Influence of transverse effects on self-induced polarization changes in an isotropic Kerr medium

Allowing for an isotropic optical nonlinearity of third order, we derive approximate Gaussian solutions of the paraxial wave equation. They describe a monochromatic elliptically polarized light signal of finite extension both in space and in time. In contrast to plane-wave results, the state of polarization is found to be strongly nonuniform in the transverse direction. Both the orientation and the shape of the polarization ellipse are not conserved. For low intensities, parameters measuring the induced optical activity depend on the intensity quadratically instead of linearly. For high intensities, saturation sets in. It is argued that by means of nonlinear ellipsometry one can evaluate two tensor components, namely, Re χxyyx(3) and Re χxxxx(3). Upon taking into account transverse as well as temporal effects, the magnitude of these components may decrease by a factor of 10.