All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator.

Ting Yang,Aoling Zheng,Jianping Chen,Liangjun Lu,Xinliang Zhang,Jianji Dong,Linjie Zhou

doi:10.1038/srep05581

Abstract

Photonic integrated circuits for photonic computing open up the possibility for the realization of ultrahigh-speed and ultra wide-band signal processing with compact size and low power consumption. Differential equations model and govern fundamental physical phenomena and engineering systems in virtually any field of science and engineering, such as temperature diffusion processes, physical problems of motion subject to acceleration inputs and frictional forces, and the response of different resistor-capacitor circuits, etc. In this study, we experimentally demonstrate a feasible integrated scheme to solve first-order linear ordinary differential equation with constant-coefficient tunable based on a single silicon microring resonator. Besides, we analyze the impact of the chirp and pulse-width of input signals on the computing deviation. This device can be compatible with the electronic technology (typically complementary metal-oxide semiconductor technology), which may motivate the development of integrated photonic circuits for optical computing.

Highlights

Photonic integrated circuits for photonic computing open up the possibility for the realization of ultrahigh-speed and ultra wide-band signal processing with compact size and low power consumption
When the voltage applied on the microring resonator (MRR) is 0 V, corresponding to a constantcoefficient of about 0.038/ps, the output waveform is depicted in Fig. 5(b), and the calculated waveform according to the ideal ordinary differential equation (ODE) solver is shown for comparison
In order to accurately evaluate the errors of ODE solutions, we need to define a parameter of average deviation, which is defined as the mean absolute deviation of measured waveforms from the calculated ones on certain pulse period (200 ps)[24]

Summary

Introduction

Photonic integrated circuits for photonic computing open up the possibility for the realization of ultrahigh-speed and ultra wide-band signal processing with compact size and low power consumption. Many optical signal processing systems, which are counterparts of the ‘‘basic functionalities’’ in electronic circuits, have been proposed and demonstrated over the years, including all-optical logics[4,5,6,7], optical differentiation[8,9,10,11,12,13,14] and optical integration[15,16,17,18,19] etc These fundamental units make more complicated optical computing functionalities come true, such as ordinary differential equation (ODE) solvers[3,20,21]. We experimentally demonstrate an integrated all-optical system for solving first-order linear ODE with constant-coefficient tunable based on a silicon microring resonator (MRR). In order to solve a linear first-order ODE as described in Eq (1) in the case of zero-state response, i.e., y(0) 5 0, the system transfer function H(v) according to Eq (1) should be expressed as www.nature.com/scientificreports

Methods

Results

Conclusion