  Inverse design algorithms are the basis for realizing high-performance,
freeform nanophotonic devices. Current methods to enforce geometric
constraints, such as practical fabrication constraints, are heuristic and not
robust. In this work, we show that hard geometric constraints can be imposed on
inverse-designed devices by reparameterizing the design space itself. Instead
of evaluating and modifying devices in the physical device space, candidate
device layouts are defined in a constraint-free latent space and mathematically
transformed to the physical device space, which robustly imposes geometric
constraints. Modifications to the physical devices, specified by inverse design
algorithms, are made to their latent space representations using
backpropagation. As a proof-of-concept demonstration, we apply
reparameterization to enforce strict minimum feature size constraints in local
and global topology optimizers for metagratings. We anticipate that concepts in
reparameterization will provide a general and meaningful platform to
incorporate physics and physical constraints in any gradient-based optimizer,
including machine learning-enabled global optimizers.
