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.
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