定义：每个偏振方向上有大于一个导波模式的光纤。

多模光纤是指在给定光频率和偏振情况下，可以支持多个横向导波模式的光纤。导模的数目取决于波长和折射率分布。对于阶跃折射率光纤，相关的量为纤芯半径和数值孔径，二者合起来决定V值。如果V值比较大，模式数目正比于V2。尤其是光纤具有相对较大的纤芯时（图1右侧），支持模式的数目会非常多。这种光纤可以传播光束质量很差的光（例如，来自于高功率二极管阵列中的光），但是为了保持具有较高亮度光源的光束质量，最好采用具有较小纤芯和中等大小数值孔径的光纤，尽管这种情况下很难实现有效耦合进入光纤。 

图1：单模光纤（左）纤芯比包层小很多，而多模光纤（右）具有很大的纤芯
与标准单模光纤相比，多模光纤的纤芯面积很大，并且数值孔径也更大，例如0.2-0.3。后者能够实现稳定的导波，即使存在很大弯曲的情况下，但同时即使在不存在弯曲的情况下也具有更大的传播损耗，因为在纤芯-包层截面处的不规则性会引起光的散射。折射率分布通常为矩形（参阅阶跃折射率光纤），有时是抛物线型的（如下所示）。 
多模光纤的基本性能指标包括纤芯直径和多模光纤的外包层直径。光纤通信中常见的类型为50/125 μm和62.5/125 μm的光纤，即纤芯直径分别为50 μm和62.5 μm，包层直径为125 μm。这种光纤可以支持几百个导模。还有大芯径光纤，其芯径为几百个微米。 

将光射进多模光纤相对较容易，因为与单模光纤相比，对入射光进入时的位置的和入射角度的允差更大。但是，光纤输出光的空间相干性就降低了，并且很难控制出射场分布。 

图2是阶跃折射率光纤导模的电场分布图，只计算了某一波长时的场分布。基模（LP01）接近于高斯强度分布，其它高阶模式具有更加复杂的空间分布。每一个模式的β值不同。任一导模场分布都可以看多一些导模的叠加。 

多模光纤任一位置处总的电场分布是来自于不同模式的叠加。强度分布不仅与所有模式的功率有关，还和它们的相对相位有关，因此在光纤特定位置会发生不同模式的相消或相长干涉。功率和相位都是由光射入光纤时的情况决定的，并且相对相位（因此干涉条件）由于传播常数与模式相关而不断变化。因此，强度分布随着时间不断变化，并且在小于1 mm的传播长度内会发生显著变化。并且，只要改变入射条件、弯曲程度或者拉伸光纤，改变波长或者温度等，相对相位都会发生改变。 

需要注意的是，对于一个很宽带宽的光（例如，对于一个白光光源）如果在不干扰器光谱各分量的情况下探测其强度时，不会产生这么复杂的分布。因为每一波长组分对应的强度分布不同，因此不同波长的贡献会发生相互抵消。光纤越长，所需要平均的光谱带宽越小。 

图2：光纤中所有导波模式的电场振幅分布。通常来说，进入多模光纤中的光激发了不同模式的叠加。 

目录

• 将光耦合进多模光纤对光束质量的要求
• 多模光纤用于传输激光
• 多模光纤用于光通信
• 活性多模光纤
• 材料和制造方法

将光耦合进多模光纤对光束质量的要求 
与单模光纤相比，将光入射到多模光纤中更加容易，尤其是多模光纤支持很多导模的情况下。为了得到很有效的耦合，需要满足下列两个条件： 

