Propagation of elliptical Gaussian vortex beam based on angular spectrum representation

Vortex beams with hollow elliptical ring structure have attracted broad interest in applications such as micro- particle trapping and manipulation. The paper investigates the dependence of the hollow elliptic ring structure of vortex beams on the beam order and the topological charge, while propagating in the near- and far-field zones. The electric field of the beam is formulated by using the angular spectrum method, which satisfies rigorously Maxwell's equation. The electric field, linear momentum and orbital angular momentum are calculated. Numerical results show that the hollow elliptical ring structure approximately remains unchanged over a finite propagation distance, accompanied by a rotation whose angle depends on the topological charge. In the far-field zone, the ring structure is broken, leading to two bright spots and several dark islands. It is found that the beam profile in the near-field zone is mainly related to the beam order but in the far-field zone is primarily affected by the topological charge. The results presented in the paper may be useful in predicting and explaining the interaction between the elliptic hollow Gaussian vortex beam and the micro-particles, such as the movement of micro-particles along the orbit and the rolling rotation.