Far Field Structural Properties of a Gaussian Vortex Beam

Based on the methods of vector angular spectrum and stationary phase, the analytical expressions of the electromagnetic field for the Gaussian vortex beam and its transverse electric (TE) and transverse magnetic (TM) terms are derived in the far field. The analytical formulae of the energy flux distributions of the Gaussian vortex beam and its TE and TM terms are also presented in the far field. The analytical expressions for the ratios of the powers of the TE and TM terms to the power of the Gaussian vortex beam are further given. Based on the second-order moment of the energy flux distribution, the analytical formulae of the far field divergence angles of the Gaussian vortex beam and its TE and TM terms are also derived without any approximation. The influences of the f-parameter and the topological charge on the energy flux distributions, the ratios of the powers of the TE and TM terms to the power of the Gaussian vortex beam, and the far field divergence angles are numerically analysed. This research further reveals the structural properties of a Gaussian vortex beam in the far field and is beneficial to the practical applications of a Gaussian vortex beam.