定义：一种长的薄波导结构，可以进行一定程度的弯曲。

光纤是一种波导，通常是由一些玻璃制作而成，可以制作的很长（几百千米），并且相对于其它波导来说更加灵活。
最常用的玻璃为二氧化硅（石英玻璃，无定型二氧化硅SiO2），有的为纯态有的掺杂某些物质。

二氧化硅之所以被广泛应用是因为其卓越的性质，尤其是其极低的传输损耗（超纯材料可以实现）以及抗拉伸和弯曲的超高机械强度（前提是表面完好）。 
激光器技术中应用的大多数光纤纤芯折射率比周围介质（包层）高。最简单的情形是阶跃折射率光纤，即折射率在纤芯和包层分别都是常数。
纤芯和包层的折射率差决定了光纤的数值孔径，差值通常很小，这样光纤是弱导波的。

进入纤芯中的光在纤芯中传播，即光主要在纤芯区域传播，尽管其光强分布会延展到纤芯区域之外。由于光纤的导波效应和低传播损耗，光强在很长距离的光纤中保持几乎不变。 

图1：将光射入光纤中的简单装置。一束准直激光光束聚焦进入光纤纤芯中。光在纤芯中传播，从光纤端口出射后变为发散光束。光纤纤芯和包层都由玻璃制作。玻璃光纤外面还有一层聚合物涂层保护。 
另一种不是很常见的导波结构是利用光子带隙（参阅光子带隙光纤）。例如，可以采用具有不同折射率的同心环形成一种二维布拉格反射镜。 
特种光纤是描述具有特别性质的一些光纤，通常不常见。 

目录 

• 光纤的应用
• 光纤模式——单模和多模光纤
• 主要参数
• 折射率分布
• 传播损耗
• 偏振性质
• 色散性质
• 光纤制造
• 光纤电缆
• 光纤器件
• 抛光，切割和熔接
• 安全问题
• 特殊种类的光纤
• 光纤损伤
• 光纤与电缆的比较

光纤的应用 
光纤光学具有很多重要的应用。其中最重要的包括： 

• 光纤通信中利用光纤进行长程数据传输，有时也用于传输短距离。大量的数据可以很快的传到光纤中，并且不受外界影响（电场和磁场等）。 
• 活性光纤装置包含稀土掺杂光纤。光纤激光器可以产生各种频率的激光，光纤放大器可以用来放大光强或者放大弱信号。 
• 光纤传感器可以用于，例如建筑物内温度分布和应力测量，石油管道和机翼等。 
• 无源光纤通常用于将光源中的光传输到另一处，来进行例如发光，二极管泵浦激光器和电力光纤。通常，它们也可以用于连接不同的光纤装置，例如干涉仪和光纤激光器。即它们类似于电子器件中的电线。 

因此，光纤光学在光子技术中是一个极其重要的领域。 

光纤模式——单模和多模光纤 
一根光纤可以支持一个或多个导波模式，其强度分布在光纤线性或者纤芯周围，强度的一部分也可能在光纤包层中传播。另外，包层模式很多，这些模式不局限在纤芯区域。包层中的模式通常在传输一段距离之后能量就会消失，但是有些情况下也可以传输很长的距离。在包层之外，通常还有保护的聚合物涂层，使光纤机械强度增大，并且防潮和其它对包层模式有害的效应。这一缓冲层可能包含丙烯酸盐，硅树脂或聚酰亚胺。在光纤端口，通常需要剥除涂层。 
单模和多模光纤最重要的差别在于： 

• 单模光纤纤芯通常比较小（直径仅有几微米），只能传输一个空间模式（不考虑该模式包含两个不同的偏振方向），该模式形状大多数情况下为高斯型。改变入射条件仅仅会改变射入光纤中导模的强度，而从光纤中出射光的空间分布是确定的。为了实现有效的将光耦合进单模光纤，通常需要激光光源发出的光具有很好的光束质量，并且为了实现模式匹配，需要聚焦光学装置严格对准。单模光纤的模式半径在5 μm量级，但是也有大模式面积光纤传播单个模式。后者情况下，位置的对准允差较低，而角度的允差更高（即不是太大问题）。 
• 多模光纤的纤芯和纤芯包层间的折射率差都更大，因此可以支持具有不同强度分布的多个模式（图2）。在这种情况下，从光纤纤芯中出射光的空间形状与入射条件有关，它决定了不同空间模式中的功率分布。 
• 长程光纤通信系统通常采用单模光纤，因为当数据传输速率很高时，不同模式具有不同的群速度会使信号发生畸变（参阅模间色散）。但在稍短距离的情况下，采用多模光纤更加方便，因为它对光源和器件的要求更低。因此局域网（LANs）通常采用多模光纤，很大带宽的情况除外。 

单模光纤通常用于光纤激光器和放大器。多模光纤通常用来将激光器光源中的光传输到需要用的地方，尤其是当光源具有较差的光束质量和高功率情况需要大模式面积的情况下。 
光纤中的不同模式可以通过各种效应发生耦合，例如，通过弯曲或者折射率曲线的不规则。这些有的是不需要的，有些是人为引入的，例如光纤布拉格光栅。波导理论表明耦合过程中一个重要的参数是不同的光学模式具有不同的波数，因此只有当空间频率匹配时才能实现有效的耦合。 

主要参数 
设计阶跃折射率光纤时两个参数非常重要，纤芯半径 a 和纤芯和包层的折射率差Δn。纤芯半径的典型值在单模光纤中为几微米，多模光纤中为几十微米或更大。 
通常不采用折射率差表征，而是利用数值孔径，定义为： 

