定义：一种可以传播光的空间不均匀结构。

光学波导是可以传播光的空间非均匀结构，即将光限制在一个空间区域内进行传播。通常，波导包含一个相比于周围介质（包层）折射率较大的区域。然而，导波还可以利用金属层界面处的反射来实现。有些波导结构还与金属介质界面处的等离子体效应有关。

图1：两种不同的波导结构。平板波导只在竖直方向传播光，而沟道波导则可以在两个方向上导波。 
大多数波导都可以在两个方向上导波，因此导波电场被限制在两个方向上，主要在一个方向上传播。例如，图1中的沟道波导。最重要的二维波导是光纤。还有一维波导，称为平板波导。 

目录 

• 波导制造
• 波导模式
• 波导色散
• 纳米光学中的等离子体波导
• 应用

波导制造 
有很多不同的技术可以制造电介质波导。例如： 

• 可以采用外延或者抛光方法利用各种晶体和玻璃材料制造平板波导。波导结构可以在器件顶端制作（如图1左侧图），也可以在其他固体层之间制作波导结构。 
• 半导体、晶体和玻璃材料中的沟道波导可以采用刻蚀方法与外延、离子交换或者热扩散方法结合制作。也可以在波导表面生长额外的一层制作掩埋式波导。这样可以得到更低的传输损耗和更对称的模式分布。 
• 光纤可以通过拉制预制棒得到，后者为一个具有内禀折射率分布的大的玻璃棒。光纤也可以通过进一步减小尺寸拉制成波导结构，极限情况下得到纳米光纤。 
• 采用聚焦的脉冲激光光束可以将波导写入透明介质中，这里利用了激光诱导击穿以及相关的现象。在玻璃中，受影响的部分具有较大的折射率，因此直接可以用于导波。在晶体中，折射率可能会减小，这时需要处理一些波导周围的区域。 

在不同制造方法之间权衡比较复杂。需要考虑诸如成本、灵活性和制造的可重复性、传播损耗、材料的副作用（例如，加热或不扩散材料引起的）、最佳模式尺寸和耦合到其它波导的对称性等因素。 

波导模式 
如果波导尺寸很大，可以采用射线光学来描述入射光的传播情况。但是，如果存在干涉效应，这种描述就不准确了，后者在很小的波导尺寸情况下会出现。这时需要将光描述成波的形式，理论基础为麦克斯韦方程，通常需要采用一些近似来简化。 
常常需要描述在给定光频率和偏振的情况下，垂直于入射平面的电场分布。感兴趣的是在传播过程中电场不发生改变的光，相位变化除外。这一场分布于波导模式有关。图2给出了多模光纤导波模式的例子。每一个模式都对应一个传播常数，其虚部表示单位传播距离的相位延迟。光纤还有很多非导波模式（包层模式），它们并不限制在光纤纤芯中。 

图2：光纤中所有导模的电场振幅分布。两个颜色代表电场的正负号。最低阶模式（l=1,m=0）的强度分布与高斯光束类似。一般来讲，进入多模光纤的光会激发不同模式的叠加，因此具有很复杂的形状。 

波导中任何初始存在的场分布都可以分解成导波模式场分布的线性叠加，再加上一些方程。后者对应于非导波。根据波导的类型，非导波或者在包层中传播或者被反射。导波的传播很容易计算，将各波导模式与通过模式的传播常数计算出来的展开系数线性叠加就可以得到。

 具有很小的横向空间尺寸和很小的折射率差（数值孔径小）的波导可能只能传导一个单横模（给定光频率和偏振的情况下），无高阶模式；因此称为单模波导（参阅单模光纤）。传播一定距离后，场分布接近于常数模场分布，与初始场分布无关，前提是非导模全部衰减掉（例如，衰减到包层中）。多模波导是可以支持很多导模的波导（有时上千个模式）。 

有些波导模式的强度分布非常不对称（例如，在图1右侧的沟道波导中）。也有的情况下导模只具有一个偏振方向，或者不同偏振方向的模式具有不同的性质。 
波导的很多性质，例如传播损耗，弯曲敏感性（对于光纤来说），传播常数和色散与导模类型有很大关系。 

波导色散 
波导限制光导致波矢沿着传播方向倾斜。这会影响单位长度的相位延迟和色散性质（参阅波导色散）。例如，小模式面积的光子晶体光纤的色散在可见光区域可能是反常色散的，尽管石英材料具有正常色散。 

