Resonant coupling effects have become a fundamental and intriguing physical concept in the study of exceptional point, topology and bound states in the continuum, significantly driving the development of high-sensitivity sensing, optical signal processing and low-threshold lasing. Coupled mode theory (CMT), as a fundamental method for understanding the underlying physical mechanisms, has been widely applied in the theoretical analysis of mechanics, optics, electricity, acoustics, etc. By fitting either the theoretically calculated or experimentally measured response of the coupled system utilizing the transmission formula derived from the CMT, the implicit physical parameters of the studied system can be computationally extracted, thereby facilitating the analysis and understanding of the system’s coupling mechanisms. However, when solving the inverse problem of extracting multi-physical parameters for coupled systems, traditional fitting methods are not only computationally cumbersome and time-consuming but also highly prone to the issue of multi-solutions, where different combinations of physical parameters yield very similar spectral responses. These challenges hinder the design of sophisticated coupled resonant systems and severely limit the application of CMT in different disciplines.
To address the above challenges, a team of researchers, led by Professor Da-Quan Yang from Beijing University of Posts and Telecommunications, Professor Yi Xu from Guangdong University of Technology, Professor Hua-Shun Wen from Nankai University and co-workers proposes and experimentally demonstrate a physics-data co-driven deep neural network, which leverages the CMT-generated low-cost datasets for training and incorporates physical constraints of eigenvalues into the loss function of deep neural network, enabling the network to capture the underlying physical characteristics of the coupled resonant system. Through simulation and experimental validations, the proposed approach trained on a dataset generated using CMT enables accurate physical parameters retrieval of intrinsic resonant frequency, intrinsic loss, coupling strength, and transmission phase in complex coupled resonant systems. Compared with the traditional fitting method, the average computation time has been reduced by three orders of magnitude and the predicted performance is improved by more than two orders of magnitude. Compared with traditional data-driven neural networks, the physical parameter prediction error is reduced by up to 81.59%. Experimental results demonstrate that the proposed physics-data co-driven deep neural network not only improves the prediction accuracy of multi-physical parameters but also further reduces the computation time, providing a new technical approach for accurate decoupling and fast detection of multi-physical parameters in complex microcavity-coupled systems.
To verify potential applications of this physics-data co-driven deep neural network, the researchers applied it to displacement sensing experiments in a two-microcavity coupled system. Displacements modify its underlying physical parameters, subsequently leading to complex spectral responses that include mode shifts, mode broadening, and mode splitting. By acquiring transmission spectra at different displacements and feeding them into the physics-data co-driven deep neural network, nanoscale displacement detection can be achieved by leveraging the pre-calibrated correspondence between changes in the physical parameters and the displacement. The experimental results demonstrate that this physics-data co-driven deep neural network maintains high performance (with R 2 values exceeding 0.979) under varying displacements.
To address the key challenges of multi-solutions and high computational complexity in the inverse problem of multi-physical parameter retrieval in complex multi-cavity coupled systems, we propose a physics-data co-driven deep neural network that achieves rapid and accurate retrieval of underlying multi-physical parameters of the coupled resonant system. Furthermore, this approach is extended to displacement sensing applications, successfully achieving precise measurement of nanoscale displacement. The proposed physics-data co-driven deep neural network framework exhibits strong generality and scalability. By further integrating with optoelectronic chip integration and multi-modal sensing technologies, it holds great promise for applications in the non-invasive quantitative morphological characterization of on-chip optical resonant systems and intelligent sensing of nanoscale particulate matter.
This research received funding from the Guangdong Major Project of Basic Research, the National Natural Science Foundation of China, the National Key Research and Development Program of China, and the State Key Laboratory of Information Photonics and Optical Communications, the Fundamental Research Funds for the Beijing University of Posts and Telecommunications, and the Beijing University of Posts and Telecommunications Excellent Ph.D. Students Foundation.
Light: Science & Applications
Deciphering optical coupled resonant systems with physics-data co-driven deep neural networks