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We propose a spatiotemporal optical differentiator of the first order based on a three-layer metal-dielectric-metal (MDM) structure operating in reflection. For describing the transformation of the incident spatiotemporal optical signal, we apply the transfer function formalism of the theory of linear systems. We demonstrate that the differentiator based on the proposed MDM structure enables generating a reflected optical pulse possessing an optical vortex in the spatiotemporal domain (referred to as the spatiotemporal optical vortex, STOV). The MDM differentiator can also be used for high-quality edge detection of the incident spatiotemporal optical signal. Moreover, we investigate a “double” MDM structure consisting of two single (three-layer) MDM structures separated by a dielectric layer, which implements the operation of spatiotemporal differentiation of the second order. By considering the generation of a reflected optical pulse with several phase singularities and studying the edgedetection operation, we show that the operation of second-order spatiotemporal differentiation is implemented with high accuracy. We also investigate the possibility of obtaining an STOV in asymmetric and symmetric dielectric slab waveguides and demonstrate that an STOV can be generated upon reflection of a spatiotemporal optical pulse propagating in the waveguide from an integrated metal-dielectric structure consisting of a few metal strips “buried” in the waveguide core layer. The obtained theoretical results are in good agreement with the results of rigorous numerical simulations of the spatiotemporal differentiation and STOV generation using metal-dielectric structures in both free-space and integrated geometries. We believe that the obtained results may find application in the creation of analog optical computing and optical information processing systems.
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