Symmetry-protected Bound States In The Continuum Research Articles

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.

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.

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.

Observation of accurately designed bound states in the continuum in momentum space

Bound states in the continuum (BICs) in artificial photonic structures have received considerable attention since they offer unique methods for the extreme field localization and enhancement of light-matter interactions. Usually, the symmetry-protected BICs are located at high symmetric points, while the positions of accidental BICs achieved by tuning the parameters will appear at some points in momentum space. Up to now, to accurately design the position of the accidental BIC in momentum space is still a challenge. Here, we theoretically and experimentally demonstrate an accurately designed accidental BIC in a two-coupled-oscillator system consisting of bilayer gratings, where the optical response of each grating can be described by a single resonator model. By changing the interlayer distance between the gratings to tune the propagation phase shift related to wave vectors, the position of the accidental BIC can be arbitrarily controlled in momentum space. Moreover, we present a general method and rigorous numerical analyses for extracting the polarization vector fields to observe the topological properties of BICs from the polarization-resolved transmission spectra. Finally, an application of the highly efficient second harmonic generation assisted by quasi-BIC is demonstrated. Our work provides a straightforward strategy for manipulating BICs and studying their topological properties in momentum space.

Observation of dual-band bound states in the continuum emerging from Mie collective lattice resonances

Collective lattice resonances (CLRs) and bound states in the continuum (BICs) are two exciting approaches for achieving high quality factors in metasurfaces. BICs emerging from CLRs have raised great interest for not only the ultrahigh quality factors but also the nonlocal field enhancement. However, experimental demonstrations remain insufficient due to the material absorption or the inappropriate parameter design. Here we experimentally demonstrate dual-band symmetry-protected BICs emerging from Mie CLRs in all-dielectric metasurfaces. We attribute these dual-band BICs to the zero emission at Γ point for the in-plane electric quadrupole and out-of-plane magnetic dipole CLRs, respectively. Such BICs feature nonlocal field enhancement and convenient spectral tunability, which are inherent to CLRs. We expect such nonlocal metasurfaces supporting BICs to find applications especially in nanolasers, nonlinear optics, and biochemical sensing.

Demonstration of bound states in the continuum in substrate integrated waveguides.

Substrate integrated waveguides (SIWs) components play a crucial role in microwave devices fabricated by printed circuit board (PCB) technology. Bound states in the continuum (BICs) have high-quality factors that approach infinity. So far, there is little research on BICs in SIWs. Therefore, we studied a symmetry-protected BIC generated by the coupling between SIW and SIW resonators to fill this gap. Using the revised coupled mode theory (CMT), we explored the mechanism of resonance generation in this system. In addition, the effect of the geometrical parameters on the resonance is also investigated and higher Q3dB factors are obtained. The findings offer new insights into the design of BIC devices by traditional PCB technology, thus contributing to future applications in the integrated circuits field.

Enhancing surface sensing performance of cascaded high contrast gratings using bound states in the continuum.

We proposed the cascaded high contrast grating (CHCG) structure to enhance surface sensing capabilities through bound states in the continuum (BICs). Utilizing the finite element method (FEM) and rigorous coupled-wave analysis (RCWA), we studied the dispersion relations, far-field contribution CHCGs, and near-field distributions of BICs corresponding to resonance peaks at different wavelengths. Results demonstrate the ability to precisely control symmetry-protected BIC (SP-BIC) and Friedrich-Wintgen BIC (FW-BIC) resonance peaks by altering incident angles and structural parameters, enhancing structure robustness and tunability. Significantly, modes 1 and 2 have demonstrated substantial enhancement in surface refractive index sensing, achieving highest sensitivities at 51 nm/RIU and the figure of merit reaching 490.8 RIU-1, indicating notable advancement in detecting subtle surface changes. In contrast, mode 3 has shown robust performance in bulk refractive index sensing, achieving a sensitivity of 602 nm/RIU and a figure of merit of 5189.65 RIU-1. These findings underscore the significant potential of the structure as a high-performance integrated sensor, particularly for precise environmental and biological monitoring in surface refractive index sensing.

