Backscattering-Immune Computing of Spatial Differentiation by Nonreciprocal Plasmonics

Spatial differentiation is a fundamental mathematical operation used in many fields of science or engineering. Recently, optical analog computing of spatial differentiation, which can overcome the speed and energy limitations of digital differentiation techniques, has been realized in some nano systems such as the excitation of surface plasmon polaritons (SPPs). However, the inevitable backscattering of SPP propagation around defects or discontinuities may bring some undesired noises to the output signal. In this work, we firstly design a backscattering-immune spatial differentiator with the utilization of the nonreciprocal plasmonic platform, where the topologically protected one-way SPP leaky mode exists, in the terahertz (THz) region. Guided by the nonreciprocal spatial coupled-mode theory, we show that the ideal transfer function of the first-order spatial differentiation is able to be realized by subtly tuning the balance between the asymmetric leaky rate stemming from the nonreciprocal nature and intrinsic absorption rate of the system. Full wave simulations show that the first-order differentiation without backscattering around defects can be precisely implemented by using the designed nonreciprocal differentiator. Our proposed backscattering-immune spatial differentiator can find widespread applications for robust edge detection and image processing in the THz frequency range.