The propagation-dependent polarization vector fields are experimentally created from an isotropic microchip laser with a longitudinal-transverse coupling and entanglement of the polarization states. The experimental three-dimensional coherent vector fields are analytically reconstructed with a coherent superposition of orthogonal circularly polarized vortex modes. Each polarized component is found to comprise two Laguerre-Gaussian modes with different topological charges. With the analytical representation, the polarization singularities, on which the electric polarization ellipse is purely circular ($C$ lines) or purely linear ($L$ surfaces), are explored. The $C$ line singularities are found to form an intriguing hyperboloidal structure.

• Received 3 July 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.233903