qBIC: Quasi-Bound States in the Continuum

• qBICs are resonant modes that, despite lying within the radiation continuum, exhibit finite leakage due to weakly broken symmetries or interference effects.
• They are engineered by controlling geometry, permittivity distribution, or excitation conditions, enabling precise tuning of radiative quality factors.
• qBICs underpin practical applications from biosensing to nonlinear optics, leveraging their ultra-narrow spectral features and high performance.

Quasi-bound states in the continuum (qBICs) are resonant states whose eigenfrequencies lie inside the radiation continuum but whose coupling to radiation is only weakly allowed, so that an ideal non-radiating BIC is converted into a finite-linewidth, externally excitable, high-$Q$ resonance. In the recent literature, qBICs appear both as practical descendants of symmetry-protected BICs and as interference-mediated states of open systems, and they underpin narrow Fano resonances, electromagnetically induced transparency analogues, electro-optic modulation, nonlinear frequency conversion, biosensing, acoustic confinement, and many-body localization analogs (Berté et al., 2022, Mangach et al., 2024, Liu et al., 2024).

1. Concept and distinguishing characteristics

A BIC in the photonic/metasurface context is a mode whose eigenfrequency lies inside the radiation continuum but which nonetheless does not couple to outgoing plane waves, so it remains perfectly trapped and, in the idealized lossless and infinitely extended limit, has infinite radiative quality factor. A qBIC is the practical version obtained when the exact decoupling condition is weakly violated. Then the mode acquires a small but finite coupling to free space, appears in transmission or reflection spectra as a very narrow resonance, and has a finite but potentially very large $Q$ (Berté et al., 2022).

The contemporary qBIC literature distinguishes at least two major physical classes. One is the symmetry-protected qBIC, where a protecting parity or point-group relation is weakly broken and a previously dark state becomes weakly radiative. The other is the accidental or Friedrich–Wintgen variant, where radiation is suppressed by destructive interference among radiative channels rather than by a pure symmetry mismatch (Mangach et al., 2024). Related interference-induced forms also appear in Fabry–Perot-type acoustic systems, where two identical leaky resonators suppress one hybrid mode’s radiation by phase-controlled cancellation (Farhat et al., 2023), and in single deformed whispering-gallery-mode microcavities, where shared leaking continua allow external strong coupling and linewidth bifurcation between hybrid states (Liu et al., 2024).

In all of these cases, the adjective “quasi” is decisive. Real devices are finite, lossy, and imperfect. The recent literature repeatedly identifies finite structure size, angular spread of excitation, disorder, roughness, parasitic asymmetry, and intrinsic material absorption as mechanisms that prevent the mathematical $Q\to\infty$ limit from being observed directly (Berté et al., 2022).

2. Routes to qBIC formation

The canonical route is controlled symmetry breaking of a symmetry-protected BIC. In all-dielectric metasurfaces this is often achieved by in-plane geometric asymmetry. A representative example is the silicon cross-shaped trimer metasurface in which broken inversion symmetry is introduced by shifting one vertical bar along $y$, thereby converting a dark symmetry-protected state into a leaky qBIC that is excitable under normally incident $x$-polarized light (Ghahremani et al., 2024). Closely related logic appears in silicon pair-rod metasurfaces, where rod-length asymmetry $a=2\Delta L/L$ controls radiative leakage without strongly shifting the resonance wavelength (Watanabe et al., 2023), and in terahertz split-ring metasurfaces, where unequal slit openings break $C_2$ symmetry and convert an ideal BIC near $2.1~\text{THz}$ into a practical qBIC (Guo et al., 2 Apr 2026).

A major refinement of that picture is that geometry is not the only control parameter. One can keep the unit-cell geometry symmetric and instead break the in-plane symmetry of the permittivity distribution. This is the basis of the $\varepsilon$-qBIC or permittivity-asymmetric qBIC, demonstrated theoretically, numerically, and experimentally in Si/TiO$_2$ metasurfaces and later exploited for refractive-index sensing in TiO$Q$0 nanorod arrays with selective dielectric covering (Berté et al., 2022, Yang et al., 29 Aug 2025). A further extension replaces in-plane symmetry breaking by out-of-plane horizontal-mirror-symmetry breaking: $Q$1-broken qBICs are produced while the in-plane lattice symmetry remains rigorously intact, and the associated transition is linked to a Zak-phase inversion and quadrupole–dipole band inversion (Chen et al., 22 Jan 2026).

