定义：用于减小表面反射的光学薄膜涂层。

抗反射涂层是涂覆在光学表面上的薄的电介质涂层，为了减小表面对某一波长区域光的反射率。大多数情况下，采用的工作原理是不同光学界面处的反射波发生消相干干涉而相互抵消。 

目录

• 单层抗反射涂层
• 多层涂层
• 设计方法
• 渐变折射率涂层
• 强吸收涂层
• 应用
• 损伤阈值

单层抗反射涂层 
最简单的情况是在正入射的情况下，设计的抗反射薄膜涂层采用材料的折射率接近于两个相邻介质折射率的几何平均值，光学厚度为四分之一波长。这时，在两界面处的反射波大小相等，发生干涉相消后互相抵消。 
这种方法存在两个限制因素： 

• 不是总能找到具有合适折射率的材料，尤其是当体介质的折射率较低时。 
• 单层涂层只能工作在很有限的带宽情形。 

多层涂层 
如果不能找到合适的单层涂层材料，或者需要在很大的波长范围内具有抗反射性质（不同波长范围的光需要同时具有，或入射角不同的情况），这时需要采用更加复杂一些的设计，通常需要采用数值计算方法。多层介质涂层设计时需要在低残余反射率和大带宽之间做出权衡。V涂层只在很窄带宽（10nm量级）内具有很好的特性，而宽带涂层则可以在很大的波长范围内具有适中的性能。 

图1：在BK7玻璃衬底上经过数值优化的对1064nm和532nm光的抗反射涂层的反射率曲线。采用了两层涂层，分别为TiO2和SiO2。 
除了以上性质，还需要考虑到生长过程的允差：很多复杂的涂层设计只有采用非常精准的加工过程才能实现很好的性能。因此生长过程允差是实际设计时一个重要的因素。 

设计方法 
简单类型的层数少的抗反射涂层通常采用分析方法进行设计。在更加复杂的设计中，需要采用数值优化的算法，该算法类似于电介质反射镜中采用的方法。设计结果通常不易理解，因为得到的结果来自于不同界面反射光非常复杂的干涉效应得到的抗反射性质。 

渐变折射率涂层 
渐变折射率涂层的材料组分是逐渐变化的，因此这种涂层就存在很多可能的性质。
最简单的情况是，两种光学材料的折射率在几个波长范围内平缓改变，可以在很大波长范围和入射角度范围内抑制反射。
但是，实际上很难实现，因为光学表面与空气接触，而固体材料的折射率与空气差别很大。
一种解决方法是，采用纳米光学方法制作亚波长的金字塔形结构或类似的结构（蛾眼结构）。
这种结构的折射率是缓慢变化为1，是通过缓慢减少固体材料的量来实现的。然而，不采用纳米光学也可以采用其它解决方法，尤其是可将渐变折射率层涂覆在多层涂层上。
这在很大角度范围内，不采用很小折射率的材料也能得到很大带宽内的抗反射性质。 

强吸收涂层 
一种特殊的抗反射涂层是包含了很薄的强吸收材料的涂层。其厚度可能只有几十纳米，即比通常的抗反射涂层的厚度小很多，因为这种介质传播常数的虚部很大，可以产生很大的相位变化。入射光被这种结构强烈吸收，而不是透射。这种抗反射结构由于其亚波长结构也称为光子超材料，然而了解这种特性只需简单的干涉现象就能描述。 

应用 
抗反射涂层通常用在光学元件上用来减小光学损耗和反射光束引起的一些有害效应。给定波长和入射角情况下的残余反射占的比例在0.2%量级，或者经过优化后可以更小（在有限带宽内）。在眼光眼睛中的应用时，能够实现的抑制的反射更小，因为涂层需要工作在很大的波长范围和很宽的入射角度范围内。抗反射涂层通常用在激光器晶体和非线性晶体上。这时，来自晶体的非均匀热学膨胀会引出附加的问题。 
大多数情况下，抗反射涂层应用在几平方毫米面积的光学界面上。但是，也可以在光纤端面涂覆这种涂层，有时甚至在保护套和装配连接器上。这时存在很多技术困难，例如，聚合物保护套漏气到真空容器中，一些光纤端口被当做一个整体处理，但是也发展了一些特殊的溅射方法来消除这些问题。得到的涂层性能可与普通的体表面的涂层相比拟，至少可与少量层数的简单涂层设计相比拟。 

损伤阈值 
除了反射性质，抗反射涂层的光学损伤阈值也需要考虑，例如，当用与调Q激光器中时。抗反射涂层根据采用的材料不同，可以具有比衬底高或低的损伤阈值。 
即使给定涂层材料，若采用的制备技术不同，涂层的损伤阈值也不同。离子束溅射方法可以得到较高的损伤阈值。

Acronym: AR coating

Definition: optical thin-film coatings for reducing reflections from surfaces

More general terms: dielectric coatings

An anti-reflection coating (AR coating) is a dielectric thin-film coating applied to an optical surface in order to reduce the reflectance (also often called reflectivity) of that surface due to Fresnel reflections – at least in a certain wavelength range. Examples for the application of such coatings are spectacles, optical systems like camera objectives, optical windows, displays and photovoltaic cells.

In most cases, the basic principle of operation is that reflected waves from different optical interfaces largely cancel each other by destructive interference.

