Title: Duality in Inverse Design
When: Thursday, May 18, (2023), 16:00 CEST
Chair: Antonio I. Fernández-Domínguez
Speaker: Sean Molesky, Polytechnique Montreal, Canada.
For a variety of forward looking applications—spanning from achieving low-power nonlinear response to modal multiplexing for optical communication—device architectures discovered via computational methods increasingly demonstrate improved efficacy compared to “intuitive” structures. Nevertheless, in all but a handful of cases, how presently achievable performance metrics compare to what physics potentially allows is unclear. Even when fundamental considerations are known to somehow restrict attainable device characteristics, well-known limits rarely incorporate sufficient practical detail to accurately estimate what can be engineered. Moreover, it is far from certain that current computational approaches provide a reliable means of determining photonic components that come within some fraction of true global optimality, or, more pointedly, how results are determined by the decisions of the programmer (e.g. fabrication constraints, choice of algorithm, material composition etc.) as opposed to underlying physics.
In this talk, I will discuss how Lagrange duality heuristics for quadratically constrained quadratic optimization problems (QCQPs) can bridge these knowledge gaps for a variety of common photonic design problems. As showcased by initial applications to topics including radiative emission from a dipolar current source and toy “math-kernel” field conversion objectives, I will also offer computational evidence that such dual-solutions are capable of predicting the results of large-scale inverse methods to within an order of magnitude in several settings.