title: A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators.
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.
authors.affiliation: State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, P.O. Box 72 (BUPT), Beijing 100876, China.|Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States.
authors.forename: Boyuan
authors.initials: B
authors.lastname: Jin
authors.affiliation: State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, P.O. Box 72 (BUPT), Beijing 100876, China.|Photonics Research Centre, Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
authors.forename: Jinhui
authors.initials: J
authors.lastname: Yuan
authors.affiliation: State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, P.O. Box 72 (BUPT), Beijing 100876, China.
authors.forename: Kuiru
authors.initials: K
authors.lastname: Wang
authors.affiliation: State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, P.O. Box 72 (BUPT), Beijing 100876, China.
authors.forename: Xinzhu
authors.initials: X
authors.lastname: Sang
authors.affiliation: State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, P.O. Box 72 (BUPT), Beijing 100876, China.
authors.forename: Binbin
authors.initials: B
authors.lastname: Yan
authors.affiliation: State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, P.O. Box 72 (BUPT), Beijing 100876, China.|Department of Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne, NE1 8ST, United Kingdom.
authors.forename: Qiang
authors.initials: Q
authors.lastname: Wu
authors.affiliation: Photonics Research Centre, Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
authors.forename: Feng
authors.initials: F
authors.lastname: Li
authors.affiliation: Photonics Research Centre, Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
authors.forename: Xian
authors.initials: X
authors.lastname: Zhou
authors.affiliation: Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, 510006 Guangzhou, China.
authors.forename: Guiyao
authors.initials: G
authors.lastname: Zhou
authors.affiliation: State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, P.O. Box 72 (BUPT), Beijing 100876, China.
authors.forename: Chongxiu
authors.initials: C
authors.lastname: Yu
authors.affiliation: Photonics Research Centre, Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
authors.forename: Chao
authors.initials: C
authors.lastname: Lu
authors.affiliation: Photonics Research Centre, Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
authors.forename: Hwa
authors.initials: H
authors.lastname: Yaw Tam
authors.affiliation: Photonics Research Centre, Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
authors.forename: P K A
authors.initials: PKA
authors.lastname: Wai