S4 Symmetry Yields Defect-Tolerant Terahertz Quasi-Bound States in the Continuum

Researchers have demonstrated a bilayer terahertz metasurface built on S4 point-group symmetry that supports robust quasi-bound states in the continuum (QBICs), offering a route to high-quality-factor photonic devices that tolerate the fabrication errors that typically cripple conventional designs. The work, published in National Science Review, combines group-theoretical analysis, simulations, and terahertz time-domain spectroscopy measurements.

Bound states in the continuum are resonant modes that, despite lying within the open radiation continuum, remain perfectly confined with near-zero radiation loss and theoretically infinite quality factors. Symmetry-protected BICs are especially attractive because breaking their protecting symmetry converts them into quasi-BICs whose Q-factors can be tuned, a property valued for lasers, filters, and sensors. Most current research, however, focuses on monolayer metasurfaces with in-plane C2 symmetry, where even slight fabrication defects cause severe Q-factor degradation and narrow usable parameter windows. Multilayer architectures that add out-of-plane degrees of freedom often demand ultra-high-precision nanofabrication, with processing deviations directly degrading device performance.

The new design consists of two identical monolayer metasurfaces rotated 90 degrees relative to each other along the z-axis, combined with broken inversion symmetry. When the two upper elliptical cylinders are parallel to each other (θ = 0°), S4 symmetry is satisfied and two discrete dark modes—symmetry-protected BICs—form. Introducing an angular perturbation that breaks S4 symmetry transforms both ideal BICs into QBICs, producing characteristic sharp Fano resonance dips in the transmission spectrum. Through group-theoretical selection rules together with scattering matrix and effective Hamiltonian analysis, the team clarified the distinct physical roles of S4 and its C2(z) subgroup: S4 simultaneously protects two sets of BIC modes at the overall representation level, while C2(z) independently suppresses radiation within each layer—an effect that does not rely on interlayer interference.

At the Γ-point, the free-space continuum belongs to the two-dimensional degenerate E representation of S4, while the TM1 and TM2 modes correspond to one-dimensional irreducible representations A and B, with characters +1 and −1 under S4 respectively. According to the Wigner–Eckart theorem, the mode–radiation channel overlap integrals are strictly zero, yielding dual BIC modes. The Q-factors evolve with the asymmetry parameter α = sinθ following the inverse-square power law Q ∝ α⁻², consistent with the classical BIC-to-QBIC transition. Near the Γ-point, the two modes exhibit counter-winding polarization distributions carrying topological charges of −1 and +1.

To test robustness against realistic nanofabrication errors, the researchers simulated lateral interlayer displacement, a common alignment error. Within a wide tolerance range of |Dx| ≤ 42 μm, the resonance frequency shifts of both QBICs remained below 0.01 THz, with relative fluctuations under 0.33%, and Q-factors stayed stably above 10². This avoids the order-of-magnitude Q-factor collapse observed in conventional structures under comparable perturbations, substantially relaxing the precision requirements for micro- and nanodevice fabrication. Multipole decomposition analysis revealed why the structure resists misalignment: QBIC1 is dominated by magnetic dipole resonance and QBIC2 by electric quadrupole resonance, distinct local electromagnetic responses that collectively endow the bilayer architecture with its misalignment immunity.

The team then fabricated three bilayer metasurface samples with different interlayer misalignments—zero offset, a left shift of −15 μm, and a right shift of 20 μm—and characterized them using terahertz time-domain spectroscopy. Even under these significant interlayer offsets, the measured spectra clearly showed double-resonance transmission dips, in close agreement with the simulation predictions. Beyond the immediate terahertz demonstration, the researchers report that the design addresses the poor robustness and extremely narrow fabrication tolerance of conventional QBICs and contributes to understanding the physical essence of symmetry-protected BIC generation in three-dimensional configurations. By coupling in-plane rotation with out-of-plane reflection, the S4 approach extends traditional monolayer in-plane symmetry concepts to multilayer architectures without demanding ultra-high-precision nanofabrication, pointing toward fabrication-defect-tolerant high-performance photonic devices built on symmetry protection principles.

Subject of Research: Symmetry-protected bound states in the continuum in an S4 point-group bilayer terahertz metasurface with fabrication-defect tolerance

Article Title: S4 point-group terahertz metasurface realizes robust quasi-bound states in the continuum

Article References: S4 point-group terahertz metasurface realizes robust quasi-bound states in the continuum. Original publication (Bibliographic details unavailable.)

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DOI: Not provided

Keywords: terahertz metasurface, bound states in the continuum, S4 point-group symmetry, quasi-BIC, Fano resonance, quality factor, topological charge, fabrication tolerance, terahertz time-domain spectroscopy, multipole decomposition, bilayer photonic structure, National Science Review