纳米光学中的等离子体波导 
在很多应用中，例如在光子晶体回路中，需要将光限制在小于波长的波导中。这时采用电介质波导会面临很多问题。例如，尽管纳米光纤具有远小于波长的尺寸，但是在纳米尺寸光纤中的光电场会延展到电介质结构中。因此，需要研究其他的利用其他物理导波机制的波导技术。一个很有前途的方向是纳米等离子体，是将纳米尺寸的金属结构嵌入电介质材料中。在这种情况下，电场分布比单独利用电介质材料更加局域化。但是，传输损耗通常也非常高。另外面临的问题是如何将光高效耦合进这种结构从而能够实现无源和有源光子器件，例如强弯曲，耦合器，滤波器，放大器和探测器。 

应用 
波导的应用非常广泛。例如： 

• 光纤可以实现光在很长距离上传播，例如，光纤通信中。 
• 用在硅光子学中的光子集成回路中，波导可以在不同光学元件中传播光。 
• 在未来的应用中，用在数据处理芯片上的硅波导和电路板上的聚合物波导可以用来在计算机器件之间进行快速的光学数据传输。 
• 有些波导用于在一定距离上保持光强大小，例如，在非线性装置中，如倍频器和拉曼激光器。波导激光器和放大器中采用的是有源（放大）波导。重要的例子为光纤激光器和光纤放大器。 
• 波导可以用于消除高阶横模，因此可看做模式清洁器。 
• 有些情况下，会利用导波的衰逝场与材料之间的相互作用，例如在有些波导传感器中。 
• 波导还可以分束或者合束，例如用在集成光学干涉仪中。 

Definition: spatially inhomogeneous transparent structures for guiding light

More specific terms: planar waveguides, channel waveguides, optical fibers

An optical waveguide is a spatially inhomogeneous structure for guiding light, i.e. for restricting the spatial region in which light can propagate. Usually, a waveguide contains a region of increased refractive index, compared with the surrounding medium (called cladding). However, guidance is also possible with other physical mechanisms, e.g. by the use of reflections at metallic interfaces, or with photonic crystal structures. Some waveguides also involve plasmonic effects at metals.

Figure 1: Two different kinds of waveguides. Planar waveguides guide light only in the vertical direction, whereas channel waveguides guide in two dimensions.

Most waveguides exhibit two-dimensional guidance, thus restricting the extension of guided light in two dimensions and permitting propagation essentially only in one dimension. An example is the channel waveguide shown in Figure 1. The most important type of two-dimensional waveguide is the optical fiber. There are also one-dimensional waveguides, called planar waveguides.

Waveguide Fabrication

There are many different techniques for fabricating dielectric waveguides. Some examples:

• Planar waveguides can be fabricated on various crystal and glass materials with epitaxy or with polishing methods. The waveguide may be made on the top of the device (as shown on the left side of Figure 1), but it can also be placed between other solid layers.
• Channel waveguides on semiconductor, crystal and glass materials can be made with lithographic methods in combination with, e.g., epitaxy, ion exchange, or thermal indiffusion. It is possible to make a buried waveguide by growing an additional layer on top of the waveguide. That may lead to lower propagation losses and a more symmetric mode profile.
• Optical fibers can be fabricated by drawing from a preform, which is a large glass rod with a built-in refractive index profile. Fibers can again be drawn into waveguides of further reduced dimensions, in the extreme case resulting in nanofibers.
• Waveguides can be written into transparent media (e.g. glasses or crystals, and even in polymers) with focused and pulsed laser beams, exploiting laser-induced breakdown and related phenomena. In glasses, the affected volume often exhibits a somewhat increased refractive index, which can be directly used for guiding light. In crystals, the refractive index may be decreased; one then has to treat some region around the desired waveguide region.

The trade-offs between different fabrication techniques can be complicated. They can involve aspects such as cost, flexibility and reproducibility of manufacturing, propagation losses, possible side effects on the material (e.g. via heating or indiffused materials), optimum mode size and symmetry for coupling to other waveguides, etc.

Waveguide Modes

For waveguides with large extensions, geometrical optics are often used for describing the propagation of injected light. Such a description, however, becomes invalid when interference effects occur, and this is particularly the case for very small waveguide dimensions. In that case, a wave description of the light is required – normally on the basis of Maxwell's equations, often simplified with approximating assumptions.

