Deep learning-assisted double strong coupling between multi-order anapoles and excitons

High-order anapoles present strongly concentrated energy and narrow resonance widths and thus become burgeoning candidates in nonlinear optical conversion and strong coupling fields. Nevertheless, existing studies are rarely focused on strong coupling simultaneously involving multi-order anapoles. Herein, we theoretically construct a three-layer stacked hybrid system with a Si nanodisk sandwiched by the MoSe₂ and MoTe₂ nanodisks with the same radius based on the neural network constructed by deep learning (DL). First-order and second-order anapoles are excited simultaneously in this system and couple with excitons of bulk MoTe₂ and MoSe₂ nanodisks, respectively. Double strong coupling behaviors are achieved between the first-order anapole and the exciton of MoTe₂ , as well as the second-order anapole and the exciton of MoSe₂, resulting in four energy branches with large Rabi splitting of 100.6 meV and 118.2 meV, respectively. Our work provides an effective approach for light-matter interaction involving multi-order anapoles and multiple excitons.