Polarization effects in four-wave mixing of isotropic samples

Abstract

The macroscopic four-wave mixing susceptibility is separated into a geometrical and a molecular factor using vector coupling algebra. The geometrical factor for isotropic samples is given explicitly for collinear circularly polarized beams and for an arbitrary geometry of linearly polarized beams. The result for four independent beams is compared with the previously derived geometrical factor for ordinary Raman scattering and 2-laser coherent anti-Stokes Raman scattering. A sum rule is derived for checking the accuracy of published expressions. Isotropic samples are fully characterized by the isotropic, antisymmetric and symmetric components of the scattering tensor. It is shown that controlling all four beams allows the measurement of each component individually. This is not possible when fewer than four beams are controlled.