Abstract
In recent years, the integration of machine learning (ML) techniques into the field of metamaterials and metasurfaces has expanded their various applications, such as serving as surrogate solvers, facilitating inverse design, and imaging, with the advantages including reduced development time, a more automated process, and the capabilities of extracting more information. These applications heavily rely on training neural networks (NNs) with simulation data for convenience, offering the advantages of simplifying and accelerating the data generation for training. However, metamaterials and metasurfaces typically contain a lot of degrees of freedom (DOFs), and practical implementations often involve fabrication errors and mismatches between the experimental setups and the idealized simulation conditions. Consequently, the performance of simulation-data-trained NNs may be suboptimal when applied to real-world experimental data. To overcome these challenges, we have proposed two solutions. The first solution involves employing a data-driven approach that utilizes unsupervised learning to automatically learn the DOFs. Such an approach enables the inclusion of unexpected experimental mismatches or errors, thereby accounting for variations that may arise during practical implementations. The second solution involves directly employing experimental data to train the NNs, where the experimental data can inherently encompass the experimental factors associated with practical physical systems.
In this thesis, I adopt both the data-driven route in setting up ML algorithms and the experimental route to investigate possible mismatches between the training and testing phase of the established ML models, with applications in both imaging and inverse design assisted by metamaterials and metasurfaces. I first developed an unsupervised feature learning approach using a variational autoencoder (VAE), demonstrating the ability to automatically discover physical parameters from either simulated or experimental wave responses. In the case of metamaterials, these physical parameters can be the constitutive parameters. e.g., Young’s modulus in elastic waves and Jones matrix elements in optical metasurfaces, or directly the geometric parameters of assembling structures. The advantage of utilizing VAE is that it can find out the exact number of DOFs in the training data. This gives us an opportunity to decide whether a particular imaging procedure is well-posed to extract the same number of DOFs from the data. To demonstrate the generality of such an approach in imaging, we applied it to both elastic wave imaging and low-light optical imaging. In the case of elastic wave imaging, both theoretical analyses using a spring-mass model and experimental validation with 3D printed elastic structures were employed to show the efficacy. Experimental data obtained from various fabricated elastic structures were subjected to post-processing and subsequently fed into the simulation-data-trained NNs, to extract geometric parameters of the structures and also the material parameters that cannot be known beforehand in simulations due to fabrication errors. In the case of optical imaging, the VAE was then applied to the low-light imaging. Low-light imaging relies on measuring two-photon coincidence in addition to conventional intensity measurement, so that more information can be extracted while a significant number of photons is still needed. In the current application, we target to extract the Jones matrix profile of an unknown object, in which a VAE can be trained to discover the Jones matrix profile directly from the measured photon arrival data. We found that the VAE-based approach exhibits superior accuracy even compared to the previously derived analytical algorithm as a benchmark, also As a result, we can use a much smaller number of collected photons to extract the Jones matrix images.
In addition to the imaging application, the inverse design of metamaterials and metasurfaces in practical experiments is another significant application of ML. In optics, the integration of metasurfaces and multiplexing holography has facilitated recent advancements in display and information processing. Among various DOFs of light employed in multiplexing, polarization is a highly accessible and flexible parameter that can be manipulated during both the excitation and analysis stages. For polarization-multiplexed holograms, the most comprehensive representation involves an arbitrary Jones matrix profile, while it requires the utilization of complex bianisotropic or bilayer metasurfaces with a lot of design parameters, introducing difficulties in the inverse design of the metasurfaces. Besides, in hologram generation, the conventional iterative algorithm used to design the required phase profiles on metasurfaces, needs case-by-case iterations and is time-consuming. To address these challenges, I developed an integrated deep neural network (DNN), integrating both hologram generation and metasurface inverse design functionalities. The integrated DNN enables the direct acquisition of metasurface designs from target polarization holograms, eliminating the need for conventional iterative procedures. This data-driven approach only requires an existing structure library, and by using bianisotropic metasurfaces as a demonstration, four distinct polarization conversion channels of holograms were successfully achieved. Furthermore, in addition to the passive metasurfaces mentioned above, reconfigurable metasurfaces have gained significant interest in the research community, offering the ability to modify their properties through external tuning. Recently, reconfigurable intelligent surfaces have demonstrated significant potential in enhancing intelligent wireless communication of Wi-Fi and 5G signals. Particularly, in modern wireless communication, power allocation plays a key role in distributing transmitted power to spatially separated users, and deep learning (DL) approaches have recently been used to design metasurfaces for this purpose. However, practical applications usually encounter many complex environmental factors that need to be considered, such as the blocking effect of obstacles. The existing DL approaches for such situations rely on training DNNs with simulation data, facing the challenges of misteaches and fabrication errors as motioned before. To address these challenges, I developed an experiment-based DL approach that directly utilizes real-world experimental data to train the DNN, by leveraging a programmable metasurface for efficient data collection. The utilization of experimental data for training can automatically encompass the complex factors inherent in practical environments, and was successfully employed to design metasurfaces for power allocation to multiple receivers in complex environments.
Overall, this thesis highlights the huge potential of ML in practical physical systems, addressing challenges associated with both imaging and inverse design of diverse metamaterials. Through practical experiments, we have found that the ML approaches need to be combined with experiments, either by using experimental data for training or by extending the NNs to include the uncertain factors in realistic experimental conditions. Besides, the utilized VAE demonstrates the ability to automatically discover the exact number of DOFs within the data in an unsupervised manner, which can serve as a valuable tool to further assist in designing imaging equipment and optimizing experimental processes. ML emerging as a promising tool to enhance the capabilities of metamaterials, thereby advancing their real-world applications.