Pancharatnam-Berry phase optical elements for generation and control of complex light: Generalized superelliptical q-plates

We present newly conceived liquid-crystal-based retardation waveplates in which the optic axis distribution has a superelliptically symmetric azimuthal structure with a topological charge q superimposed. Such devices, named superelliptical q-plates, act as polarization-To-spatial modes converters that can be used to produce optical beams having peculiar spiral spectra. These spectra reflect the topological charge of the optic axis distribution as well as the symmetry properties of the underlying superellipse. The peculiar capability of q-plates of producing optical modes entangled with respect to spin and orbital angular momentum is here extended to superelliptical q-plates in order to create more complex optical modes structurally inseparable with respect to polarization and spatial degrees of freedom. Such superelliptical modes can play a crucial role in studying polarization singularities or to develop polarization metrology.