Symmetry-protected Bound States In The Continuum Research Articles

Merging bound states in the continuum-driven ultrahigh sensing figure of merit in all-dielectric metasurfaces.

Radiation-free photonic bound states in the continuum (BIC) in metasurfaces allow ultrahigh quality (Q) factor and strongly confined mode volume, which are extremely advantageous in the development of ultrasensitive microcavity sensors. However, the conventional isolated BICs are susceptible to failure due to symmetry breaking caused by fabrication imperfection and nonzero incident angle. Here, we propose a silicon nitride-based metasurface with multiple BIC merging. The merging of accidental BIC and symmetry-protected BIC can increase the Q-factor near the Brillouin zone Γ point and thus robustly induces a figure of merit (FOM) of refractive index sensing at small incident angles two orders of magnitude higher than that in isolated BIC configuration. Specifically, the FOM in merging BIC reaches 108 at a 2° incident angle. The BIC merging can be universally achieved in square lattices with C4 symmetry, and slower decay of Q-factor and higher FOM can further occur in hexagonal lattices benefiting from higher-order topological charges. The advantage of merging BIC is also maintained when considering in-plane and out-of-plane symmetry breaking. These results offer a unique design path for high-performance metasurface sensors and can be extended to other high-Q applications such as low-threshold lasers, nonlinear frequency conversion, and low-loss waveguides.

Bound states in the continuum in a dielectric metamaterial with symmetry breaking in two dimensions

Abstract Bound states in the continuum (BICs), since their ultra-high quality (Q)-factor to extremely enhance light matter interactions, have attracted extensive interest very recently. As a typical category, symmetry-protected BICs are predictive and easily manipulated by using structure’s symmetry. However, most of the studies focus only on the structures with symmetry breaking in one dimension, in which one BIC will emerge and exhibit an inverse square relationship to asymmetry parameter. The structures with symmetry breaking in two dimensions remain rather unexplored. We here propose a dielectric metamaterial made of a square lattice of disks with a small hole. As moving the hole away from the center, the in-plane inversion symmetry can be broken either in one dimension or in two dimensions. As usual, a symmetry-protected BIC dominated by magnetic dipole (MD) occurs in the first case. In the second case, symmetry-protected dual BICs arise, consisting of the usual MD-dominated BIC and a new electric dipole (ED)-dominated BIC that is in cross-polarization to incident wave. The new BIC possesses an even higher Q-factor, which can also be continuously tuned via the position of the hole. Besides the structural modulation, we show the polarization angle of incident wave will act as another degree of freedom for designing symmetry breaking in two dimensions, where the similar symmetry-protected dual BICs are observed as well. Our work provides an alternative scheme for engineering multiple BICs and improving Q-factor, which may pave the way for practical device applications.

High-Q triple-mode quasi-bound states in the continuum in an asymmetric dielectric metamaterial

Bound states in the continuum (BICs) in metamaterials have attracted much attention due to their high efficiency in field enhancing. In this paper, we numerically demonstrated the triple-mode symmetry-protected BICs (SP-BICs) in an all-dielectric microtube metamaterial. By moving the hollows transversely and longitudinally in microtubes, three SP-BICs are transformed into high quality-factor (Q-factor) quasi-BICs (q-BICs), which are supported by asymmetric magnetic toroidal dipole electric hexapolar resonances respectively. The maximum Q-factor of q-BICs enabled by asymmetric magnetic toroidal dipole reaches 67647. This high Q-factor triple-mode q-BICs in all-dielectric microtube metamaterial has great potential in the applications of sensing, laser generation, and nonlinear optics.

