Vectorial Spatial Differentiation of the Profile of an Optical Beam Using an All-Dielectric Layered Structure

We investigate the possibility of optical implementation of the vectorial differentiation operation using an all-dielectric layered structure composed of three layers with an M-shaped refractive index profile. Our study demonstrates the feasibility of performing the vectorial differentiation in an isotropic way. In this case, the intensity of the reflected beam is proportional to the square of the magnitude of the gradient of the nonzero transverse electric field component of the incident linearly polarized optical beam. The presented theoretical results are fully supported by the results of rigorous numerical simulations. The obtained results are applicable for engineering photonic components aimed at optical computing and real-time image analysis.