It is common to consider the field distribution for a given optical frequency and polarization in a plane perpendicular to the propagation direction. Of special interest are those distributions which do not change during propagation, apart from a common phase change. Such field distributions are associated with so-called waveguide modes. As an example, Figure 2 shows the guided modes of a multimode fiber. Each mode has a so-called propagation constant, the imaginary part of which quantifies the phase delay per unit propagation distance. A fiber also has a large number of unguided modes (cladding modes), which are not restricted to the vicinity of the fiber core.

Figure 2: Electric field amplitude profiles for all the guided modes of an optical fiber. The two colors indicate different signs of electric field values. The lowest-order mode (l = 1, m = 0, 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.

Any initial field distribution, which may describe light injected at the beginning of the waveguide, can be decomposed into a linear combination of the field distributions of the guided waveguide modes, plus some function which can not be expressed as such a combination. The latter part corresponds to light which can not be guided. Depending on the type of waveguide, the not guided light may propagate in the cladding or may be reflected. The propagation of the guided part is easily calculated, using a linear combination of the waveguide modes with local expansion coefficients calculated from the propagation constants of the modes.

A waveguide with a small transverse spatial extension and/or a small refractive index difference (small numerical aperture) may be able to guide only a single transverse mode (for a given optical frequency and polarization) and no higher-order modes; it is then called a single-mode waveguide (→ single-mode fibers). The field distribution after a certain propagation distance then always resembles the constant mode field distribution, independent of the initial field distribution, provided that the unguided modes have been lost (e.g. in the cladding). Multimode waveguides are those supporting several or even many guided modes (sometimes many thousands).

Some types of waveguides (e.g. the channel waveguide on the right side of Figure 1) exhibit modes with strongly asymmetric intensity profiles. It also happens that guided modes exist only for one polarization direction, or that the modes for different polarization directions have very different properties.

Various properties such as the propagation losses, the bend sensitivity (for fibers), the propagation constant and the chromatic dispersion (see below) can substantially depend on the type of guided mode.

Waveguide Dispersion

Confinement of light in a waveguide leads to wave vectors which are tilted against the propagation direction. This affects the phase delay per unit length and thus the chromatic dispersion properties (→ waveguide dispersion). For example, the dispersion of a photonic crystal fiber with small mode area can be anomalous in the visible spectral region, although the silica material would have normal dispersion.

Plasmonic Waveguides for Nano Optics

For various applications, for example in the context of photonic integrated circuits, it is of great interest to strongly localize light in waveguides to dimensions far below the optical wavelength. Here, dielectric waveguides exhibit serious limitations. For example, although nanofibers can have diameters far below the wavelength, the electric field distributions of light guided in nanometer-scale fibers extend far beyond dielectric structure. Therefore, new waveguide technologies based on other physical guiding mechanisms are investigated. A promising field is that of nanoplasmonics [15], where nanometer-scale metallic structures embedded in dielectric materials are used. In that way, it is possible to obtain much more localized field distributions than possible with dielectric structures alone. However, the propagation losses are typically quite high. Additional challenges are to efficiently couple light into such structures and to realize various passive and active photonic components such as strong bends, couplers, filters, amplifiers and detectors.

Applications

The applications of waveguides are manifold. Some examples are:

• Optical fibers allow the transmission of light over long distances, e.g. for optical fiber communications.
• On photonic integrated circuits, as used e.g. in silicon photonics, waveguides transport light between different optical components.
• In the future, silicon waveguides (→ silicon photonics) on digital processor chips and polymer waveguides in circuit boards may be used for fast optical data transmission between components of computers.
• Some waveguides are used for maintaining high optical intensities over appreciable lengths, e.g. in nonlinear devices such as frequency doublers, Raman lasers and supercontinuum sources. Active (amplifying) waveguides are used in waveguide lasers and amplifiers. Important examples are fiber lasers and fiber amplifiers.
• A waveguide can be used for stripping off higher-order transverse modes, thus acting as a mode cleaner for improving the beam quality.
• In some cases, an interaction of the guided light with material in the evanescent field is used, e.g. in certain waveguide sensors.
• Waveguides can also be employed for splitting and combining light beams, e.g. in integrated optical interferometers.

Bibliography