This paper presents design and analysis of an optical memory and counter based on ultra-compact temporal integrators (INTs) using a graphene hybrid plasmonic add-drop ring resonator (GHP-ADRR) and pulley-type ring resonator (GHP-PRR) for optical signal processing. Due to the valuable features of graphene hybrid plasmonic technology, the footprint of these INTs is equal to 4 × 3.5 µm2 for GHP-ADRR and 5.4 × 3.6 µm2 for GHP-PRR. Also, the performance of the INTs has been analyzed by the three-dimensional finite-difference time-domain method in the frequency and time domains, and the accuracy of the results has been compared with those of the math counterparts and also key specifications of the first-order temporal INTs including phase jump, insertion loss, 3 dB bandwidth, rise time, integration time window, and energy efficiency have been investigated. Based on the results, both circuits have better performance than the photonic counterparts. Furthermore, the performance of these INTs has been evaluated in detail as a high-speed optical memory and counter. It has been illustrated that due to the greater quality factor of the GHP-PRR, this circuit has more accuracy for realizing the first-order integration, optical memory, and counter than the GHP-ADRR-based INT.
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