Achieving asymmetry parameter-insensitive resonant modes through relative shift–induced quasi-bound states in the continuum

Abstract High-Q resonances in metasurfaces, stemming from symmetry-protected bound states in the continuum (BICs), have proven to be effective for achieving high-performance optical devices. However, the properties associated with symmetry-protected BICs are inherently limited, as even a slight variation in the asymmetry parameter leads to a noticeable shift in the resonance location. Herein, we introduce the concept of relative shift–induced quasi-BICs (QBICs) within dimerized silicon (Si) meta-lattices (DSMs), which can be excited when a nonzero relative shift occurs, a result of in-plane inversion symmetry breaking and Brillouin zone folding within the structure. These QBICs have resonance locations that remain insensitive to variations in asymmetrical parameters. Additionally, their Q-factors can be flexibly tuned, benefiting from the inverse square dependence on asymmetrical parameters. In experiment, six DSMs with different relative shifts are fabricated and the asymmetry parameter-insensitive resonant modes under two orthogonal polarization states are experimentally observed in the optical communication waveband. Our results offer unique opportunities for constructing high-Q resonators with enhanced performances, which can be applied in various optical fields.

A triple Fano resonance Si-graphene metasurface for multi-channel tunable ultra-narrow band sensing.

In this work, a dielectric metasurface composed of a silicon nanodisk etched with a square hole is proposed. By introducing C4v symmetry breaking, the symmetry-protected bound states in the continuum (SP-BIC) is transformed into a quasi-BIC (Q-BIC), simultaneously inducing triple Fano resonances in the near-infrared light band corresponding to one dipole and two Q-BIC resonances. The characteristics of Q-BIC resonances are elucidated through multipole decomposition and near-field distribution analysis. Subsequently, monolayer graphene is integrated into the Si metasurface. The light field in the composite metasurface can be flexibly modulated by changing the Fermi level of graphene. This modulation enables optimal transmission with an enhancement of up to 252%, while the confined electromagnetic energy experiences a remarkable increase of about 1020%. Simulation results demonstrate that the Si-graphene composite metasurface exhibits a high refractive index sensitivity of 162 nm RIU-1, accompanied by a figure of merit of 170.526 RIU-1. This composite metasurface holds promise as a high-performance sensor in the near-infrared band and has potential for application in the fields of active tunable optical devices and biochemical sensing.

Design and analysis of a flexible Ruddlesden–Popper 2D perovskite metastructure based on symmetry-protected THz-bound states in the continuum

A Ruddlesden–Popper 2D perovskite PEA2PbX4 (X = I, Br, and Cl) is proposed for metasurface applications. Density functional theory is used to analyze the optical, electrical, mechanical properties, moisture and thermodynamic stability of PEA2PbX4. The refractive index of PEA2PbX4 varies with the halides, resulting in 2.131, 1.901, and 1.842 for X = I, Br, and Cl, respectively. Mechanical properties with Voigt-Reuss-Hill approximations indicate that all three materials are flexible and ductile. Based on the calculations of formation energy and adsorption of water molecules, PEA2PbI4 has superior thermodynamic and moisture stability. We present a novel metasurface based on 2D-PEA2PbI4 and analyze symmetry protected-bound states in the continuum (sp-BIC) excitation. The proposed structure can excite multiple Fano quasi-BICs (q-BICs) with exceptionally high Q-factors. We verify the group theoretical analysis and explore the near-field distribution and far-field scattering of q-BICs. The findings indicate that x-polarized incident waves can excite magnetic toroidal dipole-electromagnetic-induced transparency-BIC and magnetic quadrupole-BIC, while y-polarized incident waves can excite electric toroidal dipole-BIC and electric quadrupole-BIC. The influence of meta-atom and substrate losses, array size limitations, and fabrication tolerances are also discussed. The proposed structure can be employed for applications in the THz region, such as polarization-dependent filters, bidirectional optical switches, and wearable photonic devices.