Revealing the spin optics in conic-shaped metasurfaces

Ellipse and hyperbola are two well-known curves in mathematics with numerous applications in various fields, but their properties and inherent differences in spin optics are less understood. Here, we investigate the peculiar optical spin properties of the two curves and establish a connection between their foci and the spin states of incident light by introducing a geometric-phase distribution along the conic curve. We show that the optical spin Hall effect is the intrinsic optical spin property of ellipse, where photons with different spin states can be exactly separated to each of its two foci, while a hyperbola exhibits optical spin-selective effect, where only photons with one particular spin state can be accumulated at its foci. These properties are then experimentally demonstrated in near field by arranging nanoslits in conic shapes. Based on the spin properties of the curves, we design spin-based plasmonic devices with various functionalities. Our results reveal the intrinsic optical spin properties behind conic curves and provide a route for designing spin-based plasmonic devices.