Generation of polarization singularities in the self-focusing of an elliptically polarized laser beam in an isotropic Kerr medium

•The possibility of polarization singularities emergence during self-focusing in Kerr medium is shown.•In the case of initially axially symmetrical beam formed CC-lines have the shape of circumferences.•In the case of the beams with initially elliptical cross-section formed CC-lines are three-dimensional closed curves.•Total topological charge of CC-points, nucleated during self-focusing, is zero in each cross-section of the beam.

We have numerically and analytically shown that polarization singularities can emerge when a homogeneously elliptically polarized light beam undergoes self-focusing in an isotropic third-order Kerr medium without frequency and spatial dispersion (fused silica, liquids, gases etc.) In the case of axially symmetric beam the emerging CC-lines have the shape of circumference with the center at the beam’s axis and they are located in the separate transversal planes in the medium. If the axial symmetry of the incident beam is broken then the even number of CC-points with opposite topological charges are nucleated in the medium. They exist in a certain propagation coordinate range and then they collide and annihilate each other.