Accelerating and enabling the design of complex diffractive gratings using physics-informed neural networks to evaluate scattering matrices

Diffractive gratings in waveguides are utilized in various applications, including telecommunications, quantum photonics, optical sensing, display technology for augmented reality devices and space applications. As demand for diffractive gratings with multiple desirable properties increases in waveguide design, more complex grating structures need to be investigated. The design spaces of these complex gratings increase exponentially with the number of physical grating parameters (such as grating depth, duty cycle, layer thicknesses, blaze angles etc.). The effect of these gratings on incident light is often stored in electromagnetic scattering/Jones matrices that are calculated using rigorous coupled-wave analysis (RCWA). Optimising gratings within a waveguide involves storing, evaluating and often interpolation of these scattering matrices, resulting in a computational bottleneck for higher-dimensional grating parameter spaces. To address this challenge, we introduce a highly efficient, parallelisable, and lightweight approach to evaluating scattering matrices using a physics-informed neural network (PINN). This PINN is trained on a data set of scattering matrices and importantly is differentiable, can be GPU-accelerated and penalizes non-physical outputs. In this paper, we provide an optimisation example that demonstrates an exponential speedup in simulation time for high-dimensional grating parameter spaces compared to conventional methods. For inverse design of optical devices involving complex diffractive gratings, this approach opens up a new regime of computationally feasible optimisations.