This paper presents the design and comprehensive analysis of an ultra-fast fractional-order temporal differentiator (DIFF) based on a plasmonic inner-wall Bragg grating microring resonator (BG-MRR). Due to the ring radius of 1.1 µm and the strong confinement of the surface plasmon polaritons in the plasmonic waveguide with very small cross-section, the overall footprint of the DIFF circuit is significantly small (approximately 4 × 2.5 µm). By changing the coupling regimes of the microring resonator, a broad range for the differentiation order α, i.e., 0.7-1.7 and a wide 3 dB bandwidth of 3.1 THz [24.8 nm] for α = 0.7 and 3.9 THz [31.2 nm] for α = 1.7 have been realized. Comparing the outputs of the BG-MRR-based DIFF with the corresponding mathematical DIFF indicates that deviations for α > 1 are significantly larger than those of α < 1. Therefore, a fractional-order temporal DIFF circuit based on plasmonic cascaded BG-MRR has been proposed for α > 1.
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