硅基级联双微环的分数阶微分器

Fractional-Order Differentiator Using Silicon-Based Cascaded Dual Micro-Rings

采用一种半径相同的级联双微环谐振器实现n>1阶光时域微分器,并基于最小平均偏差原则,分析级联双微环微分器的微分精度、能量效率和输入信号对微分结果的影响。相比于单一微环,该结构可将微分波形平均绝对偏差最大值5.67%降至0.67%。在1<n<2微分阶数范围内,微分器整体平均绝对偏差不超过2.3%,互相关系数均大于99%,微分精度得到提高,且输入信号脉宽对级联双微环微分器的微分阶数影响更小,适用的可接受输入信号脉宽范围更大。同时,通过调节级联结构中一环的耦合状态,可改变微分器的微分阶数,实现可调谐的高精度分数阶微分器。

In this study,a cascaded dual micro-ring resonator with the same radius is used to implement an n>1 order optical time-domain differentiator.The effects of differentiation accuracy,energy efficiency,and input signal on the differentiation results of the cascaded dual-ring differentiator were analyzed using the principle of minimum average deviation.In comparison with a single micro-ring,the average absolute deviation of differential waveform can be reduced from 5.67%to 0.67%.Within the range of 1<n<2 differential orders,the overall average absolute deviation of the differentiator does not exceed 2.3%and the cross-correlation coefficients are greater than 99%.The differential accuracy is improved,the input signal pulse width is less affected the defferentiation order of the cascaded dual micro-ring defferentiator,and the applicable input-signal pulse width range is larger.Simultaneously,by adjusting the coupling state of a loop in the cascade structure,the differentiation order of the differentiator can be changed to realize a tunable high-precision fractional differentiator.