  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. 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
shape. 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 device.
