TRANSFORM RELATIONSHIP BETWEEN KERR-EFFECT OPTICAL-PHASE SHIFT AND NONUNIFORM ELECTRIC-FIELD DISTRIBUTIONS

Electric field distributions measured using the Kerr effect cause a ph ase shift between light components polarized parallel and perpendicula r to the electric field, proportional to the magnitude squared of the electric field components in the plane perpendicular to light propagat ion integrated over the light path length. One wishes to recover the e lectric field distribution from measurements of light phase shifts. Fo r axisymmetric geometries where the electric field depends only on the radial co-ordinate and whose direction is constant along the light pa th, as is the case along a planar electrode, the total phase shift for light propagating at a constant distance from the center of symmetry and the electric field distribution are related by an Abel transform p air, a special case of Radon transforms typically used in image recons tructions with medical tomography and holography. The more general Rad on transform relates the optical phase shift to non-axisymmetric elect ric field distributions but is restricted to cases where the applied e lectric field is perpendicular to the plane of light propagation. If t he applied electric field direction changes along the light path, it b ecomes necessary to account for the change in direction of the light c omponents parallel and perpendicular to the applied electric field and the light polarization equations are generalized.