Si3N4 microring (MR) stands out as a promising platform in the integrated photonics for optical filter, optical delay lines, generation of Kerr frequency comb and optical computing. In this work, we study the optical temporal differentiation in a designed Si3N4 MR array. In order to avoid the limitations of a single MR, which can not reproduce the third peak at the trailing edge when differentiation order is between 1 and 2, a MR array consisting of two add-drop MRs and one all-pass MR is designed. Simulation results show that by reusing the drop port of add-drop MRs, differential orders between 0 to 2 can be obtained from different output ports. Furthermore, we propose an optimization algorithm to select the parameters of MRs. As a result, the differentiation deviations for 4-ps input Gaussian pulse can be minimized when the interior-point method is employed. Calculation results show that the differentiation deviations for orders between 1 and 2 are reduced to around 10%, and for orders between 0 to 1 are reduced to within 33%.
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