Topological semiconductor laser solitons with polarization singularities

We predict a wide class of two-dimensional vector dissipative solitons in wide-aperture semiconductor vertical-cavity surface-emitting lasers with a saturable absorber. For them, polarization structure varies over the laser cross section and includes singularities: V points with zero total intensity, C points with purely circular polarization, and L lines with purely linear polarization. We show that the transverse motion of these solitons obeys the Eulerian mechanics dictated by soliton symmetry, taking into account the vector nature of laser solitons; presented are scenarios of soliton transverse rotation and "lunar motion."