Kerr electro-optic measurement technique for determination of nonuniform electric fields

Use of the ac modulation technique which has an ac high voltage superposed onto a dc high voltage has increased the sensitivity of Kerr electro-optic measurements. The technique has been used when the electric field magnitude and direction have been constant along the light path. Recently the technique was extended with use of the Abel transformation to recover the non-uniform axisymmetric electric field magnitude along the ground plane and along the needle axis of a point/plane electrode geometry. In these measurements the direction of light propagation is constant along the light path. The experimental results were in good agreement with analysis for the space charge free case. In this work we extend the technique to also allow the electric field direction to vary along the light path. We show that it is possible to measure three “characteristic parameters”, analogous to non-uniform photo-elastic stress analysis, that allow determination of the electric field magnitude and direction. These three parameters are related to the electric field through the matricant of the differential equations that govern the Kerr media and reduce to the electric field direction and light phase retardation proportional to the electric magnitude squared for the case where the electric field direction is constant