At present, an all optical high-order tunable ordinary differential equation (ODE) solver is very difficult to implement. A novel all-optical first to third order linear ODEs solutions with tunable constant coefficients using double Sagnac rings coupled Mach–Zehnder-interferometer (DSMZI) on silicon waveguide chips are proposed. The structural composition and size of the DSMZI have been designed, and the working principles of its first to third order ODEs solutions have been derived. By varying the input electric heating power of the thermal-optical phase shifters of the individual arms of the MZI, the constant-coefficient of the differential equation can be simply tuned in large scope. It is demonstrated that the constant coefficient k ranges from 0.0015/ps to 0.092/ps for the first-order ODE. The constant coefficient p of the second-order ODE solver can be continuously tuned from 0.013/ps to 0.174/ps, correspondingly with the q varying from 0.00004225/ps2 to 0.007569/ps2. Three constant coefficients u, v, and w of the third-order ODE can be continuously tuned from 0.105/ps to 0.252/ps, 0.003675/ps2 to 0.021168/ps2, and 0.00004288/ps3 to 0.0005927/ps3, respectively. The all-optical ODE solvers with the DSMZI can be easily integrated with other optical components based on silicon on insulator, which can provide a path for future artificial intelligence or big data processing systems in optical computing on silicon waveguide chips.

中文翻译：

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硅波导芯片上基于双Sagnac环耦合MZI的全光学三阶可调谐常微分方程解

目前，全光学高阶可调谐常微分方程（ODE）求解器的实现非常困难。提出了一种新颖的全光学一阶至三阶线性 ODE 解决方案，其常数系数可调，使用硅波导芯片上的双 Sagnac 环耦合马赫-曾德尔干涉仪 (DSMZI)。设计了DSMZI的结构组成和尺寸，并推导了其一阶至三阶ODE解的工作原理。通过改变MZI各臂热光移相器的输入电加热功率，可以在大范围内简单地调整微分方程的常数系数。结果表明，一阶常微分方程的常系数 k 的范围为 0.0015/ps 到 0.092/ps。二阶ODE求解器的常数系数p可以在0.013/ps到0.174/ps之间连续调整，相应地q在0.00004225/ps2到0.007569/ps2之间变化。三阶 ODE 的三个常系数 u、v 和 w 可以分别从 0.105/ps 到 0.252/ps、0.003675/ps2 到 0.021168/ps2 以及 0.00004288/ps3 到 0.0005927/ps3 连续调整。采用DSMZI的全光ODE求解器可以轻松地与其他基于绝缘体上硅的光学元件集成，这可以为未来人工智能或大数据处理系统在硅波导芯片上的光学计算中提供一条路径。