Versatile Metamaterial: Exploring the Resonances of Symmetry‐Protected Modes for Multitasking Functionality

AbstractIn this work, an experimental study supported by numerical modeling that demonstrates the possibility of exciting Symmetry Protected‐Bound states In the Continuum (SP‐BICs) in a 1D silicon grating fabricated on a lithium niobate substrate is presented. bBoth transverse electric and magnetic polarization states are investigated, leading to the excitation of four quasi‐ Bound states In the Continuum (quasi‐BIC) resonances, exhibiting distinct behaviors. Under standard illumination conditions (plane of incidence perpendicular to the 1D grating lines), two of these resonances are highly sensitive to illumination conditions, while the other two resonances involving unconventional illumination directions (plane of incidence parallel to the grating lines) are more robust to the angle of incidence, but just as sensitive to external stresses in terms of resonance wavelength and quality factor. Additionally, temperature detection is experimentally demonstrated with a Sensitivity of ST = 0.81∼nm °C−1, a state‐of‐the‐art value achieved due to significant electromagnetic field enhancement inside the lithium niobate substrate at the quasi‐BIC resonance. These findings pave the way for their use in various sensing applications (such as biology, electromagnetic, and temperature sensing), as well as nonlinear applications like second harmonic generation, and electro‐ and acousto‐optic modulation.

Realization of robust high-Q resonances of BICsvia eigenfield perturbations in a multiple-notched nanocube metasurface.

Non-radiative bound states in the continuum (BICs) allow the construction of resonances with high-quality (Q) factors and have emerged as an attractive platform for manipulating light-matter interactions on the nanoscale. However, current studies on symmetry-protected BICs (SP-BICs) suffer from a fundamental trade-off between the Q factor and asymmetric parameters, presenting a significant hurdle for practical applications. Here, utilizing the eigenfield perturbations, we successfully break the conventional inverse quadratic law of the SP-BICs and realize the robust high-Q resonances against the asymmetric parameters. We find the introductions of the central notch can efficiently boost the resonance of the electric quadrupole, which results in the enhancement of multiple-mode interference, and thus improving Q factors, while the constant effective refractive index guarantees the resonance with a stable wavelength. Our findings provide a promising strategy for modulating the light-matter interaction and may pave the way for applications in future high-performance optoelectronic devices.

Research on sensing characteristics of high Q-factor all-dielectric metasurfaces based on geometric breaking

The bound states in the continuum (BIC) are widely used in designing metamaterials with high quality factor (Q-factor) resonances due to their perfect localization in the continuous spectral range coexisting with expanding waves. In this study, a T-shaped nanohole all-dielectric metasurface structure is proposed based on the unique electromagnetic properties of all-dielectric metasurfaces, and the fundamental reason of its coupled state and the theoretical basis of BIC excitation are deeply investigated based on the theory of group theory, and the geometric symmetry is broken from multiple angles, and the coupling relationship between discrete eigenmodes and the external continuum is specifically analyzed during the change of symmetry, its spectral response and near-field distribution are numerically calculated. In addition, based on the modulation mechanism of the incident light polarization angle, the three-channel resonance tuning with two resonances of the same frequency and one of a different frequency is realized under the condition that the resonance position and the Q-factor are not affected. This study not only provides a theoretical basis for the excitation conditions and evolution regularity of symmetry-protected BIC, but also solves the problem in the traditional analysis of resonance phenomena without taking the high Q-factor and stability into account, which can provide new designing methods for optical metasurface devices with multi-channel resonance.

Plasmonic and photonic refractive index biosensor based on bound states in the continuum

