A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators.

Boyuan Jin,P K A Wai,Chao Lu,Hwa Yaw Tam,Binbin Yan,Jinhui Yuan,Qiang Wu,Guiyao Zhou,Feng Li,Chongxiu Yu,Xian Zhou,Xinzhu Sang,Kuiru Wang

doi:10.1038/srep14216

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.

Highlights

Microring resonators[23,24,25]
The previous works have not elaborated how the all-pass microring resonator is approximated by an ideal fractional differentiator, and the time delay characteristic of the microring-based differentiators is neglected
Compared with the previous reports in which the time-reversal characteristic is ignored, it is demonstrated that the under-coupled and the over-coupled microring resonators can be modeled as the time-reversed ideal fractional differentiators with the differentiation order n < 1 and n > 1, respectively

Summary

Introduction

Previous works use the transfer function of the microring resonator to simulate the output of the differentiator, but it is not explained how the response of a microring resonator can be fitted by an ideal fractional differentiator. These works are based on the incorrect assumption that a phase jump, which is larger or smaller than π across the resonance, can be obtained in the underor over- coupled resonators. It is revealed that the critically-coupled microring resonator can be modeled as an ideal first-order differentiator, while the under-coupled and the over-coupled resonators can be modeled as the time-reversed ideal fractional differentiators. In addition to the output deviation induced by the resonator itself, the influences of key factors such as the divergence of the carrier from the resonant wavelength, input pulse width, and finite slope of the phase response across the resonance, on the output waveform and deviation are discussed

Methods

Results

Discussion

Conclusion