• 入射光只能入射到纤芯，而不是包层。 
• 入射光传播方向与光纤轴之间的角度不能大于NA的反正弦值。 

如果入射光的M2因子足够小，上面两个条件是可以同时满足的。对于超高斯型光束，有效将光束射入多模光纤的最大M2因子可以根据下列公式进行估计： 

如果光束形状和角度分布（即在傅里叶空间的分布）都满足有效入射条件以上公式就可以成立。对于高斯光束，M2因子更小。。 

多模光纤用于传输激光 
多模光纤用于将激光光源中的光传输到需要用的地方，尤其是光源的光束质量较差或者高功率情况下需要光纤纤芯面积比较大的情况。例如，从各种稳态高功率激光器中的光传输到材料加工工作台上用于切割或者焊接，其中机器人可以移动光纤光缆端口的激光头。并且光纤耦合的高功率二极管线阵和二极管堆也采用的是多模光纤，因为其光束质量远远不能达到衍射极限。光纤耦合是非常有用的，因为这样可以在二极管泵浦固态激光器的激光头处将泵浦二极管与冷却装置分离开。但是，光纤耦合的激光二极管比较昂贵，并且根据采用不同的光束整形器，可能会引起严重的亮度损耗。 
在这些应用中，导模的数目通常不会比有效射入光纤所需的数目更大，否则激光辐射的功率会分配在不需要的模式上面，因此光束质量和亮度都会降低。 
实际上通常采用简单的阶跃折射率光纤。它的数值孔径固定为一些标准值，例如0.22，并且纤芯直径通常是根据光源的光束质量来选择的。纤芯直径的常见值为50,100,200,400,600和800μm。 

多模光纤用于光通信 

图3：抛物线型折射率分布的渐变折射率光纤。最常见的缺陷是中间存在折射率凹陷，在一般制造方法中经常遇到。 
对于短距离的光纤通信，通常选用多模光纤而不是单模光纤，因为简单的光源就能有效耦合进多模光纤中（例如发光二极管，LEDs），并且对对准的要求不是很高（例如，在光纤连接器中）。但是采用这种光纤的数据传输速率和传输距离是受限的，主要是因为模间色散现象：群速度与传播模式有关，因此超短脉冲在多模光纤中传播会分成传播速度不同的几个脉冲，可能会消除传输的信号。如果采用抛物线型折射率多模光纤（渐变折射率光纤，图3）就可以大大的减小该效应，这样可以得到更大的带宽距离乘积。但是，仍然存在一些不可避免的缺陷。一些ISO标准（例如，OM1，OM2和OM3）量化了模间色散水平，以及对传输带宽的限制（或者带宽距离乘积）。采用OM350/125-μm优化光纤可以得到最好的性能，它具有非常精确控制的折射率分布。数据发射器通常包含一个850 nm的VCSEL。 
如果进行长距离的数据传输，更适合采用单模光纤，因为其中不存在任何模间色散，但是系统造价会高很多。 
国际电信联盟（ITU）制定了用于光纤通信的不同种类光纤的各种标准。对于多模光纤的标准为： 
 

活性多模光纤 
有些高功率光纤放大器采用的是多模光纤，因为它具有更大的模式面积（参阅大模式面积光纤）。通过入射信号光进入基模并且使模间混合最小化，可以得到接近于衍射极限的输出。 

材料和制造方法 
很多材料可以用于制造多模光纤。最常见的多模玻璃光纤为石英光纤，其中纯的石英纤芯周围是掺杂降低折射率的物质（例如，氟）。或者也可以对纤芯进行掺杂，例如锗，提高其折射率。尤其是对于大芯径光纤，等离子体外部沉积（POD）方法可以有效制造纯石英芯周围掺氟的降低折射率包层的光纤。 

还有其他的玻璃材料，例如氟化物和硫化物玻璃可以传导更长波长的光，还有聚合物（聚合物光纤，POF）。这些材料需要相应的制造技术。 

还可以采用光子晶体光纤（PCF），可以由不同的玻璃制作，并且可以包含空气包层来实现非常高的数值孔径。
 

Acronym: MMF

Definition: fibers supporting more than one guided mode per polarization direction

More general term: optical fibers

Opposite term: single-mode fibers

Multimode fibers are optical fibers which support multiple (often many) transverse guided modes for a given optical frequency and polarization.

The number of guided modes is determined by the wavelength (or optical frequency) and the refractive index profile. For step-index fibers, the relevant quantities are the core radius and the numerical aperture; the latter depends on the refractive index contrast between fiber core and cladding. In combination, these quantities determine the V number of step-index fibers. For large V values, the number of modes is roughly V² / 2, when counting both polarization directions. Particularly for fibers with a relatively large core (right-hand side in Figure 1), the number of supported modes can be very high.

