Kerr Effect for Three-Dimensional Electric Fields

An optical method using the Kerr effect is useful to measure electric fields in dielectric liquids without disturbing the field. A conventional relation of the Kerr effect cannot be applied to the measurement of a three-dimensional field, the direction of which is not always perpendicular to an incident light. We have derived the relation of the Kerr effect which can be applied to three-dimensional measurement and confirmed it experimentally.