Large area optimization of meta-lens via data-free machine learning

Sub-wavelength diffractive optics meta-optics present a multi-scale optical system, where the behavior of constituent sub-wavelength scatterers, or meta-atoms, need to be modelled by full-wave electromagnetic simulations, whereas the whole meta-optical system can be modelled using ray/ wave optics. Current simulation techniques for large-scale meta-optics rely on the local phase approximation (LPA), where the coupling between dissimilar meta-atoms are completely neglected. Here we introduce a physics-informed neural network, which can efficiently model the meta-optics while still incorporating all of the coupling between meta-atoms. Unlike existing deep learning techniques which generally predict the mean transmission and reflection coefficients of meta-atoms, we predict the full electro-magnetic field distribution. We demonstrate the efficacy of our technique by designing 1mm aperture cylindrical meta-lenses exhibiting higher efficiency than the ones designed under LPA. We experimentally validated the maximum intensity improvement (up to $53\%$) of the inverse-designed meta-lens. Our reported method can design large aperture $(\sim 10^4-10^5\lambda)$ meta-optics in a reasonable time (approximately 15 minutes on a graphics processing unit) without relying on any approximation.