All optical two-dimensional spatial integration using a slab waveguide

Recently, in [Opt. Lett.42, 1954 (2017)10.1364/OL.42.001954], two approaches were introduced for performing one-dimensional (1D) optical integration, operating exclusively on either p- or s-polarized light beams using a slab waveguide. However, the proposed integrator suffers from an impractical structure, as it requires a slab waveguide sandwiched between two semi-infinite silicon (Si) layers. In this paper, we present two practical hexahedral structures for the aforementioned slab waveguide integrator. By exploiting the Brewster effect, we eliminate the need for semi-infinite Si layers and replace them with finite slanted-interface Si layers. We demonstrate that when the Brewster effect is applied only in the substrate region (from which the processed light beam travels to air), the input image, as well as the spatial integration, undergoes magnification. To mitigate this issue, the Brewster effect can instead be applied in the cover region, where the input light beam enters the structure. Furthermore, we analytically show that two-dimensional (2D) spatial integration can be achieved by cascading the two integrators, one designed for s-polarized and the other for p-polarized light beams. Finally, we propose a new hexahedral slab waveguide structure capable of performing 2D spatial integration.