# A Dual Perspective On Inverse Design

For a wide range of technologically prescient applications---spanning from achieving low-power nonlinear response to mode-multiplexing in optical communication---device architectures discovered via computational methods increasingly demonstrate improved efficacity compared to “intuitive” designs. Nevertheless, in all but a handful of cases, how presently achievable performance metrics compare to what physics potentially allows is seldom clear. 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 computational approaches provide a reliable means of determining photonic components that come within some fraction of true global optimality, or, more pointedly, how their results are determined by the decisions of the programmer (e.g. fabrication constraints, choice of algorithm, material composition, etc.) as opposed to the physics of optics. In this talk, I will discuss how Lagrange duality heuristics for quadratically constrained quadratic optimization problems (QCQPs) can substantially lessen these knowledge gaps for various 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 empirical evidence that such dual-solutions’' are capable of predicting the results of large-scale inverse methods within an order of magnitude in several settings.