Deep learning to accelerate Maxwell's equations for inverse design of dielectric metasurfaces

The inverse design of optical metasurfaces is a rapidly emerging field that has already shown great promise in miniaturizing conventional optics as well as developing completely new optical functionalities. Such a design process relies on many forward simulations of a device's optical response in order to optimize its performance. We present a data-driven forward simulation framework for the inverse design of metasurfaces that is more accurate than methods based on the local phase approximation, a factor of $10^4$ times faster and requires $15$ times less memory than mesh based solvers, and is not constrained to spheroidal scatterer geometries. We explore the scattered electromagnetic field distribution from wavelength scale cylindrical pillars, obtaining low-dimensional representations of our data via the singular value decomposition. We create a differentiable model fiting the input geometries and configurations of our metasurface scatterers to the low-dimensional representation of the output field. To validate our model, we inverse design two optical elements: a wavelength multiplexed element that focuses light for $\lambda=633$nm and produces an annular beam at $\lambda=400$nm and an extended depth of focus lens.