For the DC Kerr effect, we can neglect all except the linear terms and those in :

which is similar to the linear relationship between polarization and an electric field of a wave, with an additional non-linear susceptibility term proportional to the square of the amplitude of the external field.

For centrosymmetric media (e.g. liquids), this induced change of susceptibility produces a change in refractive index in the direction of the electric field compared with the refractive index in the direction perpendicular

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