Deciphering optical coupled resonant systems with physics-data co-driven deep neural networks.

Coupled mode theory (CMT) is a universal method for studying resonant systems in various disciplines in science. Combined with traditional fitting methods, implicit physical parameters of the resonant systems can be revealed. However, this methodology fails in tackling the scenario of multi-solution for a given resonant system, resembling a fundamental challenge that has not been addressed yet. In this work, we propose and experimentally demonstrate a CMT physics and data co-driven deep neural network (CMT-NN) that can predict the implicit physical parameters of complex resonant systems in a rapid and precise way. More importantly, the challenge of multi-solution is mitigated by incorporating physical eigenvalues and response of the system in evaluating the physics consistency of the neural network. The applicability and generality of CMT-NN are demonstrated by simulations and experiments, where the CMT-NN can capture subtle spectral features and learn the coupling physical properties effectively. Compared with the traditional fitting method, the average computation time has been reduced by three orders of magnitude and the prediction performance is improved by more than two orders of magnitude. Displacement sensing experiments further validate the robustness of CMT-NN. It is anticipated that the CMT-NN can provide a paradigm shift in using the CMT for studying resonant systems and shed new light on the understanding, design and optimization of various coupled resonant systems.