Nonlinear precession of elliptically polarized Gaussian beams

Equations describing the propagation of an elliptically polarized Gaussian beam, focused in a nonlinear medium of finite length, are derived. Allowance is made for the beam inhomogeneity, nonlinearity, diffraction, and polarization state. These equations are required for measurements of the nonlinear polarization of the medium. By using these, it is possible to explain the discrepancy between certain experimental results of measurements of the nonlinear polarizability. In particular, in the case of deep focusing of the radiation in the sample, the parameters of the polarization ellipse at the exit from the medium are identical to those at the entrance. Moreover, the combined effect of diffraction and nonlinearity amounts to nonlinear rotation of the ellipse as a whole through a certain angle which is half the conventionally used axial angle of calculated within the geometric-optics approximation. Examples are given of the use of these results to explain the scatter of the published measurements. Results are also given of original experiments to measure the nonlinear precession of elliptically polarized laser radiation and these confirm the validity of the calculations.