Propagation properties and radiation forces of the Hermite-Gaussian vortex beam in a medium with a parabolic refractive index.

In this paper, an analytical expression with a triple sum of the Hermite-Gaussian vortex beam (HGVB) propagating in a medium with a parabolic transverse spatial distribution of the refractive index is carried out. The intensity, phase, Poynting vector, and angular momentum of the HGVB are demonstrated analytically. The parabolic parameter, orders of the HGVB, and vortex topological charge affect the propagation properties, respectively. Also, the Poynting vector and angular momentum of the HGVB are shown so that we can further discover the properties. Furthermore, radiation forces are used to demonstrate the optical trapping ability of the HGVB, and several trapping positions are formed by the beam during propagation.