Second-harmonic generation of polarization singularities

Second-harmonic generation was studied theoretically for the vector singularities (daisy modes) of linearly polarized light and for the elliptic singularities (C points) of elliptically polarized light. Topological charge doubling for C points and daisy modes, similar to that found for vortices, was found. Unlike for vortices, however, it was found that for both C points and daisy modes the sign of the charge is reversed; for C points the photon spin or handedness (right or left) is also reversed; and for daisy modes the number of intensity petals is not doubled. These findings are all unexpected because neither charge nor spin nor orbital angular momentum is conserved for C points, whereas a daisy mode in which the number of intensity petals does not equal twice the magnitude of the charge is anomalous.