Wide-angle emission in cylindrical moiré lattices enabled by rolling origami

Twisted photonic lattices that form moiré superlattices have attracted significant attention owing to their unique properties, such as strong field confinement and high-quality factors, in which the localized optical modes can serve as efficient light sources. However, in conventional moiré lattices, the emission direction of confined modes is typically fixed, and achieving a broad range of emission angles through simple modulation remains a significant challenge. Here, we design and fabricate single-layer moiré photonic lattices into cylindrical geometries using a nanomembrane origami technique. This approach enables wide-angle localized-mode emission while maintaining stable single-mode operation and excellent spectral uniformity. The moiré supercells support localized flat-band modes under various effective twist angles, resulting in the observation of periodic localized-mode emission over a wide range of azimuthal angles. Our research provides an approach for developing moiré light sources on curved surfaces, offering significant potential in applications that demand spatial light control, including three dimensional imaging, light detection and ranging, and topological states manipulation.

💡 Research Summary

In this work the authors present a novel photonic platform that combines moiré superlattices with three‑dimensional cylindrical geometry to achieve wide‑angle emission from highly confined flat‑band modes. The device is fabricated by patterning two triangular nanohole lattices on a strained SiNₓ nanomembrane, then releasing the underlying Si sacrificial layer so that the membrane self‑rolls into a micro‑tube. By controlling the relative rotation (twist angle θ) between the two lattices during patterning, four effective twist angles—4.41°, 5.09°, 6.01°, and 7.34°—are realized, each giving a different moiré periodicity and unit‑cell size.

Full‑wave electromagnetic simulations (COMSOL Multiphysics) reveal that for all twist angles the moiré supercell supports a flat photonic band whose Bloch modes are strongly localized in the central air hole. The calculated mode areas shrink from 1.42 (λ/n)² to 1.05 (λ/n)² as the twist angle increases, indicating sub‑wavelength confinement and enhanced light‑matter interaction. The flatness of the band, quantified by ΔΩ = Ω/2π, grows from 1.86 THz at 4.41° to 11.56 THz at 7.34°, confirming the expected correlation between twist angle and band flattening.

Experimentally, the rolled‑up structures are probed with a confocal laser system. Spectra collected from the cylindrical moiré lattices display a single dominant peak in the 600–700 nm range with a full‑width at half‑maximum of 0.28 nm, corresponding to a quality factor Q ≈ 2.3 × 10³. Two‑dimensional intensity maps show that the localized mode resides within a single unit cell and repeats periodically along the tube axis, matching the designed lattice periodicity.

Angle‑dependent measurements are performed by tilting the incident beam from –30° to +30° relative to the substrate normal. Peak‑intensity maps for each twist angle reveal sharp angular dependence: the emission maximum shifts systematically with tilt, demonstrating that the same localized mode can be accessed over a wide azimuthal range. The intensity variation across all measured angles is less than 3 dB, indicating excellent spectral uniformity. Weak sidebands are observed, attributed to higher‑order dipole‑like modes, but they do not compromise the single‑mode character of the primary resonance.

The key enabling factors are (i) the curvature‑induced suppression of non‑local Floquet waves, which reduces radiative leakage and yields low mode volume, and (ii) the tunable inter‑layer coupling inherent to the moiré geometry. Because the SiNₓ refractive index (≈2.0) is lower than in previous high‑index moiré lattices, the intralayer coupling is weaker, allowing the flat‑band formation to be dominated by the twist‑controlled geometry rather than material contrast.

From a fabrication standpoint, the nanomembrane origami approach is compatible with batch processing, allowing the twist angle and orientation of each micro‑tube to be predefined on a wafer. The authors suggest that integrating gain media such as rhodamine dyes or quantum dots could turn these structures into on‑chip, angle‑tunable lasers. Potential applications include three‑dimensional imaging, LiDAR systems that require controllable beam steering without mechanical parts, and platforms for exploring topological photonic states on curved surfaces.

In summary, the paper demonstrates that a single‑layer moiré photonic lattice, when rolled into a cylindrical architecture, can support flat‑band localized modes with high Q, sub‑wavelength confinement, and emission that can be accessed over a broad range of azimuthal angles. This combination of spectral purity, spatial uniformity, and angular flexibility opens new avenues for integrated photonic devices where precise control of light directionality is essential.