Inverse Design of Photonic Scattering Media with Multiscale Physics-Informed Neural Networks

There is an ever-increasing interest in utilizing deep learning (DL) and artificial intelligence (AI) approaches for engineering electromagnetic waves in complex media and inverse design functional optical materials. Emerging methods include training generative models of artificial neural networks (ANNs) to tackle inverse problems and estimate relevant material parameters. While traditional DL techniques have been effective in solving inverse design challenges, they remain fundamentally data-driven techniques that require extensive and time-consuming training procedures based on large datasets. To enhance these purely data-driven methods, it is important to incorporate the constraints that arise from the underlying physics of the problems within the physics-informed neural network (PINN) approach that has shown remarkable successes in the solution of complex scalar and vector problems with applications to parameter estimation, inverse scattering, and metamaterials design. Recently, the multiscale physics-informed neural network (MscalePINN) framework was introduced to overcome the implicit spectral bias of deep neural networks that quickly learn the low-frequency content of training datasets with good generalization error but struggle in the presence of high-frequency data. Here, we utilize the novel MscalePINNs approach to determine the effective dielectric permittivity of finite-size arrays of scattering nanocylinders and to inverse design photonic metamaterials. MscalePINNs convert the learning and approximation of high-frequency data to that of low-frequency ones, using different sub-networks that operate on down-shifted frequency contents, thus enabling accurate and efficient solutions. In this work, we show the applications of MscalePINNs to the high-frequency homogenization and inverse design of finite-size scattering arrays of dielectric nanocylinders in different aperiodic geometries that provide isotropic optical responses and control of focal fields at desired locations. Our work provides an efficient avenue for the design of inhomogeneous scattering media with effective properties that are important to implement low-loss mode transformation and control for on-chip imaging and integrated photonics devices in the near-infrared spectral range.