Kerr electro-optic theory and measurements of electric fields withmagnitude and direction varying along the light path

Differential equations that govern light propagation in Kerr media are derived when the applied electric field direction and magnitude vary along the light path. Case studies predict Kerr electro-optic fringe patterns for the specific case of point/plane electrodes. We apply the characteristic directions theory of photoelasticity to understand these fringes. We also study birefringent media with small Kerr constant, in particular transformer oil. For this case we show that simplifications in the characteristic parameter theory is possible, resulting in simple integral relationships between the characteristic parameters and the applied electric field. We use these simple relationships to extend the ac modulation method to measure the characteristic parameters for small Kerr constant media. Measurements of the characteristic parameters using the ac modulation method are presented for point/plane electrodes in transformer oil. The measurements agree reasonably well with space charge free theory for infinite extent electrodes for which analytical expressions are available. We finally employ the `onion peeling' method to reconstruct the axisymmetric electric field magnitude and direction from the measured characteristic parameters and compare the results to the analytically obtained electric field