Inverse Design of Three-Dimensional Microwave Cavities for Optimizing Electromagnetic Helicity
We present a inverse-design framework framework for systematically engineering three-dimensional microwave cavity resonators that support modes with nonzero electromagnetic helicity. In contrast to heuristic approaches to cavity design, helicity maximisation is formulated as a boundary-shape optimisation problem, enabling systematic exploration of complex boundary-shape parameter spaces and the identification of high-helicity designs that are difficult to predict using heuristic design rules alone. We applied this framework to several cavity families composed of smooth, edge-free components, including globally twisted cavities with control-point-defined cross-sections realised in both linear and ring configurations, cavities defined by the intersection of orthogonal prisms, sphere-subtracted cylindrical cavities, and parametrised surface resonators. Two gradient-free optimisation strategies, a genetic algorithm and Bayesian optimisation, were independently employed to explore compact sets of design parameters for these geometries and to optimise a scaled-helicity figure of merit for the dominant helical mode, evaluated via finite-element eigenmode analysis. Robustness to manufacturing tolerances was quantified by applying Gaussian geometric perturbations to the optimised cavities and evaluating statistical robustness metrics that penalise sensitivity to geometric variation. The optimisation reveals clear physical design principles governing the generation of high electromagnetic helicity in three-dimensional microwave cavities.