Optimising Microwave Cavities for nonzero Helicity with Machine Learning

TL;DR

This work addresses the challenge of designing fully 3D microwave cavities that support modes with nonzero electromagnetic helicity by formulating helicity maximisation as a boundary-shape optimisation problem. It introduces a machine-learning-driven inverse-design framework that couples Python with COMSOL to evaluate a helicity-based fitness $F(\mathbf{x})=|\mathscr{H}_m|$ and employs gradient-free searches—genetic algorithms and Bayesian optimisation—to explore compact, manufacturable geometries. Across five edge-free cavity families, the framework uncovers geometries with high $|\mathscr{H}_i|$ and favorable surface-loss metrics, notably edge-free twisted rings that achieve $|\mathscr{H}_i|\approx 1.47$ with strong robustness, while other geometries reveal trade-offs between helicity, surface losses, and tolerance to perturbations. The results demonstrate a scalable path toward chirality-engineered, low-loss microwave resonators compatible with additive manufacturing, with potential applications in enantioselective spectroscopy, parity-violation experiments, and axion haloscopes; the method itself is adaptable to other objectives and more complex multi-parameter optimisations.

Abstract

We present a machine-learning-driven inverse design 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.

Figures (6)

• Figure 1: Block diagram of the inverse design framework used in this work to optimise microwave cavity geometries for electromagnetic helicity, $\mathscr{H}$. A COMSOL Multiphysics®comsol_multiphysics_v6.4 model file containing the parameterised cavity geometry, material properties, physics interfaces, and mesh is loaded into a COMSOL model instance via an MPh MPH client using the COMSOL Java API. A normalised design vector $\mathbf{x}\in[-1,1]^d$, generated by the optimisation algorithm, is mapped to physical geometric parameters and injected into the model. An eigenfrequency study is executed, yielding a set of cavity eigenmodes $\{i\}$, where $i$ indexes individual eigenmodes, with corresponding eigenfrequencies $\{f_i\}$ and $k$ number of post-processing volume integrals $\{I_{k,i}\}$. For eigenmodes with real $f_i \in [1,20]~\mathrm{GHz}$, the FoM $F(\mathbf{x}) = |\mathscr{H}_m|$, where $m$ denotes the most helical mode in the retained set, is computed and returned to the optimisation routine, closing the optimisation loop.
• Figure 2: (A) GA-optimised EF twisted linear cavity geometry and (B) its corresponding $h_i(\vec{r})$ field distribution. (C) BO-optimised cavity and (D) its corresponding $h_i(\vec{r})$ field distribution. (E) GA-optimised expanded-radius variant and (F) its corresponding $h_i(\vec{r})$ field distribution. (G) Histogram of $\sigma_{\text{pred}}$ across 2,000 random points in the 10D input space.
• Figure 3: (A) The optimised EF twisted ring cavity and (B) its $h_i(\vec{r})$ field distribution.
• Figure 4: (A) Two infinitely long, untwisted waveguides whose cross-sectional boundaries define (B) the optimised orthogonal prism-intersection cavity. (C) The corresponding $h_i(\vec{r})$ field distribution.
• Figure 5: (A) GA-optimised cavity based on sphere-subtracted sculpted cylinders and (B) its corresponding $h_i(\vec{r})$ field distribution. (C) BO-optimised cavity and (D) its corresponding $h_i(\vec{r})$ field distribution. (E) Histogram of $\sigma_{\text{pred}}$ across 2,000 random points in the 26D input space.