The Kerr effect or the quadratic electro-optic effect is a change in the refractive index of a material in response to the intensity of an external electric field. It is distinct from the Pockels effect in that the induced index change is directly proportional to the square of the electric field instead of to the magnitude of the field. All materials show a Kerr effect, but certain liquids display a stronger effect.
The Kerr electro-optic effect is the case in which the external electric field is a slowly-varying field applied by, for instance, a voltage on some electrodes. This is used in Kerr cells, which, in conjunction with polarizers, are used to modulate light for telecommunications applications.
The optical Kerr effect, or AC Kerr effect is the special case in which the external electric field is from light itself, such as that from a laser. The square of the electric field produces a slowly-varying refractive index which then acts on the light. This intensity-dependent refractive index is responsible for effects like self-focusing and self-phase modulation, and is the basis for Kerr-lens modelocking.
The Kerr effect was discovered in 1875 by John Kerr, a Scottish physicist.
Source in part: from Federal Standard 1037C