Polarisation singularities in the electric field at a sum-frequency generated by two collinear elliptically polarised Gaussian beams in the bulk of a nonlinear gyrotropic medium

Polarisation singularities in the electric field at a sum-frequency generated in the bulk of an isotropic gyrotropic medium with a quadratic nonlinearity are predicted to appear in the case of the collinear interaction of two uniformly elliptically polarised Gaussian beams. The parameters of the fundamental waves are found, corresponding to the formation of lines with circular and linear polarisations (C- and L-lines) in the cross section of the beam at the sum-frequency as well as to the appearance of the regions in the signal beam where the polarisation state varies smoothly from the left-hand circularly polarised state to the right-hand circularly polarised. In this case, the ellipticity degree of the polarisation ellipse takes all possible values, while its orientation remains unchanged.