Waveplate

definition:
A transparent sheet with specific birefringence, used to change the polarization state of light.

A waveplate (or delay plate) is a transparent plate with specific birefringence, typically used to control the polarization state of a light beam. A waveplate has a fast axis and a slow axis, both perpendicular to the surface and the direction of beam propagation, and mutually perpendicular. The phase velocity of light polarized in the fast axis direction is slightly higher. The required optical delay (phase delay difference in two polarization directions) can only be obtained within a limited wavelength range and a limited incident angle range.  

Types and Applications 
The most common wave plate is a quarter wave plate（λ/4 Plate and half wave plate（λ/2The phase delay difference between the two polarization directions of the film isπ/2andπThe corresponding phase propagation distances areλ / 4andλ / 2
Here are some important conclusions:

1. If the beam is linearly polarized and the polarization direction is along one axis of the waveplate, then the polarization direction does not change.  
2. If the incident polarization state does not coincide with any axis and the waveplate is a half waveplate, then the polarized light remains linearly polarized, but the polarization direction rotates. If the angle between linearly polarized light and the axis is45°So, the polarization direction rotates90°
3. If the angle between the incident polarized light and the axis is45°By using a quarter wave plate, circularly polarized light can be obtained. (Other linearly polarized light will become elliptically polarized light.) Conversely, circularly polarized light can be obtained as linearly polarized light by passing through a quarter wave plate.  

In the laser resonant cavity, placing two quarter wave plates on both sides of the gain medium can achieve single frequency operation (see twisted mode technique). Placing a half wave plate between the laser crystal and the resonant cavity mirror can reduce depolarization losses. The combination of half wave plate and polarizer can achieve an output coupler with adjustable transmittance.  
Wave plates are usually made of quartz crystals（SiO2）Made because it has high transparency over a wide wavelength range and high optical quality. There are also some other materials (applied to other wavelength ranges) that can be used, such as calcite（CaCO3）Magnesium fluoride（MgF2）, Sapphire（Al2O3）Mica (a type of silica material) and some birefringent polymers.  

Zero order and multi-stage waveplates 
There are many types of waveplates:

1. Zero order waveplates are very thin, and the phase delay of light in both polarization directions is only as small as that of half waveplatesπThis is an ideal situation, as the zero order waveplate is very thin and inconvenient, especially for strong refractive materials such as calcite, the preparation process is very difficult and requires very delicate manufacturing. The latter problem can be solved by sticking a zero order waveplate onto a thick glass substrate, which does not have birefringence but can stabilize the waveplate. And the interface between the two lowers the damage threshold.  
2. The relative phase change of the multi-stage waveplate increases, which is the required value plus2πThe integer multiple. Although the performance is the same at the designed wavelength, the optical bandwidth of this waveplate is limited by the actual relative phase change. Moreover, phase delay is more sensitive to temperature. Low level waveplates refer to multi-stage waveplates with relatively small series, which can reduce the adverse effects mentioned above.  
3. An effective zero order waveplate (or net zero order waveplate) consists of two multi-stage waveplates with slightly different thicknesses, which are glued together or in optical contact, or leave a gap between the two multi-stage waveplates at higher power. The slow axis of one wave plate is parallel to the fast axis of another wave plate, so that the birefringence of the two wave plates is almost cancelled out. It is necessary to adjust the thickness difference between the two to obtain the desired net phase change. This device can operate over a wide wavelength range.  

Two color waveplates can also be made to combine materials with different dispersions (such as quartz and magnesium fluoride), resulting in almost constant delay over a wide spectral range (several hundred nanometers). In addition, there are double wave long wave plates that can obtain fixed phase delay values at two separate wavelengths. This property is sometimes used in nonlinear frequency conversion, such as in the process of third harmonic generation.  

some issues 
In addition to the basic optical performance mentioned above, waveplates also have some related issues:

1. The material has high transparency within the wavelength range used.  
2. The relationship between phase delay, temperature, and angle is related to the specific design.  
3. High quality waveplates have consistent delay across the entire numerical aperture or most of the numerical aperture range.  
4. Surface reflection can affect performance, and anti reflective coatings can be used to reduce it.  
5. The optical damage threshold is important when applied to pulsed laser systems.  
6. Some waveplates have a casing, which makes it easy to rotate them by a specific angle or observe the direction of their fast and slow axes.  

In some applications, it is difficult to meet all the requirements of the wafer. Therefore, other methods need to be taken, such as changing the polarization direction of the laser beam. Using three45°The reflector can rotate the polarization direction90° First, tilt the beam to the right, then upwards, and finally return to its original direction.  

Related devices 
There are some devices related to waveplates:

1. Fresnel diamond shaped retarders and other prism retarders have the same basic function as wave plates, but use polarization dependent phase changes during total reflection. In principle, it can work in broadband situations.  
2. Babinet-SoleilThe compensator includes a pair of birefringent wedges that can be used as wave plates, and the degree of delay varies.  
3. There are also some fiber optic polarization controllers that have similar functions.  
4. Electro optic crystals and liquid crystal devices can be used as electrically controlled wave plates and also as active delay devices.