Optical vortices from closed-loop subwavelength slits

We report on the singular shaping of light using closed-loop subwavelength slits whose shape is homeomorphic to the circle. Various sets of optical phase singularities can be generated depending on the given closed path whose geometry tailors the spin-orbit interaction for the light that passes through the curved slit. Here three families of closed-loop curves are considered--polygons, hypocycloids, and epicycloids