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Title: A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators
Authors: Jin, B
Yuan, J
Wang, K
Sang, X
Yan, B
Wu, Q
Li, F
Zhou, X
Zhou, G
Yu, C
Lu, C 
Tam, HY 
Wai, PKA 
Issue Date: 2015
Source: Scientific reports, 18 2015, v. 5, no. , p. 1-11
Abstract: Microring-based photonic fractional differentiators play an important role in the on-chip all-optical signal processing. Unfortunately, the previous works do not consider the time-reversal and the time delay characteristics of the microring-based fractional differentiator. They also do not include the effect of input pulse width on the output. In particular, it cannot explain why the microring-based differentiator with the differentiation order n>1 has larger output deviation than that with n<1, and why the microring-based differentiator cannot reproduce the three-peak output waveform of an ideal differentiator with n>1. In this paper, a comprehensive theoretical model is proposed. The critically-coupled microring resonator is modeled as an ideal first-order differentiator, while the under-coupled and over-coupled resonators are modeled as the time-reversed ideal fractional differentiators. Traditionally, the over-coupled microring resonators are used to form the differentiators with 1<n<2. However, we demonstrate that smaller fitting error can be obtained if the over-coupled microring resonator is fitted by an ideal differentiator with n<1. The time delay of the differentiator is also considered. Finally, the influences of some key factors on the output waveform and deviation are discussed. The proposed theoretical model is beneficial for the design and application of the microring-based fractional differentiators.
Publisher: Nature Publishing Group
Journal: Scientific reports 
EISSN: 2045-2322
DOI: 10.1038/srep14216
Rights: This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit
The following publication Jin, B. et al. A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators. Sci. Rep. 5, 14216 (2015) is available at
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