Calibratable 90° hybrid based on a reconfigurable on-chip optical neural network

A 90° optical hybrid was implemented on a silicon-on-insulator (SOI) platform using a reconfigurable optical neural network (ONN), composed of cascaded four-port multimode interferometers (MMIs). This programmable network enables customized system transfer matrices by training the input-output mapping of the network to match a target matrix, eliminating reliance on the precise splitting ratios and relative phases of individual components. This approach enhances the robustness of the system against fabrication and design variations. Even after introducing error matrices to the MMIs, the network still achieved an average phase error of 0.26° and an average common-mode rejection ratio (CMRR) of -30.8<i>d</i><i>B</i>, demonstrating strong resilience to device-level imperfections. Moreover, the network architecture can adaptively compensate for output port coupling imbalances during training, effectively addressing the high sensitivity of the coupling process to port alignment and fabrication nonuniformity. This significantly reduces the complexity of optical packaging. We performed simulations to analyze the necessity of using networks with more than four layers and to evaluate the system's ability to compensate for imbalances in output coupling coefficients. The average worst-case phase error was 0.24°, and the average worst-case CMRR was -34.2<i>d</i><i>B</i>. Notably, these results showed no significant degradation with increasing coupling imbalance at the output ports. In addition, in our experiments, we demonstrated that a four-layer ONN can achieve a maximum phase error below 1.32° and a maximum CMRR better than -36.6<i>d</i><i>B</i> at the target wavelength after training.