITU) has developed a number of standards for various types of fibers as used for optical fiber communications. Some of the most important of those standards concerning single-mode fibers are given in Table 1.

Table 1: Standards for single-mode fibers.

See also the articles on dispersion-shifted fibers and bend losses.

Large Mode Area Single-mode Fibers and Effectively Single-mode Fibers

For some applications, single-mode fibers with relatively large core diameters of tens of micrometers (→ large mode area fibers) are required. This can be achieved in different ways, e.g. by making a large core with a small index difference (small numerical aperture), or with a photonic crystal fiber. In general, single-mode fibers with large mode areas tend to be more sensitive to bend losses, compared with multimode fibers, because the guiding is relatively weak.

In some cases, strictly single-mode guidance is not required; it is possible to use effectively single-mode fibers, having a few transverse modes, where however all higher-order modes have relatively high losses, and mode coupling from the fundamental mode to higher-order modes is weak. Some bending of the fiber is often used to suppress higher-order modes more efficiently, if they exhibit higher bend losses.

Applications

Single-mode guidance is important for many applications. Examples are:

• In fiber lasers and amplifiers made of rare-earth-doped fibers, single-mode guidance is the basis for reliably achieving a high beam quality of the output.
• In optical fiber communication systems, single-mode guidance avoids the problem of intermodal dispersion, which (in multimode fibers) would lead to the occurrence of multiple copies of the input signals at the receiver.
• Single-mode fibers are used for connecting different components in fiber-optic setups, such as interferometers. They can be fusion-spliced or put together with fiber connectors.
• In measurement setups, the fact is often exploited that the output of a single-mode fiber has a fixed spatial shape, independent of the launch conditions. A single-mode fiber may serve as a kind of mode cleaner.
• Nonlinear interactions in long single-mode fibers may be exploited. For example, this can be signal amplification via stimulated Raman scattering, or strong spectral broadening (supercontinuum generation).

Bibliography