Generation and transformation of light beams and pulses, containing polarization singularities, in media with nonlocality of nonlinear optical response (scientific summary)

We discuss analytically found expressions, which relate the values of two parameters characterizing the topological type of linear and circular polarization singularities in nonparaxial light fields to the values of the complex amplitude components of the electric field and their first spatial derivatives. The necessary conditions are described for the formation of light pulse at the doubled frequency in the bulk of an isotropic gyrotropic medium with a frequency dispersion of quadratic nonlinearity and they impose constraints on the spatial transverse structure of the non-uniformly polarized incident radiation pulse and its time structure. The electric field of a light beam reflected from the surface of an isotropic gyrotropic medium with spatial dispersion of quadratic nonlinearity is investigated in the case of an arbitrary structure and geometry of incidence of non-uniformly polarized fundamental light beams. The ranges of the parameters of an elliptically polarized Gaussian beam and a medium with local and nonlocal cubic nonlinearity are determined, at which the lines of circular polarization singularity appear in cross sections of self-focused beam.