In this paper, we propose a novel structure for biosensors based on a diffraction grating to diagnose four types of cancers cells. This biosensor is used to detect Hela, Jurkat, PC12, MDA-MB-231 and MCF-7 cancerous cells, based on their refractive indices. The present configuration consists of a glass layer covered by a gold layer, a grating coated by a silicon nitride layer separating the sensor from sensing medium. Bound states in the continuum (BIC) in a hybrid plasmonic-photonic structure can be achieved at Γ point and off-Γ. The symmetry-protected BIC is formed at the Γ-point of the periodic system due to the strong coupling between plasmonic or photonic modes. On the other hand, the Friedrich-Wintgen (FW) BICs can be readily achieved off-Γ due to the strong coupling between plasmonic and photonic modes. A comparative study is made on the basis of three BICs (plasmonic BIC, photonic BIC, and FW-BIC). Here, numerical analysis based on the Rigorous coupled-wave analysis method (RCWA) is performed to optimize the biosensor sensitivity, by also considering the full width at half maximum (FWHM), detection accuracy (DA), and figure of merit (FoM). The FW BIC-based biosensor for photonic mode exhibits the highest S of 1208nm/RIU, low FWHM of 0.5 nm, the maximum DA of 2 nm −1, and best FoM of 2416 RIU −1.

Miniaturized quasi-BICs based on a two-dimensional heterostructure to realize a low-threshold nanolaser.

Bound states in the continuum (BICs) have been demonstrated as an effective mechanism to achieve high quality (Q)-factor cavities for nanolasers. However, the development of a compact BIC laser with a low threshold has remained elusive. Here, we numerically report lasing action from symmetry-protected BICs in a two-dimensional heterostructure, which consists of compound gratings with finite cells surrounded by orthogonal distributed Bragg reflectors (DBRs). The compound grating is used to excite quasi-BIC resonance with a high Q-factor, and DBRs enable light confinement and localized electric fields to enhance light-matter interaction. The nanolaser with a threshold of 16.8 µJ/cm2 is achieved within a footprint as small as 3.35 × 3.35 µm2. By changing the phase adjusting gap or asymmetry degree, it is possible to control the lasing emission. This work reveals a new, to our knowledge, path toward compact BIC lasers with a simple scheme for applications that require a small footprint and low threshold.

Polarization-insensitive terahertz third-harmonic generation from degenerate pairs of mirror-coupled super-BICs

Resonant nanostructures have emerged as versatile photonic platforms for boosting optical nonlinear responses on a subwavelength scale for their ability to confine intense electromagnetic fields while relaxing the phase-matching requirements. Recent significant advances in this field are associated with the utilization of non-radiative eigenmodes above the light cone, termed bound states in the continuum (BICs), which provide a unique mechanism for light trapping to realize excitation of ultrahigh quality (Q) factor resonances. Nevertheless, the current studies on BICs predominantly focus on symmetry-protected BICs (SP-BICs), whose excitation requires symmetry breaking, and Q factors are limited by fabrication imperfections. Here, we demonstrate a simple and feasible scheme for creating degenerate pairs of mirror-coupled super-BICs by harnessing magnetic dipole resonances coupled to their mirror images in adjacent metal films. Unlike trivial SP-BICs, mirror-coupled BICs showcases the huge enhancement of Q factors and are resilient against fabrication imperfections. By combining mirror-coupled resonance with the engineered radiative loss, we obtain a perfect absorber with near-unity absorption and ultra-narrow bandwidth at a critical coupling condition. Finally, we numerically demonstrate the terahertz (THz) regime, polarization-insensitive highly efficient third-harmonic generation benefiting from the maximum field enhancement localized within the perfect absorber. Our work not only paves the way toward unlocking the full potential of BIC resonance but also promise valuable insights for developing efficient THz optoelectronic devices and metadevices across a wide range of fields.

Symmetry-protected bound states in the continuum on an integrated photonic platform

Abstract Bound states in the continuum (BICs) have attracted much attention in the field of nanophotonics owing to their ability to trap photons without loss. Recently, a low-refractive-index (RI) waveguide loaded on a high-RI slab structure was demonstrated to support BICs. However, strict control of structural parameters is required due to the accidental nature of those BICs. Here, we propose a novel structure consisting of two low-RI vertically coupled waveguides loaded on a high-RI slab. This structure supports symmetry-protected BICs (SP-BICs), which do not require strict control of the geometric parameters. Such SP-BICs can also possess an infinitely high quality factor in resonant structures, which can be harnessed for ultranarrow-bandwidth spatial and spectral filters. Our work opens a new way of harnessing BICs on an integrated photonic platform for realizing nanophotonic circuits and devices.