即入射光束相对于光纤轴的最大接收角的正弦值（考虑射线光学中光从空气进入纤芯）。NA可以量化导波强度，其典型值在单模光纤中为0.1，但是实际中它的值会在比较大的范围内变化。例如，大模式面积单模光纤的数值孔径很小，可以小于0.05，而有些稀土掺杂光纤的值为0.3，并且更高的增益效率时该值更大。多模光纤NA的典型值在0.3附近。光纤对弯曲损耗的灵敏度会极大的提高NA，导致模场被强烈束缚在纤芯中。 

图2：折射率形状为平顶的光纤（参阅阶跃折射率光纤）中所有导波模式的电场振幅形状。两种颜色代表电场的正负号。最低阶模式（l=0，m=1称为LP01模式）强度形状类似于高斯光束。通常来讲，进入多模光纤中的光会激发不同模式的叠加，因此形状非常复杂。 
另一个常用的参数为V值： 

是一个归一化频率。当V值小于约2.405时，可以实现单模传输。多模光纤具有很大的V值。模式的数目与V2成正比。 
考虑一个典型的阶跃折射率石英光纤单模工作在1500 nm光谱区域的情况作为一个例子，其截止波长为1300 nm，数值孔径为0.1。纯二氧化为包层在1500 nm时的折射率约为1.4475，即折射率差约为0.0035。纤芯直径为10μm，V值为2.1。 

折射率分布 
光纤中的折射率分布通常与阶跃折射率分布（在纤芯折射率为常数）差别较大： 

• 由于预制棒熔化过程中掺杂物优先蒸发（假设预制棒是有化学气相沉积方法制作的），这时在纤芯中心通常折射率下降。具有小模式面积的单模光纤中，这不会显著影响模场分布，其分布大多数情况下接近于高斯型。 
• 有些光纤为渐变折射率分布（渐变折射率光纤），其中折射率远离中心后逐渐变小，例如，抛物线形状。抛物线型折射率非常重要，例如在多模光纤中可以使模间色散最小。 
• 还有W型折射率分布，即纤芯由折射率小于包层介质的物质包围（凹陷型包层）。理论上来说，还可以存在附加的阶跃折射率或者平滑的折射率变化。 
• 三角形的、梯形的和高斯型折射率分布通常用在色散位移光纤中。 
• 折射率分布不必要是圆柱形的。例如，椭圆形纤芯可以提高双折射（参阅保偏光纤）或者单偏振导波（参阅单偏振光纤）。 

需要注意的是数值孔径的定义以及V值对于非矩形折射率分布不是很明确。 
另外，还有光纤晶体光纤，其中折射率分布与结构有很大的关系。 

传播损耗 
光在光纤中的传播损耗非常小，尤其是通信用的单模石英光纤中。其中的衰减主要来自于短波长处的瑞利散射和长波长处的多光子吸收。瑞利散射来自于折射率涨落，这在玻璃中基本上不能避免，但是通过采用高数值孔径光纤中的浓度涨落可以强烈抑制该效应。其它损耗来自于非弹性散射（自发布里渊散射和拉曼散射），杂质吸收和纤芯直径的涨落。 
石英光纤中1500-1600 nm光最低的损耗可以小于0.2 dB/km（约单位千米4.5%），接近于非均匀玻璃中瑞利散射的理论极限值。在1400 nm附近还存在损耗峰值，这可以通过优化纤芯的化学组分减小OH含量极大的降低损耗。但是，具有很高OH含量的光纤在紫外光区域具有更低的损耗，而在红外光谱去则具有损耗峰值。 
多模光纤通常具有很高的数值孔径，因此具有更高的传播损耗，主要是因为纤芯掺杂浓度高会增大散射损耗。稀土掺杂光纤也具有更高的损耗，但是由于这种光纤应用时长度不会大于几十米，因此不会影响应用中的性能。 

偏振性质 
除了常用的圆柱形对称结构，光纤中还存在双折射会引起光的偏振片发生变化（激光辐射偏振）。保偏光纤本身具有很强的双折射可以解决这一问题。另外，还有单偏振光纤，只会导引一个偏振方向上的光。还有各种光纤偏振控制器，可以调整光纤的偏振态。 

色散性质 
由于光纤的波导性质，光纤中的色散（chromatic dispersion）与材料色散差别很大，尤其是当模式面积很小时（参阅波导色散）。因此通过控制波导性质可以得到不寻常的色散性质。例如，色散位移光纤在1500 nm光谱区域具有非零色散，还有色散平坦光纤，即在很大波长范围内具有很小的色散，以及色散缓变光纤。光子晶体光纤在设计上具有非常高的自由度。 
光纤中的双折射使群速度与偏振有关，这称为偏振模式色散。多模光纤中通常存在模间色散，即群速度依赖于光纤模式，可以选择合适的折射率分布使其最小化，但是还是比单模光纤中的色散大。 

光纤制造 
大多数光纤是通过拉制预制棒制造的，它是一个直径为几厘米，长度约为1m的玻璃棒。沿着预制棒轴的方向，预制棒的某一区域折射率较大，会形成纤芯。当预制棒被加热到接近零点时，从底部拉预制棒可以得到直径约为125 μm长度为几千米的细光纤。在光纤被卷在一起之前，通常在外面涂覆聚合物涂层用来机械和化学防护。 
光纤纤芯可以掺杂一些激光活性离子，通常为稀土离子，例如铒，钕，镱或者钍。当采用合适的泵浦光激发这些离子时，发生光学放大过程，这可以用于光纤激光器或放大器中。 
词条光纤制造中包含更多细节知识。 

