Here, full-wave analysis and design of an electrically tunable optical fractional-order temporal differentiator (DIFF) based on an ultra-compact microring resonator (MRR) has been presented. Electrical tunability has been realized through free carrier dispersion (FCD) effect in the resonator with P-I-N and P-N junctions. The first-order optical DIFF is realized based on the critically-coupled resonator without applying any bias voltages in the junctions. Also, fractional-order DIFF with differentiation order α > 1 is realized by over-coupled resonator with the forward-biased P-I-N and P-N junctions. While, fractional-order DIFF with α < 1 is realized by under-coupled resonator with reverse-biased P-N junction. The high performance of the designed tunable optical DIFFs and their high accuracy have been confirmed considering an ultra-fast Gaussian input pulse with short full-width at half-maximum (FWHM) of 6.3 ps.

在这里，提出了基于超紧凑微环谐振器 (MRR) 的电可调光学分数阶时间微分器 (DIFF) 的全波分析和设计。通过具有 PIN 和 PN 结的谐振器中的自由载流子色散 (FCD) 效应实现了电可调性。一阶光学 DIFF 是基于临界耦合谐振器实现的，而无需在结中施加任何偏置电压。此外，微分阶α  > 1 的分数阶 DIFF是通过具有正向偏置 PIN 和 PN 结的过耦合谐振器实现的。同时，分数阶 DIFF 与α < 1 是通过具有反向偏置 PN 结的欠耦合谐振器实现的。考虑到具有 6.3 ps 的半高全宽 (FWHM) 的超快高斯输入脉冲，已确认设计的可调谐光学 DIFF 的高性能及其高精度。