Physics-data hybrid-driven neural network for radiation-pattern analysis of optical nanostructures

Far-field radiation pattern is a pivotal metric for characterizing the electromagnetic response of dielectric nanostructures. Traditional full-wave numerical methods, including the finite-difference time-domain (FDTD) method, suffer from high computational cost, whereas pure data-driven deep learning models with limited physical interpretability and fixed angular resolutions require large-scale labeled datasets. Herein, we propose a physics-data hybrid-driven neural network (PDHDNN) that integrates exact multipole expansion, including the electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole, as a physical prior for fast and accurate radiation-pattern prediction of silicon nanostructures in the optical near-infrared band. The PDHDNN maps structural parameters and frequencies to low-dimensional multipole moments through neural networks and synthesizes the far-field radiation pattern through a physics-constrained multipole-superposition layer. The predicted total scattering cross sections and radiation patterns agree well with FDTD results, showing low relative errors and high normalized correlation coefficients at resonance peaks. At 1° angular resolution, the PDHDNN reduces data storage by 99.83% and shortens training time by 92.6% compared with a conventional pure data-driven network, while enabling arbitrary-resolution radiation-pattern prediction. This work provides an interpretable, low-cost, and efficient surrogate model for nanophotonic radiation analysis and shows potential for the intelligent design of all-dielectric nanophotonic devices.