Dynamically tuneable helicity in twisted electromagnetic resonators

TL;DR

This work demonstrates the real-time generation and tuning of electromagnetic helicity in a microwave cavity by geometrically twisting the conducting boundary to break mirror symmetry. The twist induces magnetoelectric coupling that hybrids near-degenerate TE and TM modes into helical states, with helicity governed by the twist angle and an emergent effective chirality $\kappa_{\text{eff}}$. Experimental validation on a twisted rectangular (WR-137) cavity, complemented by Möbius-resonator tests and FEM simulations, shows controllable helicity and frequency shifts, as well as strong photon-photon coupling between opposing helical modes. The findings offer a tunable platform for helicity-based applications in secure communications and adaptive microwave control, leveraging both bulk twist and surface corrugation to modulate resonance conditions and mode mixing.

Abstract

We report the generation of helical electromagnetic radiation in a microwave cavity resonator, achieved by introducing mirror asymmetry, i.e., chirality, through a controlled geometric twist of the conducting boundary conditions. The emergence of electromagnetic helicity is attributed to a nonzero spatial overlap between the electric and magnetic mode eigenvectors, quantified by $\text{Im}\left[\vec{\mathbf{E}}_i(\vec{r})\cdot{\vec{\mathbf{H}}}_i^*(\vec{r})\right]$, a feature not observed in conventional cavity resonators. This phenomenon originates from magnetoelectric coupling between nearly degenerate transverse electric (TE) and transverse magnetic (TM) modes, resulting in a measurable frequency shift of the resonant modes as a function of the twist angle, $φ$. In addition to the bulk helicity induced by global geometric twist, internal helical corrugations break structural symmetry on the surface, introducing an effective surface chirality $κ_{\text{eff}}$, which perturbs the resonant conditions and contributes to asymmetric frequency tuning. By dynamically varying $φ$, we demonstrate real-time, macroscopic manipulation of both electromagnetic helicity and resonant frequency. Furthermore, we investigate the underlying mode-coupling dynamics of the system, highlighting strong photon-photon interactions.

Figures (12)

• Figure 1: Geometry of the $\phi=\pi$ twisted cavity resonator with a WR-137 rectangular cross-section ($a=35.48$ mm, $b=16.1$ mm) and length $l=312.3$ mm.
• Figure 2: The transverse electric field, $\vec{E}_\perp$ (magenta), and the transverse magnetic field, $j\vec{H}_\perp$ (black) for (a) the $\psi_{2,1,0}^+$ mode and (b) the $\psi_{2,1,0}^-$ mode in the $2\pi$-twisted resonator. The corresponding fields for the TE$_{1,1,16}$ mode are shown for twist angles (c) $\phi = 0$ and (d) $\phi = \frac{10\pi}{9}$.
• Figure 3: The eigenfrequencies $f_i$ of the resonant modes in a rectangular resonator as a function of $\phi$. The solution colour represents $\mathscr{H}_i$. The frequency separation $\Delta f \approx 82~\text{MHz}$ between the TE$_{2,0,1}$ and TM$_{2,1,0}$ modes, which hybridise to form the helical states $\psi^\pm_{2,1,0}$, is marked by the arrow.
• Figure 4: $\mathbb{H}_i$ derived from FEM simulation of the $\psi_{2,1,0}^\pm$ modes in the twisted resonator as a function of both $\phi$ and $\kappa_\text{eff}$, revealing null points where $\mathscr{H}_i$ induced by $\phi$ is cancelled by $\kappa_\text{eff}$.
• Figure 5: Experimental setup for inducing a controlled twist in a helically corrugated rectangular resonator. (a) A rotary stage was used to apply mechanical rotation to one end of the resonator, while the other end remained fixed. The resonator was driven via coaxial probes inserted through the endcaps (b, c), with the lower probe (c) connected through a rotating connector (d) to prevent cable torsion during rotation.