Optical switching with high-Q Fano resonance of all-dielectric metasurface governed by bound states in the continuum.

The discovery of bound states in the continuum (BIC) of optical nanostructures has garnered significant research interest and found widespread application in the field of optics, leading to an attractive approach to achieve high-Q (Quality factor) Fano resonance. Herein, an all-dielectric metasurface consisting of four gallium phosphide (Gap) cylinders on the MgF2 substrate is designed and analyzed by the finite element method (FEM). By breaking the symmetry of the plane, specifically by moving the two cylinders to one side, it is possible to achieve a transition from the symmetry-protected BIC to quasi-BIC. This transition enables the excitation of sharp dual-band Fano resonance at wavelengths of 1,045.4 nm and 1,139.6 nm, with the maximum Q factors reaching 1.47 × 104 and 1.28 × 104, respectively. The multipole decomposition and near-field distributions show that these two QBICs are dominated by the electric quadrupole (EQ) and magnetic quadrupole (MQ). Furthermore, bidirectional optical switching can be accomplished by changing the polarization direction of the incident light. As a result, the maximum sensitivity and figure of merit (FOM) are 488.9 nm/RIU and 2.51 × 105 RIU-1, respectively. The results enrich our knowledge about BIC and reveal a platform for the development of high-performance photonics devices such as optical switches and sensors.

Polarization-controlled third harmonic generation by quasi-bound states in the continuum in silicon nanopillar metasurfaces

All-dielectric metasurfaces have received widespread attention due to their low intrinsic loss compared to the metallic counterparts. However, relatively high radiation loss and low quality (Q) factor of the dielectric nanostructures may significantly degrade their nonlinear optical efficiency. Here, we demonstrate that silicon-nanopillar-based metasurfaces supporting quasi bound states in the continuum (BICs) can greatly enhance the efficiency of third harmonic generation (THG). We show that symmetry-protected BICs form at the Γ-point of doubly degenerate band or nondegenerate band can be selectively transformed into quasi BIC through symmetry breaking of our silicon metasurfaces. Benefiting from the high Q and resonance enhancement by the quasi BICs, the THG conversion efficiencies of the silicon metasurface reaches 4.3 × 10-4 with a peak pump intensity of 1.3 GW/cm2, which can be four orders higher than that of a silicon planar film with the same thickness. In addition, the THG intensity is polarization-dependent for the single quasi BIC while it is polarization-independent for the doublet quasi BIC. Our results provide a new strategy for the design of high-efficiency silicon-based optical nonlinear devices.

Independent ultrahigh-Q dual-band resonances via coating a resonator on a BIC-driven metasurface.

Traditional designs driven by symmetry-protected bound states in the continuum (SP-BICs) hardly support independent dual-band resonances, and they require extremely small perturbations to obtain an ultrahigh-Q. Here, we propose an SP-BIC-driven structure composed of a metasurface and a resonator, which supports independent dual-band resonances and enables ultrahigh-Q at large perturbations. The underlying mechanism enabling this is to form reasonable eigenfield distributions of two BICs by coating a dielectric layer on the metasurface. One eigenfield is confined within the metasurface and the bottom of the resonator, while the other one concentrates at the top of the resonator. Thus, two resonances with different originations can be supported, and the effect of metasurface perturbations on the eigenfields is weakened. This work provides a promising pathway for unlocking the potential of SP-BICs, enhancing light trapping and manipulation across diverse applications.

