The rapid and precise inverse design of an arbitrary Mie scatterer with functional response facilitates various applications in multiple disciplines. Compared with traditional time-consuming optimization methods, deep learning (DL) is an effective approach in predicting the electromagnetic multipole response and realizing precise inverse design. However, current DL-assisted inverse design methods for arbitrary Mie scatterers suffer from limitations of prediction accuracy and generalizability due to the inherent constraints of incorporating induced-current-based Cartesian electromagnetic multipole expansion. Herein, we propose a deep neural network (DNN) based on dataset generated from spherical-harmonic-based electromagnetic multipole expansion, enabling precise and rapid forward prediction as well as inverse design of an arbitrary Mie scatterer with target electromagnetic multipole responses. The proposed DNN can not only predict the scattering cross section (SCS) of different electromagnetic multipoles, but also accurately resolve complex-valued multipole coefficients and far-field radiation patterns, simultaneously. Microwave experiments further consolidate the accuracy of the proposed inverse design method. It is anticipated that the demonstrated spherical-harmonic-based DNN could pave a new way for the inverse design of meta-atoms with versatile electromagnetic functionalities.

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• Electromagnetic interactions
• Metamaterials
• Mie scattering
• Deep learning
• Neural network simulations
• Radio frequency techniques