
Home  About  Table of Contents  Advanced Search  Copyright  Feedback  Privacy 


Unless otherwise stated this page contains Version 1.0 content (Read more about versions) 2.5.11 Electrooptic materialsThe electrooptic effect In general, an electric field E applied to a transparent material modifies the refractive index n_{0} for a particular mode of propagation in accordance with the equation
In amorphous materials or centrosymmetric crystals the coefficients of odd powers of E are zero, and the first nonzero term RE^{2} represents the quadratic Kerr effect, usually characterized for a particular material by the Kerr constant:
where λ_{0} is the freespace wavelength. For the case of a birefringent crystal, the field E modifies the
index ellipsoid
where n_{ij} = n_{i}, for i = j, and 1/n_{ij} = 0 for i ≠ j. From a knowledge of the change in orientation and dimensions of the index ellipsoid, as given by this equation, the fieldinduced birefringence for a ray of given direction and polarization may be calculated. In practice the electrooptic effect is either predominantly linear or quadratic in E, and is therefore characterized by either r_{ijk} or R_{ijkl}, depending on the material. Since r_{ijk} is symmetrical in i, j, and R_{ijkl}, symmetrical in i, j and in k, l, pairs of values i, j and k, l are denoted by indices m and n respectively, which run from 1 to 6 according to the scheme: 1 ↔ 1, 1 2 ↔ 2, 2 3 ↔ 3, 3 4 ↔ 2, 3 5 ↔ 1, 3 6 ↔ 1, 2 When measured at low frequencies (< 10^{4} Hz), the coefficients may include contributions from the elastooptic effects of piezoelectric and/or electrostrictive strains. The linear electrooptic effect observed at frequencies sufficiently high for these contributions to be negligible is called the Pockels effect. The strain effects may contribute up to 50% of the lowfrequency effect. The quadratic effect is exhibited most markedly by materials in which the permittivity is high and varies rapidly with temperature. Here, since the R_{mn} vary accordingly, it is more convenient to replace R_{mn} E_{k}E_{l} in the equation of the index ellipsoid by g_{mn}P_{k}P_{l} (where P = D − ε_{0} E), and to express the properties of the material in terms of g_{mn}. Typical parameters for selected electrooptic materials at low frequencies are given in the table at the bottom of this page. Coordinate convention: the indicatrix and electrooptic coefficients are referred to the usual crystallographic coordinate system as follows. Ox_{3} ≡ Oz and is the fourfold axis for cubic and tetragonal symmetries, or the threefold axis for trigonal symmetry; Ox_{1} ≡ Ox; Ox_{2} ≡ Oy, except for the trigonal case in which Ox_{1} is perpendicular to the mirror plane. For uniaxial crystals n_{1} = n_{1} = n_{0}, n_{3} = n_{e}. It should be noted that the halfwave voltage V_{π} is used conventionally to characterize the sensitivity of an electrooptic material. It is the voltage required to obtain one halfwavelength of optical path difference between the two vibration components of a wavefront, using a cube of the material of side 1 cm with specified directions of light and applied field. The table overleaf gives the induced birefringence for a number of commonly used configurations:
References W. R. Cook and H. Jaffe (1979) Piezooptic and electrooptic
constants, Landolt–Börnstein New Series, K.H. Heilwege (ed.),
Group III Vol 11, 1979, SpringerVerlag. O.C.Jones Properties of selected electrooptic materials at a wavelength of 633 nm
[1] = 546 nm [2] = 550 nm. C.Forno 
Home  About  Table of Contents  Advanced Search  Copyright  Feedback  Privacy  ^ Top of Page ^ 

This site is hosted by the National Physical Laboratory 
