  We theoretically describe and numerically investigate the operation of
"vectorial" optical differentiation of a three-dimensional light beam, which
consists in simultaneous computation of two partial derivatives of the incident
beam profile with respect to two spatial coordinates in different transverse
electric field components. It is implemented upon reflection of the beam from a
layered structure by simultaneously utilizing the effect of optical resonance
and the spin Hall effect of light. As an example of a layered structure
performing this operation, we propose a three-layer metal-dielectric-metal
(MDM) structure. We show that by choosing the parameters of the MDM structure,
it is possible to achieve the so-called isotropic vectorial differentiation,
for which the intensity of the reflected optical beam (squared electric field
magnitude) is proportional to the squared absolute value of the gradient of the
incident linearly polarized beam. The presented numerical simulation results
demonstrate high-quality vectorial differentiation and confirm the developed
theoretical description.
