Metasurface generation of directional circular swallowtail beams carrying power-exponent-phase vortices

The circular swallowtail beams have recently exhibited better autofocusing ability and more tunability compared with low-order Airy or Pearcey catastrophe beams. However our attention is paid to exploring their metasurface generation and dynamics propagation of directional circular swallowtail (DCS) beams carrying power-exponent-phase vortices based on all-dielectric metasurfaces using finite-difference time-domain (FDTD) method, where the directional phase related to launch angles in x- and y- directions is considered. The combined influence of directional and power-exponent phases on dynamics propagation and orbital angular momentum (OAM) of the proposed beams is explored. It is found that their autofocusing positions can be freely adjusted along pre-designed trajectories owing to different launch angles. And rotation behavior and Archimede spiral structure originated from power-exponent phase can be also found during propagation. More importantly, the directional phase associated with launch angles can be regarded as the superposition of spiral spectrum, which can further extend OAM modes to wider multimode states compared with the non-directional cases. The OAM reduction in multiple modes with directional cases is smaller than that in non-directional cases during propagation, which indicates that multimode OAM spectra of our proposed beams provide potential for reducing OAM power attenuation in free-space propagation because the power decay is jointly undertaken by multiple modes rather than a single mode. This work may provide inspiration for guiding or trapping microparticles in three-dimension space as requirement, and for OAM-based optical communication and imaging by the modulation of multi-degrees of freedom associated with directional and power-exponent phases.