# Section 8: Nonlinearity and Electro-Optics

The electro-optic effect describes the modulation of the refractive index of a material by a low-frequency (compared with the frequency of light) electric field.

As we have learned before, there are both linear and nonlinear material responses to an applied electric field. The linear electro-optic effect, known as the Pockels effect, can only occur in noncentrosymmetric materials. The effect can be described in terms of nonlinear polarization as follows:

\begin{align} P_i{\omega} = 2\sum\chi^{(2)}_{ijk}(\omega=\omega+0)E_j(\omega)E_k(0) \end{align}