Optimal triplicator design applied to a geometric phase vortex grating.

In this work, a geometric phase liquid-crystal diffraction grating based on the optimal triplicator design is realized, i.e., a phase-only profile that generates three diffraction orders with equal intensity and maximum diffraction efficiency. We analyze the polarization properties of this special diffraction grating and then use embedded spiral phases to design geometric phase vortex diffraction gratings. Finally, the fabrication of a two-dimensional version of such a design using a micro-patterned half-wave retarder is demonstrated, where the phase distribution is encoded as the orientation of the fast axis of the retarder. This proof-of-concept element is made of liquid crystal on BK7 substrate where the orientation of the LC is controlled via photoalignment, using a commercially available fabrication facility. Experimental results demonstrate the parallel generation of vortex beams with different topological charge and different states of polarization.