We propose a graphene-on-grating nanostructure to enable second-order spatial differentiation computation in the terahertz (THz) region. The differentiation operation is based on the interference between the direct reflected field and the leakage of two excited surface plasmon polaritons counter-propagating along the graphene sheet. With the spatial coupled-mode theory, we derive that the requirement for the second-order spatial differentiation is the critical coupling condition. We numerically demonstrate such an analog computation with Gaussian beams. It shows that the spatial bandwidth of the proposed differentiator is large enough such that even when the waist radius of the Gaussian beam is as narrow as ( is the free-space wavelength), the accuracy of the differentiator is higher than 95%. The proposed differentiator is ultra-compact, with a thickness less than , and useful for real-time imaging applications in THz security detections.
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