Highly multimode fibers can guide light with poor beam quality and high optical power (e.g. generated with a high-power diode bar), but for preserving the beam quality of a light source with higher radiance it can be better to use a fiber with smaller core and moderate numerical aperture, even though efficient launching of light into the fiber may then be more difficult.

Figure 1: A single-mode fiber (left) has a core which is very small compared with the cladding, whereas a multimode fiber (right) can have a large core.

Compared with standard single-mode fibers, multimode fibers usually have significantly larger core areas, but also generally a higher numerical aperture of e.g. 0.2–0.3. The latter leads to robust guidance, even under conditions of tight bending, but also to higher propagation losses without bending, as irregularities at the core–cladding interface can scatter light more effectively. The refractive index profile is usually rectangular (→ step-index fibers), but sometimes parabolic (see below).

A basic specification of a multimode fiber contains the core diameter and the outer diameter of a multimode fiber. Common types for fiber-optic communications (see below) are 50/125 μm and 62.5/125 μm fibers, having a core diameter of 50 μm or 62.5 μm, respectively, and a cladding diameter of 125 μm. Such fibers support hundreds of guided modes. There are also large-core fibers with even substantially larger core diameters of hundreds of micrometers.

Launching light into a multimode fiber is comparatively easy, because there are larger tolerances concerning the location and propagation angle of incident light, compared with a single-mode fiber. On the other hand, the spatial coherence of the fiber output is reduced, and the output field pattern can hardly be controlled, for reasons explained below.

Figure 2: Electric field amplitude profiles for all the guided modes of an optical fiber. In general, light launched into a multimode fiber will excite a superposition of different modes. The diagram has been produced with the RP Fiber Power software.

Figure 2 shows the electric field profiles of the guided modes of a step-index fiber, as calculated for one particular wavelength. There is a fundamental mode (LP₀₁) with an approximately Gaussian intensity distribution, and a number of higher-order modes with more complicated spatial profiles. Each mode has a different β value. Any guided field distribution can be considered as a superposition of the guided modes.

For a given optical frequency, the total electric field distribution anywhere in a multimode fiber is a superposition of contributions from the different modes. The intensity profile depends not only on the optical powers in all the modes, but also on the relative phases, and there can be constructive or destructive interference of different modes at particular locations in the fiber. Both the powers and optical phases are initially determined by the launching conditions, and the relative phases (and thus the interference conditions) evolve further due to the mode-dependent propagation constants. Therefore, the more or less complicated intensity pattern changes all the time, typically with significant changes occurring within a propagation length of well below 1 mm. Also, the relative phases changes with any modifications of the launching conditions, bending or stretching of the fiber, changes of the wavelength or temperature, etc.

Figure 3 shows an example in the form of animated graphics, where the different frames represent intensity distributions occurring at the end of a multimode fiber when the input beam position is varied.

Figure 3: Intensity profiles at the end of a multimode fiber. The Gaussian input beam is scanned through the horizontal line (slightly above the center of the fiber core). This model has been made with the RP Fiber Power software and is described in more detail on a separate page.

Note that for light with a broad optical bandwidth (e.g. for a white light source) such complicated intensity patterns are not observed, if only the intensity is detected without distinguishing different spectral components. This is because the shape of the intensity pattern is different for each wavelength component, so that contributions from different wavelengths are averaged out. The longer the fiber, the lower is the optical bandwidth required to achieve this averaging.

Required Beam Quality for Launching Light into a Multimode Fiber

Compared with a single-mode fiber, a multimode fiber allows for much easier launching of light, particularly if it supports many guided modes. For efficient launching, one has to fulfill two conditions:

• The input light should essentially only hit the core, not the cladding.
• The input light should not contain significant amounts of power propagating with angles larger than arcsin NA.

If the M² factor of the input light is sufficiently small, it is possible to fulfill these two conditions simultaneously. The maximum M² factor for efficient launching of a beam with super-Gaussian profile can be estimated from the following formula:

This holds if both the spatial beam profile and the angular distribution (i.e., the profile in Fourier space) are well adapted for launching, with a kind of super-Gaussian shape. For Gaussian distributions, the M² factor needs to be somewhat lower. For more details and example cases, see Ref. [7].

