Optical analog computing offers high-throughput low-power-consumption operation for specialized computational tasks. Traditionally, optical analog computing in the spatial domain uses a bulky system of lenses and filters. Recent developments in metamaterials enable the miniaturization of such computing elements down to a subwavelength scale. However, the required metamaterial consists of a complex array of meta-atoms, and direct demonstration of image processing is challenging. Here, we show that the interference effects associated with surface plasmon excitations at a single metal–dielectric interface can perform spatial differentiation. And we experimentally demonstrate edge detection of an image without any Fourier lens. This work points to a simple yet powerful mechanism for optical analog computing at the nanoscale.

Optics naturally provides us with some powerful mathematical operations. Here, we experimentally demonstrate that during reflection or refraction at a single optical planar interface, the optical computing of spatial differentiation can be realized by analyzing specific orthogonal polarization states of light. We show that the spatial differentiation is intrinsically due to the spin Hall effect of light and generally accompanies light reflection and refraction at any planar interface, regardless of material composition or incident angles. The proposed spin-optical method takes advantages of a simple and common structure to enable vectorialfield computation and perform edge detection for ultrafast image processing.

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 w=0.68λ (λ 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 0.1λ, and useful for real-time imaging applications in THz security detections.

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