定义：
具有特定双折射的透明片，用于改变光的偏振态。

波片（或延迟板）是具有特定双折射的透明片，通常用来控制光束的偏振态。波片具有一个快轴和一个慢轴，都是垂直于表面和光束传播方向的，并且相互垂直。在快轴方向偏振的光相速度稍大。需要的光延迟（两偏振方向上的相位延迟差）只在有限波长区域和有限入射角范围内能够得到。 

种类和应用 
最常见的波片是四分之一波片（λ/4 片）和半波片（λ/2片），其中两线偏振方向的相位延迟差分别为 π/2和π，对应的相位传播距离分别为λ / 4和λ / 2。 
下面是一些重要的结论： 

1. 如果光束为线偏振的，并且偏振方向是沿着波片的某一个轴，那么偏振方向不改变。 
2. 如果入射的偏振态与任一轴不重合，波片为半波片，那么偏振光仍然是线偏振的，但是偏振方向发生旋转。如果线偏振光与轴夹角为 45°，那么偏振方向旋转90°。 
3. 如果入射线偏振光与轴之间夹角为 45°，通过四分之一波片可以得到圆偏振光。（其它的线偏振光会变成椭圆偏振光。）反过来，圆偏振光通过四分之一波片可以得到线偏振光。 

在激光器谐振腔中，在增益介质两边放置两个四分之一波片可以实现单频工作（参阅扭曲模技术）。在激光晶体和谐振腔反射镜之间放置一个半波片可以减小去极化损耗。半波片和偏振片结合使用可以实现可调透射率的输出耦合器。 
波片通常由石英晶体（SiO2）制作，因为它在很大的波长范围内具有很高的透明度，并且具有很高的光学质量。还有一些其它的材料（应用于其它波长范围）可以，例如方解石（CaCO3），氟化镁（MgF2），蓝宝石（Al2O3），云母（一种二氧化硅材料）和一些双折射聚合物。 

零级和多级波片 
有很多种类的波片： 

1. 零级波片非常薄，两偏振方向的光相位延迟对于半波片只有 π。这是理想的情形，由于零级波片很薄所以很不方便，尤其是对于强折射材料来说，例如方解石，制备过程非常困难和需要制作非常精巧。后一个问题可以通过将零级波片粘在厚的玻璃片上解决，玻璃衬底不具有双折射但是可以稳定波片。而二者界面使损伤阈值变低。 
2. 多级波片的相对相位改变变大，是所需要值再加上2π的整数倍。尽管在设计的波长处性能相同，该波片的光学带宽受实际的相对相位改变限制。并且，相位延迟与对温度更加敏感。低级波片是指具有相对小级数的多级波片，可以使上面提到的不利效应变小。 
3. 有效零级波片（或净零级波片）由两个厚度稍微不同的多级波片组成，将它们黏在一起或者光学接触，或者在更高功率时在两多级波片之间留一点空隙。一个波片的慢轴与另一个波片的快轴平行，这样两波片的双折射就几乎抵消了。需要调整二者的厚度差得到需要的净相位改变。这一装置可工作在很宽的波长范围内。 

还可以制作二色性波片，将不同色散的材料结合起来（例如，石英和氟化镁），这样在很大光谱范围内（几百纳米）具有几乎不变的延迟。另外，还存在双波长波片，它在两个分立的不同波长处都能得到固定的相位延迟值。这一性质有时会在非线性频率转换，例如三倍频过程中用到。 

一些问题 
除了以上基本的光学性能，波片还有一些相关的问题： 

1. 材料在采用的波长范围内具有很高的透明度。 
2. 相位延迟与温度和角度的关系与具体设计有关。 
3. 高质量的波片在整个数值孔径或者大部分的数值孔径范围内具有一致的延迟。 
4. 表面的反射会影响性能，可以采用抗反射涂层减小。 
5. 当应用于脉冲激光器系统时光学损伤阈值很重要。 
6. 有的波片存在一个外壳，这样很容易将其旋转某一特定角度，或者看其快轴和慢轴的指向。 

有的应用中波片很难满足全部的要求。因此，需要采取其他的方法，例如，可以改变激光光束的偏振方向。采用三个45°反射镜就可以将偏振方向旋转90° ，即先将光束偏向右侧，再向上，最终可以回到原来的方向。 

相关器件 
有一些器件与波片相关： 

1. 菲涅尔菱形延迟器和其它棱镜延迟器与波片具有相同的基本功能，但是采用的是全反射过程中与偏振有关的相位变化。原理上可以工作于宽带情况。 
2. Babinet-Soleil补偿器包含一对双折射楔，可以用作波片，并且延迟程度是变化的。 
3. 还有一些光纤偏振控制器具有类似的功能。 
4. 电光晶体和液晶装置可以用作电控制波片，也成为主动延迟器。

Definition: transparent plates with a defined amount of birefringence, used for modifying the polarization of light

Alternative terms: retarder plates, retarders

Optical waveplates (also called wave plates or retarder plates) are transparent plates with a carefully chosen amount of birefringence. They are mostly used for manipulating the polarization state of light beams. A waveplate has a slow axis and a fast axis, both being perpendicular to the beam direction, and also to each other. The phase velocity of light is slightly higher for polarization along the fast axis. The designed value of optical retardance (difference in phase delay for the two polarization directions) is achieved only in a limited wavelength range (see below) and in a limited range of incidence angles.

Common Types and Applications

The most common types of waveplates are quarter-wave plates (λ/4 plates) and half-wave plates (λ/2 plates), where the difference of phase delays between the two linear polarization directions is π/2 or π, respectively, corresponding to propagation phase shifts over a distance of λ / 4 or λ / 2, respectively.

