Propagation properties of anomalous hollow beam in uniaxial crystals orthogonal to the optical axis

The analytical formulae for anomalous hollow beam propagating in uniaxial crystals orthogonal to the optical axis are derived. The numerical results show that the anomalous hollow beam spreads at different rates in the directions along and orthogonal to the optical axis. The beam spreads more rapidly in the direction along the optical axis than orthogonal to the optical axis in positive crystal (ne/no>1), and the beam spreads more rapidly in the direction orthogonal to the optical axis than along the optical axis in negative crystal (ne/no<1).