光纤电缆 
 

图3：光纤电缆端口处的光学连接器。
虽然玻璃是一种易碎的材料，玻璃光纤却非常坚固。但是，光纤中还需要涂层保护涂层。在实验室应用中，将通信装置中的光发送到诊断仪器中，或者在大型工业装配中，使用包含连接器的光纤电缆非常方便（光纤跳线，如图3），其中真正的光纤外面还有附加的保护涂层。由于裸玻璃光纤的直径典型值为125 μm，聚合物涂层和外壳使直径增大到几百μm，因此光纤电缆的总直径约为几毫米。除了加强电缆之外，电缆材料的颜色（通常为黄色）使光纤很容易辨识，因此尽量避免恶劣的环境。 
更厚的光纤电缆用于传输高功率光束，例如，从光纤耦合半导体激光器到固态激光头中或者传到一些材料加工器件中。当功率高达几百瓦到几千瓦时，光纤电缆的直径约为几个厘米。高功率光纤电缆中也包含一些传感器来检测电缆的损伤，这样如果检测到高功率辐射跃迁从损伤点处辐射出去，可以马上关闭激光光源。这种预警措施对于激光防护很重要。 
用于长距离光纤通信的光纤电缆通常很厚，因为它们通常需要穿过恶劣环境，因此需要采取保护措施。在极限情况下，这些电缆可能放在海床上或者埋在地下。因此在安装和今后的维护中，需要很强的保护抗机械应力。 
光纤电缆可能包含多根光纤。这样单根光纤的大数据传输容量增大了很多倍。 

光纤器件 
很多光学器件直接由光纤制作。例如： 

• 光纤耦合器可以耦合两光纤中的光，耦合系数通常与光波长有关。 
• 光纤布拉格光栅提供与波长密切相关的反射和透射特性。它们可以用于光学滤波器或者将色散引入系统。 
• 光纤偏振器由一些特殊的单偏振光纤制作，它只能传播一个特定偏振方向上的光。 
• 光纤放大器可以放大特定波长区域的光。 

光纤准直器可以连接光纤光学器件和自由空间光学器件。这一装置主要包含一个准直透镜，将光纤端口出射的强的发散光束转化成准直光束。另外，还有机械对接，提供光纤间半永久性的连接。 

抛光，切割和熔接 
采用抛光技术可以得到干净平滑的光学端口。也可以制作不与光纤轴垂直的端面。倾斜角在10°附近（抛光角度），从光纤端面反射的光被有效的消除，因此可以保护对反射敏感的激光器。 
另一种更加快捷的方法产生干净的光纤端口是切割。其中，在一段拉伸光纤，然后采用振动的钻石刀片在另一端刻痕。这样保证了光纤端面非常拼花，至少在纤芯区域如此。在该过程中缠绕光纤，可以进行角度切割，但是这种方法结果的重复性比抛光技术差。 
光纤也可以熔接在一起。可以采用熔接技术制作永久性的光纤接头。另一种简单的技术是机械连接，其中光纤端口通过机械方法牢固的连在一起，但是不熔化。但是，这种情况下连接损耗很高，即使当表面折射率匹配时会减小。 
还有其他种类的光纤连接器，可以得到很好的机械接触，但是如果需要可以随时与光纤断开。 
一般来说，相比于处理电子接头来说，处理光纤端面更加精细。除了考虑尘埃，油脂等，光纤端口也很容易被划伤。处理光纤端面通常采用非常昂贵的装置（例如，高质量熔接器），尤其是考虑工作环境时需要很可靠的结果的情况下，即尤其是在比较脏的环境下。但是，光纤的很大优势是电缆不能比拟的就是其更高的传输容量。 

安全问题 
激光防护中的眼睛防护是一个很严重的问题，尤其是高功率光纤装置。受损伤的光学电缆可能辐射非常有害的高功率光，因此，这些电缆需要进行很好的保护避免受损伤，可以采用内置的传感器系统进行控制。 
在光纤通信中，功率一般足够小来避免眼睛安全问题，尤其是在1500 nm，即人眼安全的波长范围附近。但是，有时功率也高到非常危险，例如，有限TV中，高功率放大器产生的信号光非常大用来将信号分配到不同光纤用户中。 
另一个对眼睛的损伤与激光辐射无关，而是来自于光纤端口的锋利碎片，即切割光纤时得到的。这些碎片非常锋利，如果粘在手指上就有可能进到眼睛里或者插到皮肤里。它们也不能消化。因此，需要将光学碎片仔细的放置在有标记的容器中，在工作区域采取措施使它们能被看到，并且在工作区域严禁吃喝。 

特殊种类的光纤 
双包层光纤具有一个单模纤芯和多模内包层，后者传输泵浦光，例如高功率光纤激光器或放大器中的泵浦光。 
还有各种保偏光纤，通常是由强的双折射效应实现。如果入射光的偏振态与光纤的双折射轴重合，那么在光纤传播过程中偏振态不会发生改变。另外，还有单偏振光纤，即某一个方向的偏振光损耗很大。 
一种特殊的光纤为光子晶体光纤（PCF），也称为微结构光纤或者带孔光纤。这种光纤通常只包含一种材料，中间有很多很小的空气孔，直径小于1 μm。制造这种光纤需要使用带孔的预制棒，由叠层毛细管得到。通过改变空气孔的排列，得到的光纤就会具有不同的性质。例如： 

• 非常大或者小模式面积，得到极弱或极强的非线性 
• 在很大波长范围内实现单模导波（无截止单模光纤） 
• 大部分光在空气孔中传播（空气导波光子带隙光纤） 
• 不寻常的色散性质，例如在可见光谱区域为反常色散 

目前光子晶体光纤有望应用于很多应用中，包括非线性光纤装置，工作在短波长处的孤子光纤激光器和高功率光纤放大器。 
大多数光纤都使用的二氧化硅及与其有关的材料（例如，锗硅酸盐或者铝硅酸盐玻璃），有些玻璃材料也可以采用。例如： 

