Formation of an inhomogeneously polarised light beam at the sum frequency by two collinear elliptically polarised Gaussian beams focused into a chiral medium

The distribution of polarisation of a light field in the cross section of a beam at the sum frequency is investigated upon the collinear interaction of two elliptically polarised Gaussian beams in a nonlinear isotropic gyrotropic medium. It is shown that the ellipticity, the angle of rotation of the principal axis of the polarisation ellipse, and the rotation direction of the electric field vector of radiation at the sum frequency in the beam cross section strongly depend on the angle in the polar coordinate system. The ranges of parameters of elliptically polarised fundamental Gaussian beams are found where the cross section of the sum-frequency beam is divided into sectors with different rotation directions of the electric field vector. The equations of the straight lines determining the boundaries of these sectors contain parameters specifying the shape and orientation of polarisation ellipses of the fundamental waves and the ratio of their wave vectors. In the case of opposite circular polarisations of these waves, the ellipticity of the sum-frequency beam does not change in the beam cross section and the principal axes of polarisation ellipses of the light field are oriented perpendicular to the radius in polar coordinates.