Machine learning methods have been widely used in subwavelength photonic structure designs since they are capable of solving the non-intuitive and nonlinear relationship between subwavelength structures and their optical responses and are significantly faster than the traditional numerical simulation methods. However, in the inverse design problems, machine learning models usually serve as black boxes which take the desired spectrum as an input to predict the shape of meta-atoms without elucidating the physics behind it. This makes the machine learning method difficult to apply when designing structures aimed at performing complicated functions. At the same time, the multipole expansion of the scattering cross sections, i.e. multipolar resonances, has been instrumental in analyzing and designing meta-atoms. In this work, we developed forward prediction models to discover hidden relationships between scattering behavior and the shapes of meta-atoms, and an inverse design model to reconstruct the meta-atoms having desired properties under the guidance of multipole expansion theory.
Metamaterials enable tailoring of light–matter interactions, driving discoveries which fuel novel applications. Deep neural networks (DNNs) have shown marked achievements in metamaterials research, however they are black boxes, and it is unknown how they work. We present a causal DNN where the learned physics is available to the user. Here, the condition of causality is enforced through a deep Lorentz layer which takes in the geometry of an all-dielectric metamaterial, and outputs the causal frequency-dependent permittivity and permeability. The ability of the LNN to learn metamaterial physics is verified with examples, and results are compared to theory and simulations.
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