Because of the variation in refractive indices, one ray will go through the crystal in a slower rate than the opposite ray. In other words, the velocity from the slower ray might be retarded with regard to the more quickly ray. This retardation worth (the relative retardation) might be quantitatively determined employing the next equation:

In Each and every body of Determine 8, the axis in the microscope polarizer is indicated with the money letter P and it is oriented within an East-West (horizontal) course. The axis of the microscope analyzer is indicated via the letter A and it is oriented within a North-South (vertical) path. These axes are perpendicular to one another and lead to a very darkish field when noticed from the eyepieces without specimen about the microscope phase.

For propagation along the optical axis, the electric discipline can only be perpendicular to that axis, to ensure that 1 obtains the common index for just about any polarization direction. In that problem, no birefringence is experienced.

In other instances, birefringence is often induced in at first isotropic optical components (e.g. crystals with cubic construction, glasses or polymers) could become anisotropic resulting from the appliance of some external impact which breaks the symmetry:

Due to the fact a person wave is retarded with respect to another, interference (both constructive or damaging) takes place concerning the waves as they pass through the analyzer. The web result's that some birefringent samples purchase a spectrum of shade when noticed in white light via crossed polarizers.

一些激光器晶体（例如，钒酸盐晶体和钨酸盐晶体）本身就具有双折射。这在需要无去极化损耗的线偏振输出时非常有用。 

For an arbitrary angle in between propagation route and optical axis, one particular can find two linear polarization directions exhibiting various refractive indices. The very first 1 is perpendicular towards the vector as well as the optical axis; listed here, we contain the ordinary index , and this kind of wave is known as a normal wave.

For amazing waves, in which the refractive index will depend on the angular orientation, There's a spatial stroll-off: the direction of electrical power propagation is a little tilted towards that on the vector.

For optical fibers and other waveguides, it is more correct to think about the primary difference of effective refractive indices. That is straight connected to the difference in imaginary values in the propagation constants.

Just one distinguishes optimistic and negative uniaxial crystals; in the previous case, the remarkable index is greater than the common index.

On the other hand, the slowest wavefronts come about once the wave travels together the quick axis of the ellipsoid. This axis is termed the sluggish axis. In between both of these extremes, wavefronts traveling in other directions practical experience a gradient of refractive index, which happens to be dependent on orientation, and propagate with velocities of intermediate values.

这一效应可应用于双折射调谐器中，因为它是与波长相关的（尽管折射率差与波长无关）。该效应通过自相位调制和交叉相位调制而与功率相关（参阅非线性偏振态旋转），有时用于光纤激光器中的被动锁模。 

Your situation is very distinct in Figure 8(b), in which the extended (optical) axis from the crystal has become positioned at an oblique angle (a) with respect for the polarizer transmission azimuth, a scenario introduced about by means of rotation with the microscope stage. In such a case, more info a portion of The sunshine incident on the crystal through the polarizer is handed on for the analyzer. To acquire a quantitative estimate of the amount of gentle passing in the analyzer, uncomplicated vector analysis can be placed on fix the issue. The initial step is to find out the contributions through the polarizer to o and e (see Determine eight(b); the letters seek advice from the everyday (o) ray and amazing (e) ray, which happen to be reviewed earlier mentioned). Projections on the vectors are dropped onto the axis with the polarizer, and believe an arbitrary value of one for both equally o and e, which might be proportional to the actual intensities from the normal and extraordinary ray.

尽管光纤本身不具有双折射，光纤光学中常常遇到双折射效应：有时双折射来自于光纤弯曲（引起弯曲损耗）和随机扰动。并且还存在保偏光纤。 

In impact, the refractive index by which the ordinary wave passes exceeds that in the incredible wave, and the material is termed negatively birefringent. A diagrammatic ellipsoid relating the orientation and relative magnitude of refractive index in a very crystal is termed the refractive index ellipsoid, and is illustrated in Figures 5 and six.