• 磷酸盐玻璃主要用于光纤放大器和激光器（低淬灭效应，即使在很高的稀土掺杂浓度时） 
• 硫系玻璃（硫化物，碲化物，或者硒化物玻璃），声子能量很小，主要用于中红外应用 
• 氟化物玻璃，声子能量也很小，用于中红外或者上转换激光器 

低成本的多模光纤可以使用便宜的聚合物材料（塑料光纤，POF），可以使用简单的挤压方法制造，制造的光纤很坚固，甚至可以得到很大的直径。在有些应用领域中，需要使用比玻璃光纤更便宜的方法。目前甚至光子晶体光纤都可以用聚合物得到。有些聚合物光纤可以用到传播太赫兹波。 
有些情况下，光纤由晶体材料制备，例如蓝宝石，但是通常这种光纤不太灵活，可以看做是一根能够进行波导传播的细棒（纤芯结构可有可无）。它们可以用于非常高功率光纤激光器和放大器中。 

光纤损伤 
在工作中，光纤装置可能会遭受各种形式的损伤。例如： 

图4：光子晶体光纤棒低端的无芯端盖。

• 在高光强的情况下，光纤端口极易损伤。空气玻璃界面的算上阈值比体材料更低。例如，石英光纤对于1 ns波长为1000 nm的脉冲的表面损伤力约为22 J/cm2。如果脉冲具有更高的峰值强度或损伤里，那么需要使用无芯端盖（图4）。如果端口具有灰尘，那么光学表面更容易受损伤。并且，将高功率光射入光纤会早成附近的聚合物涂层过热。 
• 平均功率不是太高的情况下，光纤端口的初始损伤会造成光纤熔化，然后背向传播到整个光纤中。 
• 峰值功率过高时，会发生自聚焦，进一步提高强度，立刻引起损伤。石英光纤中，该效应的阈值功率约为4 MW，与模式面积无关。 
• 在使用稀土掺杂光纤的高增益光纤放大器中，会产生寄生激光，同时还存在Q开关效应会破坏光纤。 
• 如果单位长度耗散功率很高，那么光纤容易过热，这在丙烯酸涂层中尤其明显。水冷却可以有效抑制该效应。 

光纤与电缆的比较 
在一些技术领域，例如长距离或计算机芯片间的光数据传输，光纤（或其它波导）可以与电缆相比拟。与后者相比，光纤具有很多优势： 

• 光纤电缆比电缆轻很多。 
• 光数据传输中光纤的容量比电缆高几个数量级。 
• 光纤中的传输损耗可以非常低，最优波长处可以小于 1dB/km，该波长在1500 nm附近。 
• 如果需要传输很大的距离时，采用一个光纤放大器可以放大很多的信道。 
• 光纤实现光数据连接的情况很难被拦截和控制，因此即使不使用加密技术也能具有额外的安全性。如果需要很高安全性，需要使用量子密码。 
• 光纤连接不受电磁干扰，以及接地回路等问题， 
• 光纤中也不存在触发易爆物体的危险（除非携带高功率的光纤断裂）。 

但是，光纤也有其缺点： 

• 光纤连接器比较敏感且很难处理，尤其是使用单模光纤时。需要精确对准和超净。因此，只有在使用很高传输带宽时才使用光纤连接器。 
• 玻璃光纤不能很大程度的弯曲，因为这会引起很高的弯曲损耗甚至折断。这在光纤入户技术中是一个问题。但是，石英光纤非常坚固可以弯曲的程度远大于其他玻璃材料。 

Definition: a kind of long and thin optical waveguides which can be bent to some degree

Optical fibers are the core components of fiber optics and play a particularly important role in photonics in general. They are a kind of optical waveguides, which are in most cases made of some kind of glass, can potentially be very long (hundreds of kilometers), and are – in contrast to other waveguides – fairly flexible. Although glasses are generally quite fragile, particularly thin silica fibers protected with a polymer coating can be bent substantially – for example around your finger – without breaking.

The most commonly used glass for optical fibers is fused silica (quartz glass, amorphous silicon dioxide = SiO₂), either in pure form or with some dopants. Silica is so widely used because of its outstanding properties, in particular its potential for extremely low propagation losses (realized with ultrapure material) and its amazingly high mechanical strength against pulling and even bending (provided that the surfaces are well prepared). However, for some special applications one requires specialty fibers made from other types of glasses, e.g. fluoride fibers or chalcogenide fibers (see below).

Most optical fibers used in laser technology have a fiber core with a refractive index which is somewhat higher than that of the surrounding medium (called the fiber cladding). The simplest case is that of a step-index fiber, where the refractive index is constant within the core and within the cladding. The index contrast between core and cladding determines the numerical aperture of the fiber (see below), and is typically small, so that optical fibers are weakly guiding. Light launched into the core is guided along the core, i.e., it propagates mainly in the core region, although the intensity distribution may extend somewhat beyond the core. Due to the guidance and the low propagation losses, the optical intensity can be maintained over long lengths of fiber.

Figure 1: Simple setup for launching light into an optical fiber (not to scale). A collimated laser beam is focused into the fiber core. The light propagates along the core and leaves the other fiber end as a divergent beam. The fiber core and cladding are made of glass. A polymer jacket protects the glass fiber.

Although most fibers have only a single core, there are also so-called multi-core fibers containing a few cores or even a large number of those.

A less frequently used principle of guiding light is based on a photonic bandgap (→ photonic bandgap fibers). For example, this can be realized with concentric rings of different refractive index, forming a kind of two-dimensional Bragg mirror.

