Differential Shape Optimization with Image Representation for Photonic Design

Abstract: We propose a general framework for differentiating shapes represented in binary images with respect to their parameters. This framework functions as an automatic differentiation tool for shape parameters, generating both binary density maps for optical simulations and computing gradients when the simulation provides a gradient of the density map. Our algorithm enables robust gradient computation that is insensitive to the image's pixel resolution and is compatible with all density-based simulation methods. We demonstrate the accuracy, effectiveness, and generalizability of our differential shape algorithm using photonic designs with different shape parametrizations across several differentiable optical solvers. We also demonstrate a substantial reduction in optimization time using our gradient-based shape optimization framework compared to traditional black-box optimization methods.