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Ordinary differential equations play an important role to describe dynamic behaviors in different engineering systems. On the other hand, high-speed computations and broadband signal processing are achievable using compact photonic integrated circuits with low power consumption. So, in this paper, a dual-purpose compact all-optical integrated circuit consisting microring resonator, directional coupler, splitter, and subtractor has been designed and analyzed for ultra-fast signal processing. This all-optical circuit can be utilized simultaneously as a first-order differential equation solver and a first-order differentiator. Full-wave analysis for the mentioned components of this integrated circuit has been performed by frequency-domain simulations, and their performance has been investigated carefully. Also, performance of the designed circuit has been analyzed using the numerical three-dimensional finite-difference time-domain (3D-FDTD) method considering a Gaussian input pulse. This circuit has unique features such as high-speed performance, compactness, and compatibility with the CMOS technology.

Keywords: All-optical signal processing, Ordinary differential equation, Optical differentiator, Silicon microring resonator, Full-wave analysis.

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