The term specialty fibers is used for many different kinds of optical fibers with special properties, and is thus not very specific. Such fibers may be based on unusual glasses or just have unusual designs.

Figure 2: A fiber in which supercontinuum generation occurs. Some of the light is scattered out of the fiber, so that it can be seen. The image has been kindly provided by the Optoelectronics Research Centre, University of Southampton.

Applications of Optical Fibers

There are many important applications of fiber optics (largely of glass fibers). Some of the most important ones are:

• Optical fiber communications utilize optical fibers mostly for long-range data transmission, but sometimes also for short distances. Huge amounts of data can be quickly sent through a single fiber, which is also immune to external influences such as electric and magnetic fields.
• Active fiber-optic devices contain some rare-earth-doped fiber. Fiber lasers can generate laser light at various wavelengths, and fiber amplifiers can be used e.g. for boosting the optical power or amplifying some weak telecom signals.
• Fiber-optic sensors can be used e.g. for distributed temperature and strain measurements in buildings, oil pipelines, and wings of airplanes.
• Passive optical fibers [14] are useful for transporting light from some source to another point, e.g. for purposes like illumination, diode pumping of lasers and power over fiber. Also, they are used for connecting components in fiber-optic devices, such as interferometers and fiber lasers. They then play a similar role as electrical wires do in electronic devices.

Therefore, fiber optics has become a particularly important area within the technology of photonics.

Fiber Modes – Single-mode versus Multimode Fibers

An optical fiber can support one or several (sometimes even many) guided modes, the intensity distributions of which are located at or immediately around the fiber core, although some of the intensity may propagate within the fiber cladding. In addition, there is a multitude of cladding modes, which are not restricted to the core region. The optical power in cladding modes is usually lost after some moderate distance of propagation, but can in some cases propagate over longer distances.

Outside the cladding, there is typically a thin protective polymer coating with one or two layers, which gives the fiber improved mechanical strength and protection against moisture. Such coatings may consist of acrylate, silicone or polyimide, for example. (At the fiber ends, the coating often has to be stripped off.) Optical properties of such coatings are sometimes also relevant, e.g. concerning the attenuation of cladding modes which they cause.

In addition to the polymer coating, some fibers are also equipped with a much thicker buffer (secondary coating), e.g. with an outer diameter of 900 μm. Such buffered fibers are integrated into indoor fiber cables, for example. Another possibility is the integration of fibers in a loose tube, which is also filled with a viscous gel. That approach is common for outdoor cables.

An important distinction is that between single-mode and multimode fibers:

• Single-mode fibers usually have a relatively small core (with a diameter of only a few micrometers) and can guide only a single spatial mode (disregarding the fact that there are two different polarization directions), the profile of which in most cases has roughly a Gaussian shape. Changing the launch conditions only affects the power launched into the guided mode, whereas the spatial distribution of the light exiting the fiber is fixed. Efficiently launching light into a single-mode fiber requires a laser source with high beam quality and precise alignment of the focusing optics in order to achieve mode matching. The mode radius of a single-mode fiber is often of the order of 5 μm, but there are also large mode area fibers with single-mode guidance. In the latter case, the alignment tolerances are lower in terms of position but higher in terms of angle (which may be less problematic).
• Multimode fibers have a larger core and/or a larger index difference between core and cladding, so that they support multiple modes (possibly hundreds of more) with different intensity distributions (Figure 3). In this case, the spatial profile of light exiting the fiber core depends on the launch conditions, which determine the distribution of power among the spatial modes.

Figure 3: Electric near field amplitude profiles for all the guided modes of a fiber with a top-hat refractive index profile (→ step index fiber). The two colors indicate different signs of electric field values. The lowest-order mode (l = 0, m = 1, called LP₀₁ mode) has an intensity profile which is similar to that of a Gaussian beam. In general, light launched into a multimode fiber will excite a superposition of different modes, which can have a complicated shape.

Figure 4: Far field amplitudes for the same fiber as in Figure 3.

Long-range optical fiber communication systems usually use single-mode glass fibers, because the different group velocities of different modes would distort the signal at high data rates (→ intermodal dispersion). For shorter distances, however, multimode fibers are more convenient as the demands on light sources and component alignment are lower. Therefore, local area networks (LANs), except those for highest bandwidth, normally use multimode fiber.

Single-mode fibers are also normally used for fiber lasers and amplifiers. Multimode fibers are often used, e.g., for the transport of 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 mode area.

Different modes of an optical fiber can be coupled via various effects, e.g. by bending or often by irregularities in the refractive index profile. These may be unwanted or purposely introduced, e.g. as fiber Bragg gratings. Waveguide theory shows that an important factor for the coupling between different fiber modes is the difference in their wavenumbers, which for efficient coupling has to match the spatial frequency of a coupling disturbance.

Fiber Properties

Main Parameters

The design of a step-index fiber can be characterized with only two parameters, e.g. the core radius a and the refractive index difference Δn between core and cladding. Typical values of the core radius are a few microns for single-mode fibers and tens of microns or more for multimode fibers.

Instead of the refractive index difference, one usually uses the numerical aperture, defined as

which is the sine of the maximum acceptable angle of an incident beam with respect to the fiber axis (considering the launch from air into the core in a ray-optic picture). (n is the refractive index of the surrounding medium – close to 1 in case of air.) The NA also quantifies the strength of guidance. Typical values are of the order of 0.1 for single-mode fibers, even though actual values vary in a relatively large range. For example, large mode area single-mode fibers can have low numerical apertures of 0.05 or even lower, whereas some rare-earth-doped fibers have values of 0.3 and higher for a high gain efficiency. NA values around 0.3 are also typical for multimode fibers. The sensitivity of a fiber to bend losses strongly diminishes with increasing NA, which causes strong confinement of the mode field to the core.

