  We show that a very simple structure consisting of a single subwavelength
dielectric ridge on the surface of a slab waveguide enables spatial
differentiation and integration of the profile of optical beams propagating in
the waveguide. The differentiation and integration operations are performed in
transmission and in reflection, respectively, at oblique incidence of the beam
impinging on the ridge. The implementation of these operations is associated
with the resonant excitation of a cross-polarized eigenmode of the ridge. At
the considered parameters of the structure and incidence geometry, neither
"parasitic" out-of-plane scattering nor polarization conversion occurs. The
presented rigorous numerical simulation results confirm high-quality
differentiation and integration. We demonstrate that by choosing the quality
factor of the resonance, one can achieve the required tradeoff between the
differentiation (or integration) quality and the amplitude of the resulting
beam. The proposed integrated structure may find application in ultrafast
all-optical analog computing and signal processing systems.
