Merging Bound States in the Continuum at Off-High Symmetry Points

Free-space high-Q nanophotonics

High-Q nanophotonic devices hold great importance in both fundamental research and engineering applications. Their ability to provide high spectral resolution and enhanced light-matter interactions makes them promising in various fields such as sensing, filters, lasing, nonlinear optics, photodetection, coherent thermal emission, and laser stealth. While Q-factors as large as 109 have been achieved experimentally in on-chip microresonators, these modes are excited through near-field coupling of optical fibers. Exciting high-Q modes via free-space light presents a significant challenge primarily due to the larger fabrication area and more lossy channels associated with free-space nanophotonic devices. This Review provides a comprehensive overview of the methods employed to achieve high-Q modes, highlights recent research progress and applications, and discusses the existing challenges as well as the prospects in the field of free-space high-Q nanophotonics.

Chiral lasing enabled by strong coupling

Chiral quasi-bound states in the continuum are spin-dependent high-Q resonances in meta-photonic structures that are realized by perturbing symmetry-protected optical states by engineering in-plane and out-of-plane asymmetries, and they support chiral lasing in the vertical direction. Here, we explore the coupling between two resonances in a chiral metasurface and introduce a mechanism for high-purity chiral laser emission. We reveal that two resonances with nearly orthogonal polarizations become strongly coupled in an engineered chiral metasurface. The inherent phase difference of the resonances, associated with the coherent destruction on the decay channel, can endow high-Q factor and maximize chirality to one of the hybrid modes. We verify this approach experimentally by measuring transmission spectra, angle-resolved photoluminescence, and laser emission. We believe that this mechanism allows breaking restrictions on conventional chiral quasi-BIC lasing, enabling the realization of chiral emission at any designed direction.

Robust ultrahigh Q guided mode resonances in rectangular lattices

Mode-coupling is an important method for enhancing the quality (Q) factors of guided mode resonances (GMRs) in photonic crystal slabs. In square lattices, GMRs inherently exhibit orthogonality and degeneracy due to C4 symmetry, with different orders of GMRs typically displaying distinct frequencies at the Γ point. Here, we propose a versatile and highly effective approach to achieve ultrahigh Q GMRs in rectangular lattices by exploiting spatial degrees of freedom. Specifically, two distinct types of GMRs, supported by orthogonally oriented propagation directions, can robustly couple to form a hybridized GMR with an exceptionally ultrahigh Q value. Our theoretical analysis indicates that the formation of such hybridized GMRs requires merely the design of an appropriate period, based on the dispersion relations of the guided modes, obviating the need for complex structural modifications. This research offers a practical and innovative method for realizing ultrahigh Q GMRs in photonic crystal slabs, thereby providing more possibilities for light-matter interactions, nonlinear optics, and optoelectronic device applications.

Topological guided-mode resonances: basic theory, experiments, and applications

Guided-mode resonance (GMR) is a key principle for various nanophotonic elements in practice. In parallel, GMR structures offer an efficient experimental platform for fundamental study of novel wave phenomena because of its versatile capability to synthesize complicated potential distributions and analyze deep internal properties conveniently in the optical far-fields. In this paper, we provide a brief review of topological GMR effects as a promising subtopic of the emerging topological photonics. Starting from a conceptually minimal model, we explain basic topological parameters, associated optical properties, experimental realizations, and potential applications. We treat topics of recent interest including topological edge-state resonances, deterministic beam shaping and mode matching, bound states in the continuum, unidirectional resonances, and polarization vortices. We finally address limitations, remaining challenges, and perspective of the topic.

Observation of Berry curvature in non-Hermitian system from far-field radiation

Berry curvature that describes local geometrical properties of energy bands can elucidate many fascinating phenomena in solid-state, photonic, and phononic systems, given its connection to global topological invariants such as the Chern number. Despite its significance, the observation of Berry curvature poses a substantial challenge since wavefunctions are deeply embedded within the system. Here, we theoretically propose a correspondence between the geometry of far-field polarization and the underneath band topology in non-Hermitian systems, thus providing a general method to fully capture the Berry curvature without strongly disturbing the eigenstates. We further experimentally observe the Berry curvature in a honeycomb photonic crystal slab from polarimetry measurements and quantitatively obtain the nontrivial valley Chern number. Our work reveals the feasibility of retrieving the bulk band topology from escaping photons and paves the way to exploring intriguing topological landscapes in non-Hermitian systems.