Other formation mechanisms broaden the concept beyond perturbative geometry/permittivity asymmetry. In finite waveguide grating couplers, beam divergence can activate qBIC resonances originating in BIC resonances forbidden for strict plane-wave normal incidence, so the excitation condition itself becomes part of qBIC formation (Yezekyan et al., 10 Feb 2025). In deformed microcavities, qBICs arise from continuum-mediated interference between distinct resonances sharing the same unidirectional radiation channel (Liu et al., 2024). In driven non-Hermitian nanophotonic cavities, an explicit excitation-phase degree of freedom can create a qBIC response even when conventional eigenvalue analysis would not predict one, and can even merge a qBIC spectrally with an exceptional point (Du et al., 8 Dec 2025).

3. Spectral signatures, multipolar structure, and scaling laws

qBICs are most often observed as ultranarrow spectral features embedded in broader backgrounds. In dielectric metasurfaces, this commonly takes the form of a Fano resonance or an EIT-like response produced by interference between a broad bright mode and a narrow nearly dark mode. One representative fitting model used for a qBIC-assisted transparency line is

$Q$2

with $Q$3 the resonance frequency, $Q$4 the linewidth, $Q$5 a transmission offset, $Q$6 a continuum–discrete coupling constant, and $Q$7 the Breit–Wigner–Fano asymmetry parameter (Ghahremani et al., 2024). Reflection-mode electro-optic qBIC metasurfaces exploit the same narrow-linewidth logic: a small Pockels-induced shift of the resonance wavelength then produces a large reflectance change at fixed wavelength (Damgaard-Carstensen et al., 2024).

The quality factor is often extracted from the complex eigenfrequency,

$Q$8

or from spectral linewidth. A recurring result across the literature is inverse-square scaling between $Q$9 and the symmetry-breaking amplitude. In geometric metasurfaces, $Q\to\infty$0 with $Q\to\infty$1 or equivalent asymmetry measures (Ghahremani et al., 2024). In permittivity-asymmetric systems, the radiative quality factor obeys

$Q\to\infty$2

which is the material-asymmetry analogue of the geometric law (Berté et al., 2022). In qBIC-driven polaritonic-vortex metasurfaces, the radiative quality factor scales as

$Q\to\infty$3

with $Q\to\infty$4 the checkerboard displacement used to open the radiative channel (Baù et al., 29 May 2026).

Multipolar analysis shows that qBICs are rarely simple dipolar resonances. In the silicon cross-shaped trimer metasurface, the bright broadband background is an electric-dipole mode mainly associated with the horizontal bar, whereas the qBIC is governed by magnetic dipole and electric quadrupole contributions supplied by distinct parts of the dielectric “molecule” (Ghahremani et al., 2024). In the silicon metasurface supporting both accidental and symmetry-protected qBICs, the reported mechanism involves the interplay among out-of-plane electric and magnetic dipoles together with in-plane quadrupoles of odd parity (Mangach et al., 2024). In the terahertz split-ring sensor, the radiative qBIC channel is dominated by electric-dipole and magnetic-dipole interference, while higher-order terms remain suppressed (Guo et al., 2 Apr 2026).

4. Platforms, geometries, and extensions of momentum-space support

The dominant qBIC platform remains the dielectric metasurface or photonic slab. Recent examples include silicon cross-shaped trimers on SiO$Q\to\infty$5 (Ghahremani et al., 2024), asymmetric silicon pair-rods on SOI (Watanabe et al., 2023), TiO$Q\to\infty$6 nanorod dimers with environmental permittivity asymmetry (Yang et al., 29 Aug 2025), low-contrast silicon metasurfaces operating in liquid (Watanabe et al., 12 Mar 2026), and lithium-niobate-on-gold electro-optic reflective metasurfaces (Damgaard-Carstensen et al., 2024). The underlying geometries range from disconnected dimers to physically connected trimers, shallow-etched low-contrast gratings, and metallic-electrode-loaded guided-wave structures.

