RP Photonics logo
RP Photonics
Encyclopedia
Technical consulting services on lasers, nonlinear optics, fiber optics etc.
Profit from the knowledge and experience of a top expert!
Powerful simulation and design software.
Make computer models in order to get a comprehensive understanding of your devices!
Success comes from understanding – be it in science or in industrial development.
The famous Encyclopedia of Laser Physics and Technology – available online for free!
The ideal place for finding suppliers for many photonics products.
Advertisers: Make sure to have your products displayed here!
… combined with a great Buyer's Guide!
VLib part of the
Virtual
Library

Pockels Effect

<<<  |  >>>

Definition: the phenomenon that the refractive index of a medium exhibits a modification which is proportional to the strength of an applied electric field (linear electro-optic effect)

German: Pockels-Effekt

Category: physical foundations

How to cite the article; suggest additional literature

The Pockels effect (first described in 1906 by the German physicist Friedrich Pockels) is the linear electro-optic effect, where the refractive index of a medium is modified in proportion to the applied electric field strength. This effect can occur only in non-centrosymmetric materials. The most important materials of this type are crystal materials such as lithium niobate (LiNbO3), lithium tantalate (LiTaO3), potassium di-deuterium phosphate (KD*P), β-barium borate (BBO), potassium titanium oxide phosphate (KTP), and compound semiconductors such as gallium arsenide (GaAs) and indium phosphide (InP). A relatively new development is that of poled polymers, containing specifically designed organic molecules. Some of these polymers exhibit a huge nonlinearity, with nonlinear coefficients which are an order of magnitude larger than those of highly nonlinear crystals.

Mathematically, the Pockels effect is best described via the induced deformation of the index ellipsoid, which is defined by

index ellipsoid

in a Cartesian coordinate system. An electric field can now change the coefficients according to

index change for Pockels effect

with the electro-optic tensor rij. (The equation describes the change of n−2, rather than directly the change of the refractive index.) Note that the first index (i) runs from 1 to 6 in this contracted notation, where e.g. i = 4 corresponds to the y-z component.

Usually, only some of the coefficients rij are nonzero, depending on the crystal symmetry and the orientation of the coordinate system with respect to the crystal axes. For example, for lithium niobate (LiNbO3) or lithium tantalate (LiTaO3), which belong to the symmetry group 3m, the non-zero coefficients for the commonly used coordinate system are r12 = −r22 = r61, r13 = r23, r33, r42 = r51. For application of these materials e.g. in Pockels cells for electro-optic modulators, the largest tensor element (r33) is often used. Its magnitude is of the order of 30 pm/V for LiNbO3, with some wavelength dependence. Most other nonlinear crystal materials (e.g. BBO) have significantly lower electro-optic coefficients of a few pm/V, whereas some electrically poled polymers exhibit substantially higher values than LiNbO3.

As the index changes are usually small, the approximation

index change from Pockels effect

is often used.

See also: Pockels cells, electro-optic modulators, electro-optic effect, nonlinear crystal materials
and other articles in the category physical foundations

If you like this article, share it with your friends and colleagues, e.g. via social media:

arrow