Dynamically tuneable helicity in twisted electromagnetic resonators

TL;DR

The paper demonstrates dynamic control of electromagnetic helicity in a microwave Möbius resonator by twisting the conducting boundary, breaking mirror symmetry to induce spin-redirection Berry phases in TE1,0,n modes. Using the Wilczek–Zee non-Abelian holonomy framework, it shows that magnetoelectric coupling between nearly degenerate TE/TM modes yields geometric phases $\Pi_{(n,j)}$ that shift resonant frequencies with the twist angle, linking $\Pi_{(n,j)}$ to measurable frequency shifts via the group velocity. The authors derive explicit analytical and experimental formulas for $\Pi_{(n,j)}$, validate them with FEM simulations and 3D-printed aluminum resonators of $D_3$ and $D_2$ geometries, and reveal two distinct Berry phases of $\pm\frac{2\pi}{3}$ in a single cavity, while higher-order modes may show no Berry phase. This work demonstrates real-time, macroscopic control of photonic helicity and mode dynamics in topologically structured resonators, with implications for robust photonic devices and topological photonics applications.

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 (21)

• Figure 1: Examples of the geometries considered; (a) the $D_3^1{}_A$ resonator, (b) the $D_3^1{}_S$ resonator and (c) the $D_3^0{}_S$ resonator.
• Figure 2: The cross-section of the FEM simulated $D_3^0{}_S$ resonator showing the charge on the surface and electric field pattern in the bulk of the resonator for the TE$_{1,0,n}$ modes that have preferentially built up charge on the (a) inner surface of the resonator and (b) the outer surface of the resonator, resulting in a non-degenerate doublet pair. This doublet splitting defines the spectral gap within which the fractional modes of the twisted $D_3^1{}_A$ and $D_3^2{}_A$ resonators shift into as a result of the accumulated $\Pi_{(n,j)}$.
• Figure 3: The surface plots of $|\mathbf{K}_{\beta\perp}|$ for the (a) TE$_{1,0,15\frac{2}{3}}$ mode in the $D_3^1{}_A$ resonator and the (b) TE$_{1,0,16}$ mode in the $D_3^0{}_S$ resonator. The number of antinodes are shown: for the $D_3^1{}_A$ resonator, a closed loop requires three windings, each contributing 2$n$ antinodes, yielding a total of 6n; for the $D_3^0{}_S$, one winding suffices, giving 2$n$ antinodes. (c) The modal spectrum of the TE$_{1,0,n}$ modes as a function of $n$ for the $D_3^1{}_A$ and $D_3^0{}_S$ resonators.
• Figure 4: The eigenfrequencies of the $D_3^0{}_S$ and $D_3^1{}_S$ resonators as a function of axial mode number $n$ for the TE$_{1,0,n}$ modes.
• Figure 5: $\Pi_{(n,j)}$ as a function of $n$ for the TE$_{1,0,n}$ modes in the $D_3^1{}_A$ resonator for $R=23.67$ mm (simulated and experimental) and $R=79.58$ mm (simulated), with associated $\mathscr{H}_n$ depicted by colour. Asymptotic limits of $\pm2\pi/3$ are shown as black lines. Error bars on the experimental results represent systematic errors.