Optical computation of the Laplace operator at oblique incidence using a multilayer metal-dielectric structure

We investigate the possibility of the optical computation of the Laplace operator in the oblique incidence geometry using a layered structure consisting of a set of homogeneous thin films. For this, we develop a general description of the diffraction of a three-dimensional linearly polarized optical beam by a layered structure at oblique incidence. Using this description, we derive the transfer function of a multilayer structure consisting of two three-layer metal-dielectric-metal structures and possessing a second-order reflection zero with respect to the tangential component of the wave vector of the incident wave. We show that under a certain condition, this transfer function can coincide up to a constant multiplier with the transfer function of a linear system performing the computation of the Laplace operator. Using rigorous numerical simulations based on the enhanced transmittance matrix approach, we demonstrate that the considered metal-dielectric structure can optically compute the Laplacian of the incident Gaussian beam with the normalized root-mean-square error of the order of 1%. We also show that this structure can be effectively utilized for optical edge detection of the incident signal.