Optical computation of the divergence of a vector field using a metal-dielectric multilayer

We theoretically describe the optical computation of the divergence of a two-dimensional vector field, which is composed of the transverse electric field components of an incident light beam. The divergence is computed in reflection at oblique incidence of light on a layered structure. We show that in the particular case of a linearly polarized incident beam, the layered structure implementing the divergence operator also allows one to compute the gradient and perform the isotropic differentiation. As an example of a layered structure computing the divergence, we propose a metal-dielectric multilayer consisting of two pairs of metal and dielectric layers on a metal substrate. The presented numerical simulation results of the designed multilayer confirm that the divergence operator is computed with high accuracy. We also demonstrate the possibility of using the designed structure for optical directional differentiation and computation of the gradient and Laplace operators.