Robust high-Q quasi-BICs in double-layer high-contrast metagrating with temperature self-compensation for refractive index sensing

We propose a double-layer high-contrast metagrating structure with robust high-quality (Q) and temperature self-compensation for four-band refractive index sensing. The structure supports four-band symmetry-protected bound states in the continuum (SP-BICs) that transform into quasi-BICs as a result of structural symmetry breaking. However, the Q-factor of these quasi-BICs are limited by perturbation parameters, hampering practical fabrication. Interestingly, tuning the cavity length, we implement four-band Fabry–Pérot bound states in the continuum (FP-BICs) to transform the resonance mode back into high-Q quasi-BICs even at large perturbations. This approach is conducive to improving robustness and modulation freedom of Q-factors. In addition, we achieve temperature self-compensation by using the double-layer high-contrast metagrating consists of two materials with opposite thermo-optic (TO) dispersions. The simulation results indicate that the largest refractive index sensitivity is 470.9 nm RIU−1, its figure of merit is 427 818.2, and its Q-factor up to 9.3 × 105. The proposed double-layer high-contrast metagrating has potential application prospects for multiplex and high-performance sensing.

Dielectric terahertz metasurface governed by symmetry-protected BIC for ultrasensitive sensing

The non-radiative bound states in the continuum (BIC) have attracted much attention in achieving theoretically infinite quality (Q) factor. In this paper, a dielectric terahertz metasurface with C 4v symmetry is proposed, and a toroidal dipole resonance is easily obtained under incident plane wave. Moreover, by slightly tuning the asymmetry parameter δ to break the in-plane symmetry of the structure (side length perturbation), a magnetic dipole BIC mode radiates as quasi-BIC (QBIC) with extremely narrow linewidth and ultrahigh Q of 1.2 × 104 at δ = 0.4 μm. It shows significant performance in THz sensing with the sensitivity around 446 GHz/RIU and figure of merit (FoM) up to 2267. The designed metasurface in the case of symmetry-breaking by position perturbation also achieves ultrasensitive sensing. Additionally, the effects of geometric parameters on the resonance modes have been comprehensively investigated. Our work provides a route to design symmetry-protected BIC metasurface with simple structure, and the Q factor as well as resonant frequency can be controlled using a single geometric parameter, which may facilitate designing high-performance metasurface in sensing applications.

High-performance gas sensing in metagrating-based vertical cavity with larger fabrication tolerances driven by quasi-bound states in the continuum

We proposed a novel vertical cavity structure for gas sensing, utilizing double-layer metagratings and a distributed Bragg reflector (DBR). By adjusting the position of the upper-layer grating, we were able to achieve symmetry-protected bound states in the continuum (SP-BIC) and Fabry-Pérot BIC (FP-BIC). The resonance peaks of these quasi-BICs can be tuned by modifying structural parameters like grating thickness, width, and cavity length. Notably, our structure exhibited high sensing performance while allowing for significant fabrication tolerances. Simulation results indicate that the sensitivities of the gas sensor can reach 927 nm/RIU and 1026 nm/RIU, corresponding to figure of merit (FOM) of 15450 RIU−1 and 24604 RIU−1. The proposed structure with large fabrication tolerances has potential applications in gas sensing.

Merging mechanical bound states in the continuum in high-aspect-ratio phononic crystal gratings

Mechanical bound states in the continuum (BICs) present an alternative avenue for developing high-frequency, high-Q mechanical resonators, distinct from the conventional band structure engineering method. While symmetry-protected mechanical BICs have been realized in phononic crystals, the observation of accidental mechanical BICs—whose existence is independent of mode symmetry and tunable by structural parameters—has remained elusive. This challenge is primarily attributed to the additional radiation channel introduced by the longitudinal component of elastic waves. Here, we employ a coupled wave theory to predict and experimentally demonstrate mechanical accidental BICs within a high-aspect-ratio gallium arsenide phononic crystal grating. We observe the merging process of accidental BICs with symmetry-protected BICs, resulting in reduced acoustic radiation losses compared to isolated BICs. This finding opens up new possibilities for phonon trapping using BIC-based systems, with potential applications in sensing, transduction, and quantum measurements.

