定义：
双折射介质中干涉效应的周期。

当两束不同方向的线偏振光在双折射介质中传播时，它们的相位变化不同。假设每个偏振波都沿着介质的一个主轴方向传播，因此在传播过程中偏振方向保持不变。对于具有相同频率的单色波来说，相位延迟的差值与传播长度L和波数差值Δk（体介质）或者传播常数Δβ的虚部（波导中）成正比： 

这表明经过整数倍的偏振拍长（或偏振拍距离）后，两波的相位关系是不变的，偏振拍长为： 

假如两束光最初相位为0（L=0），总的偏振态是线偏振的，那么经过四分之一偏振拍长后，相位差为π / 2，可以得到圆偏振光。经过一半拍长后，重新得到线偏振光，只是与初始方向之间夹角为90°。而经过一整个拍长后，得到的偏振方向与初始的方向相同。 
保偏光纤的偏振拍长仅为几厘米，甚至几个毫米。这比将光纤弯曲成径向对称的设计得到的双折射还要强。采用光子晶体光纤甚至能实现亚毫米的偏振拍长。强的双折射造成偏振拍长较短，从而光纤对模式耦合效应的灵敏度减小，这是由于制作过程做的瑕疵或者机械应力引起的。 
尽管对称设计的光纤中由于存在瑕疵以及受到机械应力而产生双折射，但是光纤并没有准确的偏振拍长，甚至没有一个准确的偏振轴。 

测量光纤中的偏振拍长
可以采用多种方法测量光纤中的偏振拍长。由于很难直接检测光纤中的光，以及改变光纤长度，因此测量时光纤的长度是固定的，为L。一种方法是注入线偏振的宽带光（例如，来自于超发光光源），然后记录光纤中透射光的光谱。光谱是振荡的，周期为Δλ，因此可以得到偏振拍长为： 

以上方程采用了有效折射率差与波长几乎无关的假设。 

还有一些更复杂的测量方法，例如，利用光纤非线性效应，如布里渊散射。有些可以空间上分辨光纤中的双折射。 

Definition: the period of interference effects in a birefringent medium

When two waves with different linear polarization states propagate in a birefringent medium, their phases will evolve differently. We assume that the polarization of each wave is along one of the principle directions of the medium, so that this polarization will be preserved during propagation. For monochromatic waves with identical optical frequencies, the difference in phase delay will be proportional to the propagation length L and to the difference in wavenumbers Δk (for a bulk medium) or in the imaginary parts of the propagation constants Δβ (for a waveguide):

This means that the phase relation between both waves is restored after integer multiples of the so-called polarization beat length (or polarization beat distance):

where λ is the vacuum wavelength (not the wavelength in the medium). More generally, the polarization evolution is periodic, with the polarization beat length being the period of evolution.

If the two waves were in phase originally (L = 0), the total resulting polarization state was linear. After a quarter of the polarization beat length, the phase difference is π / 2, and we have circularly polarized light. After half the beat length, we have linearly polarized light again, but with the direction rotated by 90°. After one full beat length, the original polarization direction is obtained.

Typical Beat Length Values

For PM fibers, a rather short polarization beat length is desirable.

Polarization-maintaining fibers can have polarization beat lengths of a few centimeters or even only a few millimeters. This is a much stronger birefringence than achievable by strongly bending a fiber with radially symmetric design. Even sub-millimeter beat lengths are possible with some photonic crystal fibers. Tentatively, a short beat length, as results from strong birefringence, reduces the sensitivity of the fiber to mode coupling effects, which may result from imperfections in manufacturing or from mechanical stress.

The characterization of nominally non-bire­frin­gent fibers is more difficult.

Fibers with a nominally symmetric design would theoretically have an infinitely large polarization beat length. In practice, they can have some birefringence due to imperfections and mechanical stress. Do to the randomness of such influences, they do not have a well-defined polarization beat length, and not even a well-defined polarization axis. One may nevertheless define a statistical value of the polarization beat length; one typically finds values of a few meters or some tens of meters. One may also specify a birefringence correlation length beyond which the birefringence changes substantially.

Measurement of Polarization Beat Length of Fibers

There are different methods for measuring the polarization beat length of an optical fiber. As it is difficult to access the light within the fiber or to vary the fiber length, the preferred methods work with a fixed length L of fiber. One method is to inject linearly polarized broadband light (for example, from a superluminescent source) and to record the optical spectrum after transmission through the fiber and another polarizer. That spectrum will exhibit oscillations with a period Δλ, from which the polarization beat length can be calculated:

This equation is based on the usually well justified assumption that the difference of effective indices depends only weakly on the wavelength.

There is a number of more sophisticated measurement techniques, often exploiting fiber nonlinearities such as Brillouin scattering. Some of them can spatially resolve the birefringence in the fiber.

Relation to Polarization Mode Dispersion

Polarization mode dispersion is the polarization dependence of the group delay of light. The differential group delay is essentially the derivative of the difference in propagation constant with respect to optical frequency. One can thus not directly calculate PMD from the polarization beat length, at least not if one has that only for one particular wavelength.

Bibliography