---
title: Quasi-BICs in Photonics and Beyond
url: https://www.emergentmind.com/topics/quasi-bound-states-in-the-continuum-quasi-bics
type: topic
---

# Quasi-BICs in Photonics and Beyond

Quasi-bound states in the continuum (quasi-BICs, q-BICs) are weakly radiative resonant states obtained when an ideal bound state in the continuum is slightly opened by a perturbation. In the ideal BIC limit, the mode lies in the radiation continuum in frequency and momentum yet cannot couple out because symmetry forbids the coupling; once exact decoupling is weakly disturbed, the mode acquires finite leakage, a very large but finite \(Q\)-factor, and typically a narrow Fano resonance [2006.05484]. Recent work places quasi-BICs in periodic dielectric metasurfaces, deformed whispering-gallery microcavities, twisted bilayer photonic slabs, compact acoustic resonators, coupled waveguide lattices, and interaction-modulated Bose-Hubbard models, indicating that the concept is not restricted to a single material system or a single protection mechanism [2409.00201, 2206.13694, 2104.05539, 2103.14293, 2312.15664].

## 1. Definition, spectral character, and quality-factor scaling

The canonical photonic picture treats a quasi-BIC as a long-lived resonance created by weakly opening a symmetry-protected or interference-protected BIC. In temporal coupled-mode descriptions, the perturbation magnitude \(\delta\) sets the radiative leakage, with the usual scaling
\[
\tau=\frac{Q}{\omega_0}\propto \frac{1}{\delta^2},
\]
so smaller perturbations produce weaker leakage, longer lifetime, and sharper resonances [2006.05484]. In experimentally fitted transmission or reflection spectra, the line shape is typically Fano-like, for example
\[
T=\left|a_1+i a_2+\frac{b}{\omega-\omega_0+i\gamma}\right|^2,\qquad Q=\frac{\omega_0}{2\gamma},
\]
which makes the quasi-BIC identifiable as a narrow interference feature on top of a broader background [2408.10106].

This narrow linewidth is the operational basis of quasi-BIC functionality. In metasurfaces it yields ultrasharp spectral filtering and wavefront control; in nonlinear platforms it increases field buildup and modal overlap; in microcavities it suppresses leakage loss; and in scattering experiments it appears as a high-\(Q\) Fano resonance rather than a perfectly dark state. A quasi-BIC is therefore not an exact embedded eigenstate, but a controlled finite-lifetime descendant of one.

## 2. Formation mechanisms

The literature now contains several distinct routes to quasi-BIC formation. In periodic dielectric structures, the most familiar route is a small symmetry-breaking perturbation that converts a dark mode into a leaky resonance. Chiral metasurfaces extend this beyond linear eigenpolarizations by breaking the horizontal mirror symmetry with a two-interface perturbation, allowing arbitrary elliptical eigenpolarizations and full circular dichroism under the quarter-wave condition [2006.05484]. Doubly degenerate quasi-BICs can also be produced while preserving \(C_{4v}\) rotational symmetry, by breaking translation symmetry in a diatomic silicon metasurface without losing polarization independence [2412.16852].

A second class is Friedrich–Wintgen interference, where two leaky resonances share the same radiation continuum and destructively interfere in loss. In a single deformed Limaçon whispering-gallery microcavity, boundary deformation creates stable unidirectional leakage channels, enabling strong external coupling between a high-\(Q\) quasi-WGM and a lower-\(Q\) 6-bounce mode; one hybrid branch suppresses radiation while the other becomes more lossy [2409.00201]. A related avoided-crossing mechanism in finite photonic crystals is used to realize the “super quasi-BIC,” where parameter-space hybridization and momentum-space BIC merging act simultaneously [2211.03675].

A third class relies on out-of-plane or non-Hermitian perturbations. In bianisotropic metasurfaces, perforating the top of cylinders breaks \(\sigma_h\), activates coupling between electric-like and magnetic-like q-BIC resonances, and drives Rabi-like splitting in the strong-coupling regime [2512.08927]. In a \(\mathcal{PT}\)-symmetric ENZ trilayer, spontaneous \(\mathcal{PT}\)-symmetry breaking at a singular point coincident with the BIC position turns the ideal BIC into a high-\(Q\), nearly perfectly transmitting quasi-BIC [2103.07109]. A closely related but topological formulation shows that preserving in-plane symmetry while breaking \(\sigma_h\) can convert a BIC into a quasi-BIC and induce a Zak phase inversion with band inversion between quadrupole and dipole modes [2601.15569].

