Generating a 64 × 64 beam lattice by geometric phase modulation from arbitrary incident polarizations

A laser beam lattice from tailoring spatial dimensions of lights is a kind of structured optical field, which already have found many applications in lots of domains. Here we propose a geometric phase element made from polymerized liquid crystals to transform Gaussian beams into a 64 × 64 beam lattice with high performance. Different from other geometric phase elements, the proposed element can introduce identical phase modulations for any polarizations, indicating that the beam lattice could be well generated with arbitrary incident homogeneous polarizations but not limited to specific circular polarizations. In the experiment, a 64 × 64 beam lattice is well generated. It is estimated that the uniformity of the obtained lattice fluctuates about 60% among various incident polarizations, which is very close to the prediction. This work opens a new site for producing high-dimensional beam lattices and will inspire more advanced applications.