Angular Momentum Density of a Gaussian Vortex Beam in the Source Region: Investigation from the Vectorial Structure for Lasers
G-Q. Zhou and G-Y. Ru
Though the beam spot of a Gaussian vortex beam in the source plane is solid, the beam spot develops into dark hollow upon propagation. Therefore, the behaviour of the Gaussian vortex beam in the source region receives considerable interest, not least for lasers. In the source region, the Gaussian vortex beam is expressed as a sum of the transverse electric (TE) and the transverse magnetic (TM) terms, and the analytical expressions for the TE and the TM terms have been derived without any approximation. The corresponding magnetic field is obtained by taking the curl of the electric field. By using the accurate expressions for the electromagnetic fields of the Gaussian vortex beam and its TE and TM terms, the angular momentum densities of the Gaussian vortex beam and its TE and TM terms can be calculated. The angular momentum density distributions of the TE term, the TM term, and the Gaussian vortex beam are numerically demonstrated in the source region. The effects of the propagating part and the evanescent part on the angular momentum densities of the TE term, the TM term, and the Gaussian vortex beam are examined in the source region. This research is useful to optical trapping, optical guiding, and optical manipulation using Gaussian vortex beams.
Keywords: Laser beam, Gaussian vortex beam, angular momentum density, source region, vectorial structure