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We propose a graphene-on-grating nanostructure to enable second-order spatialdifferentiation computation in terahertz (THz) region. The differentiationoperation is based on the interference between the direct reflected field andthe leakage of two excited surface plasmon polaritons counter-propagating alongthe graphene sheet. With the spatial coupled-mode theory, we derive out thatthe requirement for the second-order spatial differentiation is the criticalcoupling condition. We numerically demonstrate such an analog computation withGaussian beams. It shows that the spatial bandwidth of the proposeddifferentiator is large enough such that even when the waist radius of theGaussian beam is as narrow as ${{w}_{0}}=0.68\lambda $ ($\lambda $ is thefree-space wavelength), the accuracy of the differentiator is higher than 95\%.The proposed differentiator is ultra-compact, with a thickness less than$0.1\lambda $, and useful for real-time imaging applications in THz securitydetections.

On-grating graphene surface plasmons enabling spatial differentiation in terahertz region