Fig. 1: Design principle of topological vectorial metasurfaces with EPs pair.

a Perspective view of the structural unit of topological vectorial metasurface. The incidence of horizontally linear polarized (LP-H) light is perpendicular to the metasurface along the -z direction. The inset figure on the upper right depicts the top view of the structure layer. The lengths of the three rods in the meta-structure are denoted by L₁, L₂ and L₃, respectively. b, c Simulated surface current distributions of (b) meta-structures \(S\) and c \({S}^{m}\) with x-direction linear polarized incidence. d Top view of mirror-symmetry structures with different \({L}_{1}\) and \({L}_{3}\), where \({L}_{1} < \)0 in \({S}^{m}\) and \({L}_{1} > \)0 in \(S\). e, f Complex amplitude of the simulated CP conversion coefficients in the parameter space covered by L₁\(\in\)[−100, 100 nm] and L₃\(\in\)[50, 250 nm], where the length and angle of the arrows represent the amplitude and phase of the complex amplitude. The solid white and black stars represent the EP pair observed for both structures \(S\) and \({S}^{m}\) respectively, while the hollow stars show the other CP conversion channel. g, h Schematic of the asymmetric wavefront modulation by the combination of EPs and PB phase with rotating mirror-symmetric structures. The LP-H input light can be decomposed into RCP + LCP beams. The structures \(S\) in (g) work for LCP input light and the structures \({S}^{m}\) in (h) work for RCP. The polarization states of the output beams are marked on the Poincaré sphere below, where the north and south poles represent RCP and LCP, respectively. i Full-polarization-reconstruction through the superposition of output RCP and LCP beams at the EP pair with arbitrary phase and amplitude is realized by inputting the same LP beams. With the arrangement of two types of meta-atoms (\(S\) and \({S}^{m}\)) on a single metasurface, arbitrary output polarization states can be realized.