Formation of the lines of circular polarization in a second harmonic beam generated from the surface of an isotropic medium with nonlocal nonlinear response in the case of normal incidence

For the first time we have obtained the analytical expressions describing the spatial distribution of the polarization of a second harmonic beam's light field reflected from the surface of an isotropic gyrotropic medium in the case when a normally incident fundamental beam contains a polarization singularity of an arbitrary type. The contribution of bulk and surface responses of the nonlinear medium in the formation of the lines of circular polarization in the second harmonic beam were analyzed. The relation between topological characteristics and polarization states of the singularities in the incident and reflected beams was established.