A fourth class broadens the concept beyond simple symmetry breaking. In quasi-BFICs, mirror-symmetric disorder inside a periodic supercell produces band folding, mode localization, and multiple topological charges in \(k\)-space, so that a whole flat band above the light line exhibits quasi-BIC behavior [2511.05024]. In a many-body Bose-Hubbard chain, the quasi-BIC is a multiparticle maximally localized Wannier state in which a bound pair is localized by the standing wave of a third particle under periodic boundary conditions [2312.15664].

| Mechanism | Representative system | Reported consequence |
|---|---|---|
| Small symmetry-breaking perturbation | Dielectric or chiral metasurfaces | Finite leakage, large \(Q\), narrow Fano resonance |
| Shared leaking continuum | Deformed microcavity; avoided-crossing PhC | Loss suppression in one branch, larger loss in the other |
| Out-of-plane or non-Hermitian symmetry breaking | \(\sigma_h\)-broken metasurfaces; \(\mathcal{PT}\)-symmetric ENZ trilayers | Controlled radiation coupling and quasi-BIC formation |
| Disorder or flat-band engineering | quasi-BFICs; moiré flat bands | High-\(Q\) response over extended \(k\)-space |

This diversity shows that “quasi-BIC” has become a general language for controlled partial decoupling from a continuum, not merely a label for one perturbative geometry.

## 3. Theoretical descriptions

Temporal coupled-mode theory (TCMT) remains the most compact description of photonic quasi-BICs. For chiral quasi-BIC metasurfaces, the scattering matrix is written as
\[
S=C+\frac{|d\rangle\langle d^*|}{i(\omega-\omega_0)+1/\tau},
\]
where \(C\) is the direct scattering pathway and \(|d\rangle\) encodes resonant coupling to the external channels [2006.05484]. This form makes explicit how the high-\(Q\) resonant term interferes with the broad background and produces polarization-selective Fano features.

When more than one mode participates, non-Hermitian two-mode models become central. In the single deformed microcavity, the effective Hamiltonian
\[
H=\begin{pmatrix}E_1 & \kappa_1\\ \kappa_2 & E_2\end{pmatrix},
\qquad
E_i=\operatorname{Re}(E_i)+i\,\operatorname{Im}(E_i),
\]
distinguishes internal strong coupling from external strong coupling through a shared leaking continuum; the decisive effect is a redistribution of the imaginary parts of the eigenvalues, not merely a shift of the real parts [2409.00201]. In bianisotropic metasurfaces, a two-mode TCMT with electric-like and magnetic-like resonances,
\[
\Omega=\begin{pmatrix}\omega_p & g\\ g & \omega_m\end{pmatrix},
\]
produces hybrid eigenfrequencies
\[
\omega_\pm=\frac{\omega_p+\omega_m}{2}\pm \sqrt{\left(\frac{\omega_p-\omega_m}{2}\right)^2+g^2},
\]
which encode the avoided crossing and Rabi-like splitting of opposite-symmetry q-BIC-derived modes [2512.08927].

Finite-size theories emphasize that quasi-BICs are not solely vertical-radiation phenomena. For few-cell photonic-crystal slabs, the total quality factor is decomposed as
\[
\frac{1}{Q}=\frac{1}{Q_\perp}+\frac{1}{Q_\parallel},
\]
with vertical radiation set by reciprocal-space overlap with the infinite-slab \(Q(k)\) landscape and in-plane loss set by the finite cavity extent [1705.09842]. In one-dimensional quasi-BIC gratings, coupled-mode equations for counter-propagating modes,
\[
\frac{\partial u}{\partial t}=-V_g\frac{\partial u}{\partial x}+c_1u+c_2v,\qquad
\frac{\partial v}{\partial t}=V_g\frac{\partial v}{\partial x}+c_1v+c_2u,
\]
yield the dispersion relation
\[
V_g^2k_x^2=(\omega-\omega_{p1})(\omega-\omega_{p2}),
\]
which makes the continuous \(\omega\)-\(k\) quasi-BIC branch explicit [2201.08156].