Note that there are also anti-glare surfaces, which suppress reflections in a completely different way: by diffuse scattering from a microscopically rough surface. Such surfaces are suitable e.g. for some displays and viewing ports, but normally not for laser applications, and should be carefully distinguished from anti-reflection surfaces.

Single-layer Anti-reflection Coatings

In the simplest case, an anti-reflection thin-film coating designed for normal incidence consists of a single quarter-wave layer of a material the refractive index of which is close to the geometric mean value of the refractive indices of the two adjacent media. In that situation, two reflections of equal magnitude arise at the two interfaces, and these cancel each other by destructive interference.

The limitations of this approach are twofold:

• It is not always possible to find a coating material with suitable refractive index, particularly in cases where the bulk medium has a relatively low refractive index (e.g. in case of plastic optics).
• A single-layer coating works only in a limited bandwidth (wavelength range) and a limited angular range.

Multilayer Coatings

If no suitable medium for a single-layer coating can be found, or if anti-reflective properties are required for a very broad wavelength range (or for different wavelength ranges simultaneously, or for different angles of incidence), more complicated designs may be used, which usually have to be found using numerical techniques, implemented in suitable thin-film design software. A general trade-off of such multilayer designs is between a low residual reflectance and a large bandwidth. So-called V coatings have a high performance only in a narrow bandwidth (order of 10 nm), whereas broadband coatings offer moderate performance but in a wide wavelength range.

Figure 1: Reflectance curve for a numerically optimized anti-reflection coating on a BK7 glass substrate for 1064 nm and 532 nm. Two layer pairs of TiO₂ and SiO₂ are used. The coating design was made with the software RP Coating.

Apart from those properties, the tolerance to growth errors may also be of interest: there are sophisticated coating designs which reach a high performance only for very precise manufacturing. The growth error tolerance is therefore an important aspect to be considered in the design.

Multilayer anti-reflection coatings are often applied to optical glasses and crystals, but they can also be used for plastic optics.

Design Methods

Analytical design rules exist for simple types of anti-reflection coatings with very few thin-film layers. For more sophisticated designs, numerical optimization algorithms similar to those described in the article on dielectric mirrors can be used. The resulting designs are normally not easily understood, as the anti-reflection properties result from a complicated interference of the reflections from various interfaces.

Gradient Index Coatings

A wide range of possibilities arises from gradient index coatings (or graded-index coatings) [2, 3, 11], where the composition of a layer material is gradually varied (as in rugate filters). In the simplest case, a smooth index transition between two optical materials over a length scale of a few wavelengths can suppress fairly well the reflection over a wide spectral and angular range. This is difficult to realize, however, for surfaces next to air, since all solid materials have a refractive index significantly different from that of air. One solution is to use nanooptics in the form of sub-wavelength pyramid structures or the like (moth eye structure), see e.g. Refs.  [1], [2] and [7]. Such structures (which can be called photonic metamaterials) imitate a smooth transition of the refractive index to 1 by smoothly reducing the amount of solid material in a plane parallel to the surface. However, there are also solutions without nanooptics, in particular the integration of gradient index layers into a multilayer coating. This allows for good broadband anti-reflection properties in a wide angular range without using materials with a very small refractive index.

Coatings with Strongly Absorbing Layers

An unusual type of anti-reflection coating is one consisting of a very thin layer of some strongly absorbing material. The thickness can be only some tens of nanometers, i.e., far less than usually required for lossless AR coatings, as strong imaginary components of the propagation constant of such media lead to substantial phase changes. The incident light is largely absorbed by such structures, rather than transmitted. Such anti-reflection structures are called photonic metamaterials due to the combination of sub-wavelength structures, although simple interference phenomena are sufficient for understanding their characteristics [13].

Applications of AR Coatings

Anti-reflection coatings [3] are often used for optical components in order to reduce optical losses and sometimes also the detrimental influence of reflected beams. The residual reflectance for a given wavelength and angle of incidence is often of the order of 0.2%, or less (in a limited bandwidth) with careful optimization. For application on prescription glasses, the achievable suppression of reflections is significantly lower, since the coating must operate in a wide wavelength range and for a wide range of incidence angles. AR coatings are also used on laser crystals and nonlinear crystals. In such cases, additional challenges can arise from anisotropic thermal expansion e.g. of lithium triborate (LBO) crystals.

In most cases, AR coatings are used on optical interfaces with an area of at least a few millimeters squared. However, it is also possible to produce such coatings on the ends of optical fibers, sometimes even in jacketed and connectorized assemblies. There are various technical difficulties, e.g. related to outgasing of polymer jackets in a vacuum chamber and to the limited number of fiber ends which can be treated in one batch, but specialized sputtering processes have been developed which mitigate these problems. The coating performance can be as good as for normal bulk surfaces, at least for simple coating designs with only fewer layers.

Damage Threshold

Apart from the reflection properties, the optical damage threshold of anti-reflection coatings can be of interest, for example for use in components for Q-switched lasers. Depending on the material combination, an AR coating can have a higher or lower damage threshold than the substrate material.

Even for given coating materials, the damage threshold can vary considerably depending on the fabrication technique. Ion beam sputtering is known to allow for relatively high damage thresholds.

Bibliography