Spatiotemporal optical differentiation and vortex generation with metal-dielectric-metal multilayers

We consider a spatiotemporal differentiator of the first order based on a three-layer metal-dielectric-metal (MDM) structure. We show theoretically and numerically that, in contrast to all-dielectric layered structures, the differentiator based on this MDM structure enables generating an optical pulse possessing an optical vortex in the spatiotemporal domain. High-quality edge detection of the incident spatiotemporal optical signal using the MDM differentiator is also demonstrated. Moreover, we investigate a ``double'' MDM structure consisting of two single (three-layer) MDM structures which implements the operation of spatiotemporal differentiation of the second order. By considering the generation of an optical pulse with several phase singularities and studying the edge-detection operation, we demonstrate that the operation of second-order spatiotemporal differentiation is implemented with high accuracy. The obtained results may find application in the creation of analog optical computing and optical information processing systems.