Optical Computation of Divergence Operation for Vector Fields

Topological physics requires stable methods to measure polarization singularities in optical vector fields. Here, the use of a periodic plasmonic metasurface is proposed for computation of the divergence of vectorial paraxial beams. We design such an optical device to perform spatial differentiation in two directions, parallel and perpendicular to the incidence plane, simultaneously. The divergence operation is achieved by creating constructive interference between two derivative results. We demonstrate that such optical computations provide a direct pathway to identifying specific polarization singularities in vector fields.