A distinct theoretical reformulation derives quasi-BICs from a two-band model with an arbitrary confining potential rather than from symmetry protection or topology. In that framework, a quasi-BIC is a bound state weakly coupled to a continuum band, and an exact BIC appears when the real-pole contribution is eliminated through the condition
\[
\mathcal{F}_{\pm p_1}\!\left(V(x')B\psi(x')\right)=0,
\]
or its multiband analogue [2506.19678]. This does not replace symmetry-based quasi-BIC theory, but it broadens the formal criteria under which exact and approximate embedded states can be defined.

## 4. Reciprocal-space structure, finite size, and band generalizations

A recurrent limitation of conventional quasi-BICs is that they are confined to a very narrow range in \(k\)-space and are highly sensitive to disorder [2511.05024]. Several recent directions explicitly target that limitation. One-dimensional quasi-BICs in a binary grating form a continuous family of resonances over a broad spectral band along a dispersion line in \(\omega\)-\(k\) space, with \(Q\) approximately following \(Q\propto 1/\delta^2\) as the ridge-width asymmetry shrinks [2201.08156]. A related photonic-slab experiment reports a symmetry-protected quasi-bound band in the continuum (qBBC) extending continuously along \(\Gamma\)–X, with linewidth about \(3\)–\(6\) meV through at least half the Brillouin zone [2511.03803].

Disorder-enabled flat-band engineering pushes the same idea further. In quasi-BFICs, a mirror-symmetric supercell with disorder strength \(\delta/W=0.15\) yields a flat band whose Bloch modes all behave quasi-BIC-like above the light line; angle-resolved measurements give \(Q\)-factors around \(7319\), \(8569\), \(7652\), and \(9204\), with the overall statement that \(Q\) stays near \(8000\) from \(18.3^\circ\) to \(47.4^\circ\) [2511.05024]. In moiré quasi-BICs, the flat-band condition is achieved by balancing interlayer coupling and twist angle in a twisted bilayer photonic slab, and the \(\Gamma\)-point mode approaches a perfect BIC as the twist angle is reduced [2206.13694].

Finite-size engineering supplies a complementary route. A photonic-crystal slab can retain very high-\(Q\) quasi-BIC behavior with only two or three unit cells, provided the finite cavity mode in reciprocal space is matched to the infinite-slab BIC dispersion [1705.09842]. The “super quasi-BIC” combines avoided crossing in parameter space with merging BICs in momentum space, changing the asymptotic behavior of the quality factor over the number of resonators from \(N^2\) to exclusive \(N^3\) for symmetry-protected BIC-derived modes [2211.03675]. Taken together, these results show that quasi-BIC physics can be extended from isolated singular points to lines, bands, merged topological structures, and even few-cell cavities.

## 5. Representative implementations and functionalities

Chiral and polarization-structured metasurfaces provide one of the clearest demonstrations of how quasi-BIC perturbations become a design resource rather than a parasitic leakage channel. In conventional planar ultrathin implementations with horizontal mirror symmetry, the q-BIC eigenpolarization is limited to linear polarization, circularly polarized illumination couples only half of the incident power to the resonance, and anomalous-reflection efficiency is capped at \(25\%\). By introducing a chiral two-interface perturbation, the eigenpolarization spans arbitrary elliptical states on the Poincaré sphere; under the quarter-wave condition the eigenpolarization becomes pure RCP or LCP, and geometric-phase engineering then yields full amplitude-phase control within the resonant band, with a reported anomalous-reflection diffraction efficiency of \(96.1\%\) [2006.05484].

Quasi-BICs have also become a platform for analog optical computing. An all-dielectric metasurface composed of four silicon nanodisks per unit cell on an SOI platform supports a polarization-independent quasi-BIC with \(C_4\) symmetry and implements isotropic two-dimensional spatial differentiation directly in free space, without a 4-f lens system. At the resonant wavelength \(1488.84\) nm, the transmission is near zero at normal incidence and rises approximately quadratically with \(k_\parallel\), giving a numerical aperture of about \(0.08\), spatial resolution on the order of \(1~\mu\)m, and an output-to-input peak intensity ratio about \(1:5\) in edge-detection imaging [2408.10106].

