Twist-Tuned Strong Coupling in Sub-GHz Wire Metasurface Bilayers

TL;DR

This work tackles twist-angle control in sub-GHz resonant metasurfaces using a double-layer wire metasurface (DLWM) where the in-plane rotation $φ$ and interlayer separation $G$ govern near-field coupling. A minimal two-resonator LC model with mutual inductance $M(φ,G)$ and mutual capacitance $C_m(φ,G)$ explains twist-driven spectral dispersion, while one-port $S_{11}$ measurements and full-wave simulations reveal bias-free, large-tunability in the strong-coupling regime and moiré-like magnetic near-field textures. Key results include normalized coupling up to $g≈0.43$ and cooperativity $C>1$ over broad angles, plus a continuous redshift of the lowest resonance from about $409$ MHz to $210$ MHz in the small-$G$ regime, corresponding to an electrical size $ρ=2Lf_{res}/c ≈ 0.49$. The near-field origin is reinforced by the collapse of tunability at large $G$, and the work demonstrates bias-free, twist-programmable sub-GHz resonators/filters with scalable potential for printed implementations and multilayer stacks, accompanied by moiré-like magnetic textures and an electromagnetic superperiod $Λ_{EM}$.

Abstract

Twist-angle control offers a bias-free route to reconfigurable metasurfaces, yet its extension to deeply subwavelength resonant platforms at VHF/UHF remains limited. We demonstrate a sub-GHz double-layer wire metasurface formed by two identical wire grids separated by a gap G, with in-plane rotation angle as the sole tuning parameter. One-port, loop-coupled S11 measurements supported by full-wave simulations reveal twist-driven hybridization of the dominant resonant manifold. For small G, the lower hybrid resonance redshifts continuously from 409 MHz to 210 MHz (2:1 tuning), enabling compact, twist-programmable resonant surfaces. Simulations further show that twisting imprints moire-like magnetic near-field super-modulations. From resonance frequencies, linewidths, and normal-mode splitting extracted from the complex response, we obtain normalized coupling up to g = 0.43 with cooperativity exceeding unity over broad angular ranges, meeting the resolved-splitting criterion. The rapid collapse of tunability at larger G confirms the near-field origin of the interaction.

Figures (6)

• Figure 1: Twist-controlled double-layer wire metasurface (DLWM) platform and operating concept. (a) Sketch of the macroscale prototype showing two identical copper-wire grids (each with $N_w=31$ wires of length $L=350~\mathrm{mm}$, radius $r=0.9~\mathrm{mm}$, and in-plane period $a\approx5~\mathrm{mm}$) separated by a low-permittivity foam spacer of thickness $G$ ($\varepsilon_r\approx1.05$). The top grid is rotated in-plane by the twist angle $\phi$ relative to the bottom grid. (b) Schematic of the measurement and the two key twist-enabled effects explored in this work: twist-dependent hybridization (mode splitting/dispersion in the one-port $S_{11}$ response) and twist-programmable magnetic near-field super-modulation. The two grids lie in planes $z=\pm G/2$. For a fixed spacer thickness $G$, the only in-situ tuning knob is the relative rotation $\phi$; varying $G$ is used to access weak- and strong-coupling regimes. We exploit the symmetry $S_{11}(f,\phi)=S_{11}(f,-\phi)=S_{11}(f,\phi+\pi)$ and therefore restrict $\phi\in[0,\pi/2]$.
• Figure 2: Twist-controlled hybridization using the two-resonator model (Eqs. \ref{['eq:omega_pm']}--\ref{['eq:Omega_envelope']}). (a) Predicted modal branches $f_{\pm}(\phi)$ for a strong-coupling gap ($G=2$ mm) and a weak-coupling gap ($G=30$ mm). (b) Corresponding resolved splitting $\Omega_{\mathrm{res}}(\phi)$. Parameters are chosen for the present structure scale ($L=350$ mm, $a\approx 5$ mm) to reproduce the observed order-of-magnitude tuning and to highlight the collapse of twist tunability with increased separation.
• Figure 3: Plane-wave simulation of twist-dependent hybridization and near fields for $G=2$ mm. (a) Peak magnetic-field enhancement at the mid-gap plane $z=0$ versus frequency for several twist angles. (b) Representative $F_H$ maps and (c) $F_E$ maps at selected resonant frequencies. Twist induces hybridized resonances and programmable moiré-like magnetic super-modulations; in the text, the dominant superperiod $\Lambda_{\mathrm{EM}}$ is obtained directly from the fringe spacing of $F_H$ (e.g., from line cuts or autocorrelation) and compared to the geometric scale $\Lambda_{\mathrm{geo}}$.
• Figure 4: One-port characterization in the strongly coupled (small-gap) regime, $G\approx3$ mm. (a) Measured referenced $S_{11}$ for representative twist angles. (b) Loop-driven full-wave simulations (emulating the probe geometry in Fig. \ref{['fig:dlwm_schematic']}(b)) reproduce the main twist-dependent spectral trends; residual fine-structure differences are attributed to probe position/height tolerances and environment-dependent interference pathways.
• Figure 5: Suppression of twist tunability in the weak-coupling (large-gap) regime, $G\approx30$ mm. (a) Measured referenced $S_{11}$ shows that the dominant resonance is largely insensitive to twist. (b) Loop-driven simulations reproduce the same collapse of twist tunability at large separation, confirming the near-field origin of the interaction.