Some important cases are:

• When a light beam is linearly polarized, and the polarization direction is along one of the axes of the waveplate, the polarization remains unchanged.
• When the incident polarization does not coincide with one of the axes, and the plate is a half-wave plate, then the polarization stays linear, but the polarization direction is rotated. For example, for an angle of 45° to the axes, the polarization direction is rotated by 90°.
• When the incident polarization is at an angle of 45° to the axes, a quarter-wave plate generates a state of circular polarization. (Other input polarizations lead to elliptical polarization states.) Conversely, circularly polarized light is converted into linearly polarized light.

Within a laser resonator, two quarter-wave plates around the gain medium are sometimes used for obtaining single-frequency operation (→ twisted-mode technique). Inserting a half-wave plate between a laser crystal and a resonator end mirror can help to reduce depolarization loss. The combination of a half-wave plate and a polarizer allows one to realize an output coupler with adjustable transmission.

Many waveplates are made of quartz (crystalline SiO₂), as this optical material exhibits a wide wavelength range with very high transparency, and can be prepared with high optical quality. Other possible materials (to be used e.g. in other wavelength regions) are calcite (CaCO₃), magnesium fluoride (MgF₂), sapphire (Al₂O₃), mica (a silicate material), and some birefringent polymers. The choice of material can depend on many requirements, e.g. concerning wavelength range, open aperture, absorption losses and high-power capability.

Zero-order and Multiple-order Plates

There are different kinds of waveplates:

• True zero-order waveplates are so thin that the relative optical phase delay between the two polarization directions is just π, for example, for a half-wave plate. The key advantage of true zero-order waveplates is that they can be used in a substantial wavelength range and range of incidence angles. In addition, their temperature sensitivity is weak.
• While zero-order waveplates offer best performance, the device thickness can be inconveniently small, particularly for strongly birefringent materials such as calcite, so that the optical fabrication becomes difficult and the handling delicate. The latter problem can be eliminated by cementing (or bonding) a zero-order plate to a thicker glass plate, which is not birefringent but provides mechanical stabilization. The resulting interface, however, leads to a lower damage threshold such as 10 MW/cm².
• Multiple-order waveplates (= multi-order plates) are made so that the relative phase change is larger than the required value by an integer multiple of 2π. Although the performance at the design wavelength can be essentially the same, the optical bandwidth in which the plate has roughly the correct relative phase change is quite limited, e.g. to a few nanometers. Similarly, the allowed range of incidence angles can be quite small. Also, the retardance has a higher temperature sensitivity.
• Low-order waveplates are multiple-order plates with a relatively small order, keeping the mentioned detrimental effects low.
• Effective zero-order waveplates (or net zero-order waveplates) can be made from two multiple-order plates with slightly different thicknesses, which are cemented or optically contacted, or air-spaced for application with higher optical power levels. The slow axis of one plate is aligned with the fast axis of the other plate, so that the birefringence of the two plates is nearly canceled. The difference in thickness must be adjusted to obtain the required net phase change. Such devices can work in a broad wavelength range, since wavelength-induced changes of retardance in one plate are compensated by the other plate. However, the problem of a small usable angular range and temperature range remains.

It is also possible to make achromatic waveplates, combining materials with different chromatic dispersion (e.g. quartz and MgF₂), which can have a nearly constant retardance over a very wide spectral range (hundreds of nanometers). Also, there are dual-wavelength waveplates, which have well-defined retardance values at some discrete very different wavelengths. Such features are sometimes required in the context of nonlinear frequency conversion, such as frequency tripling.

Various Issues

In addition to the fundamental optical performance, various other issues can be relevant:

• The materials should have a high transparency in the wavelength region of interest.
• The sensitivity of the phase retardance to temperature and angle depends on the design.
• High-quality waveplates exhibit a uniform retardance over the full open aperture, or a large portion of it. Where that is not the case, depolarization (more precisely, spatially dependent polarization states) can result.
• Surface reflections can be disturbing, and may be reduced with anti-reflection coatings.
• The optical damage threshold can be important for applications in pulsed laser systems.
• Some waveplates are provided with a housing which makes it easy to rotate the plate by a well-defined angle, and/or to see the orientation of the fast and slow axis.

For some applications, it can be difficult to obtain a waveplate fulfilling all the requirements. Therefore, one sometimes has to use alternative methods, for example for turning the polarization direction of a laser beam. For example, a 90° rotation of polarization (and also the beam profile) can be obtained with a combination of three 45° mirrors, subsequently deflecting the beam to the right, then upwards and finally into the original direction.

Depolarization Compensators

There are waveplates with spatially varying polarization properties, which are used within a laser resonator to reduce depolarization loss [9].

Diffractive Waveplates

Waveplates can also be realized based on a completely different principle of operation: with photonic metasurfaces containing sub-wavelength gratings. These devices are also called diffractive waveplates [6]. They can have remarkable properties, e.g. very wideband operation.

Related Devices

There are optical devices which are somewhat related to waveplates:

• Fresnel rhomb retarders and other types of prism retarders have the same basic function as waveplates, but exploit polarization-dependent phase changes during total internal reflection. This principle allows broadband (achromatic) operation.
• A Babinet–Soleil compensator, containing a pair of birefringent wedges, can be used as a waveplate with a variable degree of retardation. Other versions of tunable waveplates such as the Berek compensator are based on variable tilting of birefringent plates.
• There are various types of fiber polarization controllers with similar functions.
• Electro-optic crystals and liquid crystal devices can be used to make electrically controllable waveplates, also called active retarders.

Bibliography