Grating and slab implementations show that qBIC support need not be confined to an isolated $Q\to\infty$7-point. A binary ridge grating on a slab waveguide supports what is explicitly called a one-dimensional qBIC family: a continuous high-$Q\to\infty$8 branch in $Q\to\infty$9 space whose normal-incidence point is an ideal BIC and whose off-normal states are qBICs (Sun et al., 2022). A photonic slab consisting of a square array of aluminum nanodisks supports a “quasi-bound band in the continuum” extending along the $y$0-X direction, with narrow linewidth maintained through at least half of the Brillouin zone (Tsoi et al., 5 Nov 2025). A more radical generalization is the “quasi-bound flat band in the continuum,” where every Bloch mode on a flat band above the light line behaves like a qBIC because disorder-induced localization, band folding, and multiple topological charges suppress radiation across the entire band (Qin et al., 7 Nov 2025).

Finite structures also preserve qBIC behavior in nontrivial ways. Photonic crystal slabs with only two or three unit cells can sustain qBIC microcavity modes, and a four-unit-cell three-dimensional cavity was reported with $y$1 in a footprint below $y$2 (Taghizadeh et al., 2017). Finite waveguide grating couplers show that realistic beam size, beam offset, and Bragg-reflector extent can reshape which qBIC resonances are visible under laboratory excitation conditions (Yezekyan et al., 10 Feb 2025).

The concept is no longer limited to periodic optical metasurfaces. A single Limaçon-shaped Si$y$3N$y$4 microdisk can host a Friedrich–Wintgen qBIC through continuum-mediated interference between different whispering-gallery-like modes, with more than a threefold enhancement of $y$5 and $y$6 for the long-lived branch (Liu et al., 2024). An underwater ultrasound resonator made of two coupled silicon slit metasurfaces realizes an acoustic qBIC near $y$7 with experimental $y$8–$y$9 (Farhat et al., 2023). In a distinct many-body direction, the interaction-modulated Bose–Hubbard model supports a three-boson hybrid state under periodic boundary conditions that is explicitly identified as a quasi-BIC: a bound pair localized within the standing wave of a third particle (Huang et al., 2023). This suggests that qBIC has become a cross-platform organizing concept rather than a purely photonic specialty.

5. Functional roles and application domains

Sensing and biosensing are the most developed application area. Cross-shaped silicon trimers were used to realize qBIC-assisted metamaterial-induced transparency with reported refractive-index sensitivities of $x$0 for $x$1 and $x$2 for $x$3, while the sensing figure of merit exceeded $x$4 in the weak-asymmetry regime (Ghahremani et al., 2024). In permittivity-asymmetric TiO$x$5 metasurfaces, the environment itself modulates the qBIC asymmetry factor, producing both resonance shift and modulation-depth change; the reported single-wavelength transmittance sensitivity is about $x$6/RIU, the linear-response operating point reaches $x$7, and the linear window area is approximately $x$8 times larger than that of the geometry-asymmetric comparator (Yang et al., 29 Aug 2025). Low-contrast silicon qBIC metasurfaces in heavy water achieved an experimental $x$9 factor of $a=2\Delta L/L$0 and resolved step-like $a=2\Delta L/L$1 shifts caused by single $a=2\Delta L/L$2 polystyrene particles (Watanabe et al., 12 Mar 2026). In the terahertz domain, a gold-on-quartz split-ring qBIC sensor reported refractive-index sensitivity up to $a=2\Delta L/L$3 and cysteine detection down to $a=2\Delta L/L$4 (Guo et al., 2 Apr 2026).

Nonlinear optics and vibrational strong coupling use the same high-$a=2\Delta L/L$5 but externally addressable character. One-dimensional qBICs distributed continuously in $a=2\Delta L/L$6 space enabled angle-selectable dual-resonant excitation in x-cut LiNbO$a=2\Delta L/L$7, with a reported sum-frequency-generation enhancement factor of $a=2\Delta L/L$8 relative to a bare film of the same thickness (Sun et al., 2022). In SOI silicon pair-rod metasurfaces, the qBIC linewidth is tuned through asymmetry while the mode stays nearly resonant with the PMMA C=O vibrational line, producing anti-crossing and a measured Rabi splitting of $a=2\Delta L/L$9 at $C_2$0 (Watanabe et al., 2023).

Dynamic modulation is another major direction. Reflection-mode lithium-niobate qBIC metasurfaces based on the Pockels effect achieved modulation depth reaching $C_2$1, corresponding to modulation of $C_2$2 of the total incident power, under $C_2$3 bias within an electrical bandwidth of $C_2$4 (Damgaard-Carstensen et al., 2024). The same work used the strong angle dependence of the qBIC resonance for electrically tunable phase-contrast imaging.