Another frequently used parameter is the V number

which is a kind of normalized frequency. Single-mode guidance is achieved when the V number is below ≈ 2.405. Multimode fibers can have huge V values. The number of guided modes then scales with V².

As a numerical example, consider a typical step-index silica fiber for single-mode operation in the 1.5-μm spectral region, with a cut-off wavelength of 1.3 μm and a numerical aperture of 0.1. The refractive index of the pure silica cladding at 1.5 μm is ≈ 1.444. The core index is ≈ 1.4475, i.e., the index difference is ≈ 0.0035. The core diameter is 10 μm, and the V number is 2.1.

Refractive Index Profiles

The refractive index profile of optical fibers often deviates substantially from that of a step-index profile (with constant refractive index within the core):

• Due to preferential evaporation of the dopant during the collapse of the preform (assuming that the preform is made with chemical vapor deposition, see below), there is often a pronounced index dip at the center. For single-mode fibers with small mode areas, this does not need to have a strong impact on the mode field distribution, which in most cases closely resembles a Gaussian shape.
• Some fibers are made with graded index profiles (graded-index fibers) where the refractive index is gradually reduced away from the center, e.g. with a parabolic shape. Parabolic index profiles are useful e.g. for multimode telecom fibers because they minimize intermodal dispersion (see below).
• There are also “W profiles”, where the core is surrounded by a region with a refractive index lower than that of the cladding (depressed cladding). In principle, there can even be additional index steps, or combinations with smooth refractive index variations.
• Triangular, trapezoidal and Gaussian index profiles are used for dispersion-shifted fibers.
• Index profiles are not always radially symmetric. For example, an elliptical core shape can provide increased birefringence (→ polarization-maintaining fibers) or even single-polarization guidance (→ single-polarization fibers) (see below).

Note that the definitions of the numerical aperture and consequently of the V number become somewhat ambiguous for non-rectangular index profiles.

In addition, there are so-called photonic crystal fibers (see below), where the refractive index profile is strongly structured.

Propagation Losses

The power losses (propagation losses) for light propagating in an optical fiber can be extremely small, particularly for single-mode silica fibers as used in telecommunications. The resulting attenuation is typically dominated by Rayleigh scattering for short wavelengths (and absorption if one gets closer to the band gap) and by multiphonon absorption at long wavelengths. Rayleigh scattering results from refractive index fluctuations, which are to some extent unavoidable in a glass, but may be strongly increased due to concentration fluctuations in fibers with high numerical aperture and by other imperfections. Other loss contributions come from inelastic scattering (spontaneous Brillouin scattering and Raman scattering), from absorbing impurities, and from fluctuations of the core diameter.

One may further reduce Rayleigh scattering by optimizing the glass composition (e.g. low with germania content and with dopants reducing the viscosity and therefore the fictitious glass temperature), but also with particularly slow fiber drawing to allow for some degree of annealing.

For silica fibers, the loss minimum occurs around 1.5–1.6 μm and can be a bit below 0.15 dB/km (≈ 3.4% per km), which is close to the theoretical limit based on Rayleigh scattering in fused silica. There is often a loss peak around 1.4 μm, which can be largely eliminated, however, by carefully optimizing the chemical composition of the core so as to reduce the OH content (i.e. the concentration of hydroxyl bonds). Interestingly, fibers with high OH content can exhibit lower losses for ultraviolet light, whereas they exhibit pronounced loss peaks in the infrared spectral region.

Multimode fibers, and in general fibers with high numerical aperture, tend to have significantly higher propagation losses, essentially because the higher doping level of the core increases the scattering losses. Rare-earth-doped fibers also have much higher losses, but as more than some tens of meters of such a fiber are rarely used, this usually does not matter for their applications.

Polarization Properties

Despite the typically cylindrical symmetry, fibers usually exhibit some amount of random birefringence which can cause the polarization state of light to evolve in an uncontrolled way (→ polarization of light). There are special polarization-maintaining fibers with a strong built-in birefringence to solve this problem. In addition, there are single-polarization fibers, which guide only light with one polarization direction. There are also various types of fiber polarization controllers, which allow one to adjust the state of polarization in a fiber.

Chromatic Dispersion Properties

As a result of the waveguide properties, the chromatic dispersion of an optical fiber can deviate significantly from its material dispersion, particularly when the mode area is small (→ waveguide dispersion). This makes it possible to obtain unusual dispersion properties by engineering the waveguide properties. For example, dispersion-shifted fibers can have near zero dispersion in the 1.5-μm spectral region, and there are dispersion-flattened fibers with small dispersion over a large wavelength range or dispersion-decreasing fibers. A particularly high design freedom exists for photonic crystal fibers (see below).

Other Kinds of Dispersion

The birefringence makes the group delay polarization-dependent; this is often called polarization mode dispersion. (That effect can be largely suppressed by using spun fibers.)

For multimode fibers, there is also intermodal dispersion, i.e., a dependence of the group velocity on the fiber mode, which may be minimized by choosing a suitable refractive index profile but is typically larger than the dispersion of single-mode fibers.

Fiber Fabrication

Most optical fibers are fabricated by pulling from a so-called preform, which is a glass rod, e.g. with a diameter of a few centimeters and 1 m length. Along its axis, the preform contains a region with increased refractive index, which will form the core. When the preform is heated close to the melting point in a furnace (oven), a thin fiber with a diameter of typically 125 μm and a length of many kilometers can be pulled from the bottom of the preform. Before the fiber is wound up, it usually obtains a polymer coating for mechanical and chemical protection.

