All optical third order tunable ordinary differential equation solutions based on double Sagnac rings coupled MZI on silicon waveguide chips

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.