On-Chip Constant-Coefficient Second-Order Differential Equation Solver Based on Microdisk with Dual- Mode Alignment

This paper proposed an all-optical constant- coefficient second-order ordinary differential equation (2-ODE) solver based on a microdisk resonator (MDR) with dual-mode alignment. We validate the feasibility of our structure for solving constant-coefficient 2-0DEs using optical Gaussian pulses and super-Gaussian pulses. The results demonstrate a good agreement between the solutions obtained with the designed MDR and those obtained through mathematical calculations for constant- coefficient 2-0DEs. Furthermore, we have discussed the influence of the pulse width of the input optical signal on the solution result. The device footprint is approximately
$20\times 30\ \mu m^{2}$
, and the maximum Q-factor reaches
$9.38\times 10^{4}$
.