Comparative study of theoretical Kerr electro-optic fringe patterns in 2-D and axisymmetric electrode geometries

Kerr electro-optic fringe patterns have long been used to study space charge injection and transport phenomena in highly birefringent materials such as nitrobenzene, Most past experimental work has been limited to 1 or 2-dimensional geometries where the electric field magnitude and direction have been constant along the light path such as two concentric or parallel cylinders or parallel plate electrodes. For these geometries the extrema in the fringe patterns can be used directly to find the electric field magnitude and direction. In this work we extend the fringe based Kerr electro-optic measurement technique to a point/plane electrode geometry which often is used in HV research to create large electric fields for charge injection at known location and at reasonable voltages. We calculate theoretical Kerr electro-optic fringe patterns for this point/plane electrode geometry with and without space charge distributions, for which the electric field magnitude and direction vary along the light path. We particularly compare the calculated space charge free optical patterns for the point/plane electrodes to the optical patterns of the 2-dimensional analog blade/plane geometry. We underline the differences and study how these fringe patterns can be used to reconstruct the axisymmetric electric field components in practice.