Bounds as blueprints: towards optimal and accelerated photonic inverse design

In pursuit of optimal photonic designs, substantial progress has been made on two complementary fronts: bottom-up structural optimizations (inverse design) discover complex high-performing structures but offer no guarantees of optimality, while top-down field optimizations (convex relaxations) reveal fundamental performance limits but offer no guarantees that structures meeting these limits exist. We bridge the gap between these two parallel paradigms by presenting a ``verlan'' method that exploits local and global wave information encoded in performance bounds to guide inverse design towards better-performing structures.