Nonlinear nanophotonics has adopted quasi-BICs because simultaneous linewidth narrowing and field confinement directly enhance nonlinear polarization. In an etchless lithium niobate resonant grating waveguide, dual quasi-BICs at \(1271.63\) nm and \(1334.74\) nm produce sum-frequency generation with conversion efficiency \(3.66\times 10^{-2}\), five orders of magnitude higher than that of LiNbO\(_3\) films of the same thickness, and a full-width at half-maximum less than \(0.2\) nm [2305.18693]. In a silicon metasurface with doubly degenerate \(C_{4v}\)-protected quasi-BICs, a maximum THG conversion efficiency up to \(1.03\times10^{-5}\) is recorded under a pump intensity of \(5.85\) GW/cm\(^2\), and the THG signal is about \(2200\) times stronger than from a plain silicon film of the same thickness [2412.16852]. In a twisted bilayer photonic slab, SHG assisted by moiré quasi-BICs is nearly ten times larger than that based on dispersive quasi-BICs with similar quality factors under a wide-angle optical source [2206.13694].

Quasi-BICs also support chiral emission and directional absorption. In intrinsic chiral silicon metasurfaces loaded with achiral dye, the quasi-BIC mode produces circularly polarized photoluminescence with \(g_\mathrm{PL}\) over \(0.1\), and the reported dissymmetry factor remains robust against variations in emission angle and dye thickness because of strong lateral field confinement [2508.18927]. In deeply subwavelength bianisotropic metasurfaces embedded in a reflective slab, q-BIC-enabled strong mode coupling yields dual-band asymmetric absorption with more than a \(70\%\) directional absorption difference and fitted coupling strength \(g=1.21\) THz, well above the strong-coupling threshold \(g_{\rm strong}=0.21\) THz [2512.08927].

## 6. Beyond planar optics: microcavities, acoustics, many-body analogs, and open questions

The quasi-BIC concept now extends well beyond planar dielectric metasurfaces. In a single deformed Limaçon whispering-gallery microcavity on a Si\(_3\)N\(_4\) platform, strong external coupling through a shared leaking continuum yields a Friedrich–Wintgen quasi-BIC with highest measured \(Q\) exceeding \(3\times 10^5\), more than a 3-fold increase relative to the uncoupled mode [2409.00201]. In compact acoustic resonators immersed in fluid, breaking the symmetry of a genuine acoustic BIC mixes non-radiating torsional multipoles with radiative channels and produces quasi-BICs that appear in scattering spectra as high-\(Q\) Fano resonances, with absorption-limited \(Q\) estimated around \(10^4\) to \(10^6\) depending on the loss factor [2104.05539]. In coupled photonic waveguide lattices, breaking mirror symmetry and allowing non-nearest-neighbor couplings creates a doublet of quasi-BIC states enabling weakly damped embedded Rabi oscillations, with a reported regime where \(\Omega_R/\gamma\sim 1228\) [2103.14293]. In the interaction-modulated Bose-Hubbard model, the quasi-BIC under periodic boundary conditions is a multiparticle maximally localized Wannier state, and Thouless pumping shifts its center of mass by a unit cell while the bound pair moves opposite to the standing wave [2312.15664].

Two objective clarifications follow from this broader landscape. First, it is incomplete to identify quasi-BICs only with symmetry-protected resonances at isolated high-symmetry points of planar photonic crystals. Counterexamples include shared-continuum Friedrich–Wintgen states in a single microcavity [2409.00201], quasi-BICs induced by \(\mathcal{PT}\)-symmetry breaking in ENZ trilayers [2103.07109], disorder-assisted quasi-BFICs spanning a flat band [2511.05024], and the two-band criterion for exact BIC formation that requires neither symmetry protection nor topological constraints [2506.19678]. Second, the main practical limitations remain bandwidth, angular window, and disorder or fabrication sensitivity. The free-space edge-detection metasurface is explicitly not broadband in the absolute sense and depends on fabrication precision [2408.10106], while conventional quasi-BICs are explicitly described as highly sensitive to disorder and confined to a narrow range in \(k\)-space [2511.05024].

These developments suggest three converging research directions. One is the extension from point-like singular resonances to line, band, and flat-band quasi-BICs. A second is the use of additional symmetry knobs—especially \(\sigma_h\) breaking, chirality, and non-Hermitian coupling—to control not just \(Q\), but also polarization, directionality, and modal hybridization. A third is the search for more general exact-BIC criteria that unify symmetry-protected, interference-based, disorder-assisted, and many-body embedded states within a common continuum-coupling framework.

Source: https://www.emergentmind.com/topics/quasi-bound-states-in-the-continuum-quasi-bics