Mechanism of formation and evolution of bound states in the continuum of split-hole all-dielectric metasurface under asymmetric displacement perturbation

Bound states in the continuum (BICs) with ultra-high Q properties have attracted much attention for their perfect localization in the continuous spectral range coexisting with extended waves. In this study, breaking the traditional excitation form of structure breakage or excitation field asymmetry, a monolithic silicon nanodisk array with relative displacement generated by the complete splitting of square nanopores is proposed based on the unique electromagnetic properties of all-dielectric metamaterials. During the introduction of perturbations by asymmetric displacements of splitting holes, it is shown by numerical simulations that two BICs at different wavelengths can be realized. Combined with eigenmodes of group theory, the symmetric matching relationship between the symmetry-protected BICs and the free-space radiation during the evolution process is analytically demonstrated, and the formation mechanism and the evolution law of the BICs excited by this metasurface are deeply investigated. meanwhile, it also provides a theoretical basis for the polarization dependence of quasi-BICs excitation and the ultra-high Q factor expression of BICs. Furthermore, near-field distribution and multipole decomposition show that the field distribution and surface currents support the excitation of BIC-driven toroidal dipole and magnetic quadrupole dual modes. This study not only provides an effective reference for the stability of high-Q resonance wavelengths, but also solves the problem of the lack of universality in analyzing the resonance mechanism based on resonance phenomena, and provides solid theoretical support for the study of displacement-mediated BICs resonance excitation and evolution.

Mixed bound states in the continuum: Disclosing BIC’s content via bulk normal modes

We present a nonperturbative theory of bound states in the continuum (BICs) based on the analytical theory of infinite-grating eigenmodes in the case of a planar grating waveguide, that is, 1D photonic crystal slab. We describe a mixed BIC mainly formed by a coherent mixture of two photonic-crystal normal modes in a vicinity of their avoided crossing where both of them have a nonzero coupling with a radiation-loss channel. We reveal the universal properties of the mixed BIC associated with the spatial parity symmetry breaking and self-similar spectral behavior of the bulk normal modes near Γ-point. We show that the mechanism of the mixed-BIC formation constitutes a special kind of the generic Friedrich–Wintgen mechanism. A cutoff from the radiation-loss channel and extremely high-Q narrow resonance are achieved due to the destructive interference of the two crossing normal modes. On the contrary, a conventional symmetry-protected BIC is formed mostly by a single photonic-crystal normal mode which has vanishing coupling Fourier coefficient with every available radiation-loss channel. Implementation of the mixed BICs in various photonic-crystals structures could lead to interesting applications.

Optical switching with high-Q Fano resonance of all-dielectric metasurface governed by bound states in the continuum

The discovery of bound states in the continuum (BIC) of optical nanostructures has garnered significant research interest and found widespread application in the field of optics, leading to an attractive approach to achieve high-Q (Quality factor) Fano resonance. Herein, an all-dielectric metasurface consisting of four gallium phosphide (Gap) cylinders on the MgF2 substrate is designed and analyzed by the finite element method (FEM). By breaking the symmetry of the plane, specifically by moving the two cylinders to one side, it is possible to achieve a transition from the symmetry-protected BIC to quasi-BIC. This transition enables the excitation of sharp dual-band Fano resonance at wavelengths of 1,045.4 nm and 1,139.6 nm, with the maximum Q factors reaching 1.47 × 104 and 1.28 × 104, respectively. The multipole decomposition and near-field distributions show that these two QBICs are dominated by the electric quadrupole (EQ) and magnetic quadrupole (MQ). Furthermore, bidirectional optical switching can be accomplished by changing the polarization direction of the incident light. As a result, the maximum sensitivity and figure of merit (FOM) are 488.9 nm/RIU and 2.51 × 105 RIU−1, respectively. The results enrich our knowledge about BIC and reveal a platform for the development of high-performance photonics devices such as optical switches and sensors.