Multimode Fibers for Transporting Laser Light

Multimode fibers are used for transporting light from a laser source to the place where it is needed, particularly when the light source has a poor beam quality and/or the high optical power requires a large area of the fiber core. For example, light from stationary high-power lasers of various types can be sent to laser material processing stations for cutting or welding, where e.g. a robot moves a laser head mounted at the end of a fiber cable.

Also, fiber-coupled high-power diode bars and diode stacks use multimode fibers, as their beam quality is far from diffraction-limited. Fiber coupling is useful because it allows one e.g. to separate the pump diodes and their cooling arrangement from the laser head of a diode-pumped solid-state laser. However, fiber-coupled laser diodes are more expensive, and depending on the beam shapers used, there can be some significant loss of radiance.

For such applications, the number of guided modes of the fiber should often not be larger than necessary for efficient launching, since otherwise the laser radiation might be distributed over a large than necessary number of modes, and the beam quality and brightness would be reduced.

In practice, a simple step-index refractive profile is normally used. The numerical aperture is often held constant at some standard value such as 0.22, and the core diameter is chosen according to the beam quality of the light source. Common values for the core diameter are 50, 100, 200, 400, 600 and 800 μm.

Multimode Fibers for Optical Communications

For short-distance optical fiber communications, multimode fibers are often preferred over single-mode fibers, because they can accept light from simpler light sources (e.g. light-emitting diodes = LEDs), and their alignment (e.g. in fiber connectors) is less critical. However, the possible data rates and/or transmission distances achievable with such fibers are limited by the phenomenon of intermodal dispersion: the group velocity depends on the propagation mode, so that ultrashort pulses propagating in a multimode fiber may be split into several pulses with different arrival times, possibly smearing out any transmitted signal. This effect can be greatly reduced by making multimode fibers with a parabolic refractive index profile (graded-index fibers, Figure 4), so that a substantially larger bandwidth–distance product can be achieved. Unavoidable imperfections still set limits. There are ISO standards like OM1, OM2, OM3, OM4 and OM5, which quantify the residual level of intermodal dispersion, limiting the transmission bandwidth (or the bandwidth–distance product). Highest performance is achieved e.g. with OM4 50/125-μm laser-optimized fibers, having a very precisely controlled refractive index profile. The data transmitter then often contains an 850-nm VCSEL.

Figure 4: Parabolic refractive index profile of a graded-index multimode fiber.

See the article on graded-index fibers for more details.

For long-haul data transmission, single-mode fibers are preferable, as they do not exhibit any intermodal dispersion, whereas the system cost is substantially higher.

The International Telecommunications Union (ITU) has developed a number of standards for various types of fibers as used for optical fiber communications. The standards for multimode fibers are:

Active Multimode Fibers

Some high-power fiber amplifiers are based on multimode fibers, because these can have larger mode areas (→ large mode area fibers). Such fibers have only a few guided modes (→ few-mode fibers), i.e., they still have a relatively small core compared to most other multimode fibers. It is often possible to obtain a nearly diffraction-limited output by launching the input signal light into the fundamental mode and by minimizing mode mixing.

Materials and Fabrication

Various materials can be used for multimode fibers. The most common multimode glass fibers are silica fibers, where a pure silica core is surrounded by a region which is doped with some index-lowering agent (e.g. fluorine). Alternatively or in addition, the core can have some additional doping, e.g. with germania, to increase the refractive index. Particularly for large-core fibers, the plasma outside deposition (POD) method allows the efficient fabrication of fluorine-doped “depressed index claddings” around a pure silica core.

There are also other glasses, e.g. fluoride and chalcogenide glasses for guiding light with longer wavelengths, and polymers (polymer optical fiber, POF). Such materials require adapted fabrication techniques.

Another possibility is to use photonic crystal fibers (PCF), which can be made from different glasses and can have, e.g., an air cladding to achieve a very high numerical aperture.

Bibliography