ИСТИНА

C-points (points of circular polarization) are phase singularities of the circularly polarized (CP) components of the electromagnetic radiation. Their trajectories in propagating paraxial light beams are known as C-lines. The features accompanying the formation of polarization singularities in nonlinear optical processes and their subsequent evolution are almost unknown up to day. In our work we have numerically modeled and studied the interaction of C-points in collinearly propagating beams in isotropic gyrotropic medium with spatial dispersion (nonlocality) of cubic optical response. We assume the beams each having the following structure: the right-hand circularly polarized (RHCP) component has Gaussian profile, while the left-hand circularly (LHCP) polarized one has Laguerre-Gaussian profile. So, each of two beams has RHCP C-point in its center. In the course of propagation (both linear and nonlinear) the C-points undergo creation and annihilation processes. In the linear medium two Gaussian beams (RHCP) merge in the center forming an intensity maximum there (“central maximum”), while the Laguerre-Gaussian beams (LHCP) lose their cylindrical symmetry, and form intensity maxima (“spots”) at their “rings” ( “lateral maxima”). In a nonlinear medium the features of the interaction of the polarization singularities are similar to those in linear medium. They are determined by the initial distance between the C-points, phase shift between the beams and the nonlinear susceptibilities of the medium. If the CP components undergo mutual focusing, then the events of pairwise creation and annihilation of C-points take place at smaller distances traversed in a medium with the growth of the intensity and/or nonlinear susceptibilities, compared to the case of linear interaction. The lateral maxima will be attracted by the two Gaussian intensity maxima, and there will appear not three, but only two intense peaks in the transversal section of the propagating light. Otherwise, (in case of mutual defocusing, which depends on the medium parameters) all the characteristic events happen faster (at closer distances) with the increase of the intensity than in linear medium, and the intensity maxima with opposite handedness of the polarization rotation defocus each other and tend to occupy different (not overlapping) areas in the transversal plane of the propagating field. The presence of the spatial dispersion causes faster pairwise creation of the C-points with corresponding handedness; positive values of spatial dispersion parameter favor the formation of RHCP C-points, and vice versa).