The trefoil and cinquefoil vector field are of essential significance for fundamental topology properties as the Hopf link and trefoil knots in the light field. The spatially multiplexing metasurfaces were designed with two sets of periodical nanoslits arranged alternately, each had independent geometric spiral phases and metalens phases to produce and focus vortex of the corresponding circular polarized (CP) light. By arranging the orientations of the two slit sets, the two CP vortices of the desired topological charges were obtained, the superposition of the vortices were realized to generate the vector field. With the topological charges of the vortices set to one and two, and three and two, respectively, the focused trefoil and cinquefoil vector light fields were acquired. The work would be important in broadening the applications of metasurface in areas as vector beam generations and topology of light field.

Manipulation of multichannel vector beams (VBs) with metasurfaces is an important topic and holds potential applications in information technology. In this paper, we propose a novel metasurface for the generation of dual VBs, which is composed of orthogonal slit pairs arranged on multiple groups of combined semicircular rings (CSRs). A group of CSRs include a right-shifted set and a left-shifted set of semicircular rings, and each set of semicircular rings has two halves of circles with different radii, sharing the same shifted center. Under the illumination of linearly polarized light, the two shifted sets of semicircular rings generate the two VBs at the shifted center positions on the observation plane. The slit units of each set are designed with independent rotation order and initial orientation angle. By adjusting the linear polarization of illumination, both two VBs with their orders and polarization states are independently controlled simultaneously. The principle and design are demonstrated by the finite-difference time domain (FDTD) simulation. The work is of significance for miniatured devices of VB generators and for related applications.

We investigated the optical spin Hall effect (OSHE) of the light field from a closed elliptical metallic curvilinear nanoslit instead of the usual truncated curvilinear nanoslit. By making use of the characteristic bright spots in the light field formed by the noncircular symmetry of the elliptical slit and by introducing a method to separate the incident spin component (ISC) and converted spin component (CSC) of the output field, the OSHE manifested in the spot shifts in the CSC was more clearly observable and easily measurable. The slope of the elliptical slit, which was inverse along the principal axes, provided a geometric phase gradient to yield the opposite shifts of the characteristic spots in centrosymmetry, with a double shift achieved between the spots. Regarding the mechanism of this phenomenon, the flip of the spin angular momentum (SAM) of CSC gave rise to an extrinsic orbital angular momentum corresponding to the shifts of the wavelet profiles of slit elements in the same rotational direction to satisfy the conservation law. The analytical calculation and simulation of finite-difference time domain were performed for both the slit element and the whole slit ellipse, and the evolutions of the spot shifts as well as the underlying OSHE with the parameters of the ellipse were achieved. Experimental demonstrations were conducted and had consistent results. This study could be of great significance for subjects related to the applications of the OSHE.