The core of a fiber can be doped with laser-active ions, normally rare earth ions of erbium, neodymium, ytterbium, or thulium. When these ions are excited with suitable pump light, optical amplification occurs, which can be used in fiber lasers or amplifiers.

More details are given in the article on fiber fabrication.

Fiber-optic Cables

Figure 5: A fiber connector at the end of a fiber cable. The photograph has been kindly provided by NKT Photonics.

Glass fibers are amazingly robust, although glasses are known to be particularly fragile materials. However, additional protection is often required when fibers are used in an environment which is e.g. accessible by operators. For laboratory use, e.g. for sending light from a telecom setup to some diagnostic instrument and also in large industrial assemblies, it is convenient to use connectorized fiber cables (fiber patch cables, see Figure 5), where the actual fiber is surrounded by additional protective layers. While the bare glass fiber may have a typical diameter of 125 μm, and the polymer buffer and jacket increase this to a few hundred micrometers, the total diameter of the fiber cable is typically several millimeters. Apart from considerably strengthening the cable, the (typically yellow) cable material also makes it much easier for operators to recognize the fiber, thus avoiding too harsh treatment in the first place.

Thicker fiber cables are used for the delivery of high-power beams, e.g. from fiber-coupled diode lasers to a solid-state laser head or to some laser material processing equipment. For power levels of hundreds of watts to many kilowatts, the fiber cable may have a diameter of several centimeters. High-power fiber cables may also contain sensors for detecting damage to the cable, so that the laser source can be immediately switched off when there is a risk that high-power laser radiation exits the cable at a damaged point. Such precautions can be very important for laser safety.

Fiber cables for long-haul optical fiber communications are also fairly thick, because they often have to be used over long times in harsh environments and must be protected accordingly. In extreme cases, such cables may be lying on the sea bed or are slightly buried there. A high level of protection is required against the mechanical stress both during installation and at later times.

A fiber cable can contain multiple fibers. In this way, the already huge data transmission capability of a single fiber can be multiplied to enormously high levels.

Fiber-optic Components

Many optical components can be directly made from fibers. Some examples are:

• Fiber couplers allow to couple light typically between two fibers, typically with the coupling coefficient depending on the optical wavelength.
• Fiber Bragg gratings provide strongly wavelength-dependent reflection and transmission properties. They can be used e.g. as optical filters or for introducing chromatic dispersion into a system.
• Fiber polarizers can be made e.g. with special single polarization fibers which can guide only light with a certain polarization direction.
• Fiber amplifiers can amplify light in certain wavelength regions.

Other fiber-optic components contain bulk elements with attached fiber connections. Examples of so-called fiber-pigtailed devices are:

• Semiconductor optical amplifiers can provide amplification in a semiconductor waveguide.
• Fiber-coupled diode lasers send light into a single-mode or multimode fiber.
• Various types of optical modulators such as electroabsorption modulators and electro-optic modulators are usually based on other types of waveguides which can be coupled to fibers.
• Faraday isolators, Faraday mirrors and circulators contain bulk-optical rotator elements and collimation optics.
• Fiber-optic switches as used e.g. for fiber-optic networks can be realized with various technologies, e.g. with electro-optic modulators or with micro-electromechanical systems (MEMS).

Fiber collimators provide a connection between fiber optics and free-space optics. Essentially, such a device contains a collimation lens, transforming the strongly divergent beam from a fiber end into a collimated beam. Finally, there are mechanical splices, providing semi-permanent connections between fibers.

Polishing, Cleaving, and Splicing of Glass Fibers

Clean and smoothly shaped fiber ends can be produced with polishing techniques. These can also be used to produce end faces which are not perpendicular to the fiber axis. With a tilt angle of the order of 10° (angle polishing), reflections from fiber ends can be effectively eliminated from the beam path, so that e.g. reflection-sensitive lasers are well protected. See the article on polishing of fibers for details.

A much faster technique for preparing fiber ends is cleaving. Here, one typically pulls the fiber while scratching it from a side, e.g. with a vibrating diamond blade. This makes the fiber break with normally fairly smooth end faces – at least around the core region. By twisting the fiber during this process, angle cleaves can be fabricated, but the results are less reproducible than for polishing techniques.

Glass fibers (particularly those made of silica) can also be spliced together. One may use the technique of fusion splicing for making permanent fiber joints. A simpler technique is mechanical splicing, where the fiber ends are firmly held together by some mechanical means, but not fused. Here, however, the splice losses are typically higher, even when reduced with an index-matching gel between the surfaces.

There are also many types of fiber connectors which allow one to obtain good mechanical contact (as in a mechanical splice), but also to disconnect the fibers easily as required.

In general, the handling of fiber ends is fairly delicate, compared with the handling of electrical connections. Apart from problems with dust, grease and the like, fiber ends are relatively sensitive and are easily scratched. Their handling often requires very expensive equipment (e.g. high-quality fusion splicers), particularly when reliable results are required under field conditions, i.e., in a comparatively dirty environment. On the other hand, a fair comparison with electrical cables has to take into account the much higher transmission capacity of a fiber.

For plastic fibers, adapted techniques of cleaning and splicing have been developed.

Safety Issues

Laser safety in terms of eye safety is a serious issue with high-power fiber devices. Very harmful high-power light could exit a damage fiber cable; therefore, such cables must be well protected against damage and possibly monitored with built-in sensor systems.

In optical fiber communications, the optical power levels are often small enough to avoid eye safety problems, particularly when using the eye-safe wavelength region around 1.5 μm. However, dangerous power levels can sometimes occur, e.g. in cable TV applications, where a high-power amplifier creates sufficiently signal power for splitting signals into many fibers.

