基于集成微环谐振器的可变系数微分方程光子计算

The photon calculation for differential equations with variable coefficients

摘要:

基于硅基片上微环谐振器，本文提出了一种系数可变一阶光子微分方程的光子计算方法，实现了不同系数的光子微分方程超快速求解。基于耦合模理论，对微环谐振器的传递函数进行了时域与频域的分析，所设计的硅基脊形波导刻蚀深度为220nm，宽500nm，微环谐振器形状为跑道型，由两个半圆夹两根长直波导组成，半圆半径为30μm，直波导长度为60.75μm，能够实现微分方程a与b系数的可调谐，仿真得到调节范围为a0：1.5007e10-1.5562e10，b0：4.5343e9-5.6473e9。同时，仿真分析了实现了温度调节电控，系数不同的微分方程的数值求解过程，归一化之后与真实微分方程曲线进行对比，误差不超过0.02。

Abstract:

In this paper, a microring resonator on silicon substrate with variable coefficients is proposed to solve the first order photonic differential equation.The ultrafine solution of the photonic differential equation with different coefficients is realized.Based on the coupled mode theory, the transfer function of microring resonator is analyzed in time domain and frequency domain.The etching depth is designed to be 220mm,and the silica-based ridge waveguide is designed to be 500mm. The shape of the micring-ring resonator is track type,which is composed of two semicircle sandwiches with two long straight waveguides.The radius of the semicircle is 30um,and the length of the straight waveguide is 60.75um.The a and b coefficient of differential equation can be adjusted,and the adjustment range is by fitting:1.5007e10 and :4.534e9.The simulation realizes the numerical solution process of the differential equation with different coefficient and the adjustment of electric control. After normalization,it compares with the real differential equation curve,and the error is less than 0.02.