Hexagonal vector field of polarization singularities with a gradient basis structure

The coherent superposition of vector fields can yield interesting field distributions. For example, the superposition of two right-handed polarization singularities can result in left-handed polarization singularities. Unlike the coherent superposition of scalar fields which modulate resultant intensity, the vector field superposition can modulate additional parameters such as ellipticity and azimuth in the field distribution. By making use of computational optics and programmable spatial light modulators, we demonstrate here the generation of a polarization singularity lattice structure with gradient basis, which is normally not possible by a conventional optical interference method.