Automatic Differentiation Accelerated Shape Optimization Approaches to Photonic Inverse Design in FDFD/FDTD

Abstract

Shape optimization approaches to inverse design offer low‐dimensional, physically‐guided parameterizations of structures by representing them as combinations of primitives. However, on fixed grids, computing the gradient of a user objective via the adjoint variables method requires a product of forward/adjoint field solutions and the Jacobian of the simulation material distribution with respect to the structural shape parameters. Shape parameters often perturb global parts of the simulation grid resulting in many non‐zero Jacobian entries. These are often computed by finite‐difference (FD) in practice, and hence can be non‐trivial. In this work, the gradient calculation is accelerated by invoking automatic differentiation (AD) in instantiations of structural material distributions, enabled by the development of extensible differentiable feature‐mappings from parameters to primitives and differentiable effective logic operations (denoted AutoDiffGeo or ADG). ADG can also be used to accelerate FD‐based shape optimization by efficient boundary selection. AD‐enhanced shape optimization is demonstrated using three integrated photonic examples: a blazed grating coupler, a waveguide transition taper, and a polarization‐splitting grating coupler. The accelerations of the gradient calculation by AD relative to FD with boundary selection exceed 10, resulting in total optimization wall time accelerations of – on the same hardware with no compromise to device figure‐of‐merit.