Another risk for eyes is not associated with laser radiation, but with the sharp scraps of fiber ends, as are obtained e.g. when cleaving fibers. These scraps are extremely sharp, may be transported into eyes e.g. when they stick to a finger, and may also penetrate the skin. They should also not be ingested. For such reasons, one should carefully dispose fiber scraps into a properly marked container immediately when they occur, take precautions to make them well visible in the working area, and avoid any eating or drinking near the work area.

Special Types of Fibers

So-called double-clad fibers can have a single-mode core and a multimode inner cladding, the latter transporting the pump light e.g. of a high-power fiber laser or amplifier. A further extension of the concept lead to triple-clad fibers.

There are various kinds of polarization-maintaining fibers, mostly realized on the basis of strong birefringence. The linear polarization of light is preserved provided that the initial polarization axis is aligned with a birefringent axis of the fiber. In addition, there are also single-polarization fibers (polarizing fibers) where one polarization direction experiences strong losses.

A special kind of optical fibers is the photonic crystal fiber (PCF), also called microstructure fiber or holey fiber. Such fibers typically consist only of a single material (usually silica), containing very small air holes with diameters well below 1 μm. Fabrication of such fibers is possible by using preforms with holes, made e.g. by stacking capillary tubes, or sometimes with extrusion techniques (particularly for soft glasses). By varying the arrangement of air holes, fibers with extremely different properties can be made, e.g.

• extremely large or small mode areas, leading to extremely weak or strong nonlinearity
• single-mode guidance in very large wavelength regions (endlessly single-mode fibers)
• guidance with the light field dominantly propagating in an air hole (air-guiding photonic bandgap fibers)
• unusual chromatic dispersion properties, e.g. anomalous dispersion in the visible spectral region

Photonic crystal fibers are now attracting strong interest for a wide range of applications, including extremely nonlinear fiber devices, soliton fiber lasers operating at short wavelengths, and high-power fiber amplifiers.

Although most fiber cores consist of some variant of silica (e.g. germanosilicate or aluminosilicate glass), other glass materials can also be used. Examples are

• phosphate glasses mainly for fiber amplifiers and lasers (low quenching tendency even for high rare earth doping concentrations)
• chalcogenide glasses (sulphide, telluride, or selenide glasses), having small phonon energies, mainly used for mid-infrared applications
• fluoride glasses, also with small phonon energies, used in fluoride fibers for mid-infrared and upconversion lasers

Low-cost multimode fibers can be made of polymers (plastic optical fibers, POF), which are cheap materials, allow simple production by extrusion, and are robust and flexible even when made with larger diameters. In some application areas, they allow for substantially cheaper solutions than possible with glass fibers. Even photonic crystal fibers can nowadays be produced from polymers. Some polymer fibers can also be used to guide terahertz waves.

In some cases, fibers are made of crystalline materials such as sapphire, but these fibers are usually not flexible and can be seen as thin rods using waveguide propagation (with or without a core structure at the center). They can be used for very high-power fiber lasers and amplifiers.

Damage of Fibers

Optical fiber devices can be damaged in various ways during operation. Various aspects are relevant in this context:

Figure 6: A core-less end cap on a photonic crystal fiber rod. The photograph has been kindly provided by NKT Photonics.

• The fiber ends are particularly vulnerable to laser-induced damage. The air–glass interface has a lower damage threshold than the bulk material. For example, for silica fibers the surface damage fluence is ≈ 22 J/cm² for 1-ns pulses with wavelengths around 1 μm [11]. For pulses with higher peak intensity or fluence, it may then be necessary to use core-less end caps (Figure 6). Fiber surfaces become even more vulnerable if there is any dust. Also, launching a high optical power into a fiber end can overheat the nearby polymer coating.
• For not even very high average powers, initial damage of a fiber end can have the consequence of a fiber fuse propagating through the whole fiber in the backward direction.
• For too high peak powers, self-focusing can occur, which further increases the intensity and leads to immediate damage. For silica fibers, this effect tends to occur above a threshold power of roughly 4 MW, relatively independent of the mode area.
• In high-gain fiber amplifiers made with rare-earth-doped fibers, parasitic lasing can occur, followed by a kind of Q-switching effect which can destroy the fiber.
• For a too high dissipated power per unit length, a fiber can become overheated. This applies particularly to acrylate coatings. Water cooling is an effective method for suppressing such effects.

Comparison of Optical Fibers with Electric Cables

In some technical areas, such as optical data transmission over long distances or between computer chips, optical fibers (or other waveguides) compete with electric cables. Compared with the latter, they have a number of pronounced advantages:

• Fiber cables are less heavy than electric cables.
• The capacity of a fiber for optical data transmission is orders of magnitude higher than for any electric cable.
• The transmission losses of a fiber can be very low: well below 1 dB/km for the optimum wavelengths, which are around 1.5 μm.
• A large number of channels can be reamplified in a single fiber amplifier, if required for very large transmission distances.
• Optical data connections via fibers are comparatively hard to intercept and manipulate, which gives additional security even without using encryption techniques. For very high security, quantum cryptography can be used.
• Fiber connections are immune to electromagnetic interference, problems with ground loops, and the like.
• Fibers do not introduce fire hazards or the risk of triggering explosive substances (unless a fiber carrying a high optical power breaks).

On the other hand, fibers also have their disadvantages:

• Fiber connections are comparatively sensitive and difficult to handle, particularly when single-mode fibers are used. Precise alignment and high cleanliness are required. For such reasons, fiber connections are often only competitive if a high transmission bandwidth can be utilized.
• Most glass fibers may not be bent very tightly, because this can cause high bend losses or even breakage. This can be a problem e.g. in the context of fiber-to-the-home technologies. Relatively bend-insensitive fibers have been developed for such applications, but still these can tolerate less bending than electrical cables.

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