Freeform inverse design in photonics by re-thinking the question

Recent developments in computational freeform inverse design have provided a fertile landscape of structures and topologies for nanophotonics. However, simply dumping millions of parameters into a simulation can easily lead to intractable computational problems. Fortunately, a given engineering problem often admits many different mathematical formulations, and by carefully matching the formulation to the available electromagnetic solvers and optimization algorithms one can set the stage for extraordinarily flexible automated design. In this talk, we will show that, with careful consideration and reformulation of the design problem, powerful inverse design techniques can be successfully applied to a multitude of interesting problems with rich physical behavior, ranging from light confinement in nonlinear multi-resonant cavities, robust bandgap maximization in 3D photonic crystals to beam-forming and manipulation through multi-layered metasurfaces.