More specialized functions have also appeared. Chiral q-BIC metasurfaces extend resonance selectivity from linear eigenpolarizations to arbitrary elliptical states and support wavefront shaping with simulated diffraction efficiency $C_2$5 in anomalous reflection for the selected spin channel (Overvig et al., 2020). qBIC-driven dielectric metasurfaces covered by hBN generate deeply subwavelength hyperbolic-phonon-polariton vortices locked to a single orbital angular momentum, with HPhP wavelengths around $C_2$6–$C_2$7 times smaller than the incident light (Baù et al., 29 May 2026). In microcavities, qBIC formation is used as a loss-engineering tool rather than a spectral filter: continuum-mediated interference redistributes linewidth so that one branch narrows while its partner broadens (Liu et al., 2024).

6. Design trade-offs, limitations, and common misconceptions

A frequent misconception is that qBIC engineering is synonymous with maximizing $C_2$8. The recent literature repeatedly shows that the best operating point is often not the smallest asymmetry. In the terahertz split-ring biosensor, the selected design parameter is $C_2$9, chosen by maximizing the optimization metric $2.1~\text{THz}$0, which reached $2.1~\text{THz}$1 at that point (Guo et al., 2 Apr 2026). In the PMMA vibrational-coupling platform, the enhanced molecular signal is non-monotonic in asymmetry and is maximized near $2.1~\text{THz}$2, not at the highest-$2.1~\text{THz}$3 limit (Watanabe et al., 2023). In low-contrast silicon nanoparticle sensors, the experimentally optimal point is the critical-coupling asymmetry $2.1~\text{THz}$4, where radiative and non-radiative $2.1~\text{THz}$5 factors are balanced (Watanabe et al., 12 Mar 2026).

A second misconception is that qBICs are always point-like in momentum space. Recent work explicitly contradicts that picture: one-dimensional qBICs occupy a continuous dispersive line in $2.1~\text{THz}$6 space (Sun et al., 2022), qBBC states occupy a narrow band along $2.1~\text{THz}$7-X (Tsoi et al., 5 Nov 2025), and quasi-BFICs distribute quasi-BIC behavior across a flat band above the light line (Qin et al., 7 Nov 2025). This suggests that isolated high-symmetry-point qBICs are only one part of a broader design landscape.

A third misconception is that qBICs are controlled only by in-plane geometry asymmetry. The present literature includes in-plane permittivity asymmetry (Berté et al., 2022), environmental permittivity asymmetry (Yang et al., 29 Aug 2025), out-of-plane $2.1~\text{THz}$8-breaking with in-plane symmetry preserved (Chen et al., 22 Jan 2026), finite-beam and finite-angle activation of nominally forbidden resonances (Yezekyan et al., 10 Feb 2025), continuum-mediated interference in a single deformed cavity (Liu et al., 2024), and excitation-phase-controlled qBIC responses in driven non-Hermitian cavities (Du et al., 8 Dec 2025). The broader lesson is that qBICs are symmetry-controlled leakage resonances of the full open system, not merely of its lateral shape.

Limitations remain substantial. The highest predicted $2.1~\text{THz}$9 factors are routinely reduced by finite size, angular spread of the incident field, surface roughness, parasitic asymmetry, Ohmic loss, and disorder (Berté et al., 2022, Yezekyan et al., 10 Feb 2025, Farhat et al., 2023). Claims of robustness are also mechanism-specific rather than universal. The accidental qBIC in a silicon metasurface was reported to maintain $\varepsilon$0 against substantial symmetry and geometric variation, while the symmetry-protected branch approached $\varepsilon$1 but depended directly on unit-cell symmetry disruption (Mangach et al., 2024). The $\varepsilon$2-broken topological qBIC literature reports $\varepsilon$3 together with a defect-immune regime, but only within a particular topological band-inversion scenario (Chen et al., 22 Jan 2026). The quasi-BFIC literature explicitly uses disorder as a resource, yet only mirror-symmetric disorder with an optimal disorder strength near $\varepsilon$4 produced the highest generation probability for high-$\varepsilon$5 flat bands (Qin et al., 7 Nov 2025).

Taken together, these results define qBIC as a family of controllably leaky, high-$\varepsilon$6, continuum-embedded resonances whose behavior is set by how symmetry, interference, material loss, finite size, and external driving jointly regulate access to radiation channels. That breadth, rather than any single geometry or scaling law, now characterizes the subject.