ИСТИНА

The space where a heterogeneously polarized monochromatic light beam propagates can possess certain lines, along which the polarization of the beam's electric field is pure circular (C-lines). Their intersections with the beam transversal section are the points of circular polarization singularity, or C-points. Polarization singularity is characterized by its topological charge, which is equal to total winding number of polarization ellipse during one full counter-clockwise loop around the point of singularity. We considered sum-frequency generation in the bulk of an isotropic gyrotropic medium by two-colored singular beam, which consists of two collinear beams. The polarization pattern of the signal beam resembles that of the nonlinear polarization of the medium if there is no wave vector mismatch, i.e. no frequency dispersion of the medium. However, in the presence of the dispersion the C-lines in the signal beam experiences drastic transformation. If the nonlinear polarization beam carries non-zero topological charge of its singularities then C-lines gain helical structure; the greater is absolute value of the wave vector mismatch the shorter is the mean step of each spiral. In the other configuration of the fundamental modes, when total topological charge of nonlinear polarization vector polarization singularities is zero, the loop of C-lines undergoes deformation and then splits into new loops.