Geometric-Phase Waveplates for Free-Form Dark Hollow beams

We demonstrate the possibility to create optical beams with phase singularities engraved into exotic intensity landscapes imitating the shapes of a large variety of diverse plane curves. To achieve this aim, we have developed a method for directly encoding the geometric properties of some selected curve into a single azimuthal phase factor without passing through indirect encryption methods based on lengthy numerical procedures. The outcome is utilized to mould the optic axis distribution of a liquid-crystal-based inhomogeneous waveplate. The latter is finally used to sculpt the wavefront of an input optical gaussian beam via Pancharatnam-Berry phase.