  Vortex beams with orbital angular momentum has been attracting tremendous
attention due to their considerable applications ranging from optical tweezers
to quantum information processing. Metalens, an ultra-compact and
multifunctional device, provide a desired platform for designing vortex beams.
A spin-dependent metalens can boost the freedom to further satisfy practical
applications. By combining geometric phase and propagation phase, we propose
and demonstrate an approach to design a spin-dependent metalens generating
dual-focused vortex beams along longitudinal or transverse direction, i.e.,
metalenses with predesigned spin-dependent phase profiles. Under the
illumination of an elliptical polarization incident beam, two spin-dependent
focused vortex beams can be observed, and the relative focal intensity of them
can be easily adjusted by modulating the ellipticity of the incident beam.
Moreover, we also demonstrated that the separate distance between these
dual-focused beams and their topological charges could be simultaneously
tailored at will, which may have a profound impact on optical trapping and
manipulation in photonics.
