Optical vectorial-mode parity Hall effect: a case study with cylindrical vector beams.

The vectorial optical field (VOF) assumes a pivotal role in light-matter interactions. Beyond its inherent polarization topology, the VOF also encompasses an intrinsic degree of freedom associated with parity (even or odd), corresponding to a pair of degenerate orthogonal modes. However, previous research has not delved into the simultaneous manipulation of both even and odd parities. In this study, we introduce and validate the previously unexplored parity Hall effect for vectorial modes using a metasurface design. Our focus lies on a cylindrical vector beam (CVB) as a representative case. Through the tailored metasurface, we effectively separate two degenerate CVBs with distinct parities in divergent directions, akin to the observed spin states split in the spin Hall effect. Additionally, we provide experimental evidence showcasing the capabilities of this effect in multi-order CVB demultiplexing and parity-demultiplexed CVB-encoded holography. This effect unveils promising opportunities for various applications, including optical communication and imaging.