Merging of Accidental Bound States in the Continuum in Symmetry and Symmetry-Broken Terahertz Photonic Crystal Slabs

Recently, the merging of accidental bound states in the continuum (BICs) has attracted significant attention due to the enhanced light-matter interactions. Here, we theoretically demonstrate the merging of accidental BICs in perturbed all-silicon terahertz photonic crystal (PhC) slabs with C2 and C2 broken-symmetry structures. The PhC slabs consist of an array of four cylindrical holes and support a TM symmetry protected (SP) vector BIC at the Γ point. Our results indicate that the merging and band transition of accidental BICs can be achieved by varying the diameter of diagonal holes in a C2-symmetry structure. Notably, in a C2 broken-symmetry PhC slab, the SP BIC will first convert to a quasi-BIC, then transit to a new accidental BIC, which are well displayed and interpreted by tracing the accidental BICs in momentum space. We believe that the results presented in this work show potential for the design and application of BICs in both symmetric and asymmetric PhC slabs.

Chiral Guided Mode Resonance with Independently Controllable Quality Factor and Circular Dichroism

Chiroptical resonances with high quality factors (Q factors) have recently garnered extensive attention due to their broad applications in lasing and optical sensing. However, the independent manipulation of the Q factor and circular dichroism (CD) of chiroptical resonances has rarely been proposed. Here, we demonstrate that the Q factor and CD of guided mode resonance (GMR) can be independently manipulated by simply varying two structural parameters in a diatomic dielectric metasurface grating, offering a new paradigm for chiroptical resonance manipulation. We reveal that the independent manipulation of the Q factor and CD of the GMR is attributed to the modulation of the collective interference of guided mode fields excited by the two orthogonal linearly polarized normal incidence. GMRs with a Q factor of 183 and CD of ±0.62 have been experimentally validated, which is comparable to state-of-the-art chiral quasi-BICs. These findings provide a powerful platform for the realization of high-Q chiroptical resonances.

Dynamically tunable robust ultrahigh-Q merging bound states in the continuum in phase-change materials metasurface

Bound states in the continuum (BICs) are localized states within the radiative continuum that exhibit high quality-factor (Q-factor) resonance, which significantly boosts light-matter interactions. However, out-of-plane radiation losses can arise from inherent material absorption and inevitable technological imperfections during fabrication process. Merging BICs have been introduced as a solution to address the issue of out-of-plane radiation losses. By merging BICs, it is possible to expand the area of high Q-factor resonance in momentum space, thereby enhancing the system's robustness against external perturbations. However, achieving this enhancement is contingent upon altering the geometrical parameters of the structure, which inherently restricts its dynamic tunability. Here, we propose an emerging approach that integrates phase change materials (PCMs) into photonic crystal slabs (PCs) metasurface, enabling dynamically tuning of merged BICs. By utilizing low-loss Sb2S3 as a tunable PCMs, we demonstrate that altering its phase state can merge BICs, leading to a substantial increase in the high Q-factor across an extended range of wave vectors space. Furthermore, this study validates the universality and robustness of merging BICs against common unit-cell topology fabrication defects. Additionally, by twisting the square holes to break in-plane symmetry, asymmetric merging and inversion of topological charge at the Γ -point are achieved. This approach leverages phase-transition states of PCMs to enable reconfigurable polarization distribution of radiation field without scale and parameter changes, which is tunable and offers promising potential applications in optical vortices and nano-lasers.

Tunable bound states in the continuum with loss compatibility

Dynamic control of bound states in the continuum (BICs) is usually achieved by engineering structural geometries of lossless optical systems, leading to a passive nature for most current BIC devices. Introducing materials with tunable permittivity, i.e., refractive index and loss, may offer a new degree of freedom in designing reconfigurable BIC metadevices with active functionalities. However, achieving loss-accompanied or loss-driven BIC manipulation while preserving its ultrahigh Q factor is extremely challenging. Here, we report a loss-compatible BIC manipulation mechanism based on far-field interference in a mirror-assisted photonic crystal slab, wherein the loss of tunable material not only harmoniously coexists with ultrahigh Q factor, but also serves as a pivotal joystick of BIC dynamics in momentum space. By modulating loss and refractive index of tunable material through the amorphous-crystalline phase transition, simulation results show the active switching of topological charge for BICs, as well as the multidimensional control of chiroptical effect for quasi-BICs, including steerable response/emission direction and chirality continuum with far-field ellipticity ranging from -0.944 to +0.943. Our findings suggest a distinct route to construct BIC metadevices with active functionalities and foster deeper exploration of intrinsic loss applications within the ultrahigh-Q photonic system.

Origins and conservation of topological polarization defects in resonant photonic-crystal diffraction

We present a continuative definition of topological charge to depict the polarization defects on any resonant diffraction orders in photonic crystal slab regardless they are radiative or evanescent. By using such a generalized definition, we investigate the origins and conservation of polarization defects across the whole Brillouin zone. We found that the mode crossings due to Brillouin zone folding contribute to the emergence of polarization defects in the entire Brillouin zone. These polarization defects eventually originate from the spontaneous symmetry breaking of line degeneracies fixed at Brillouin zone center or edges, or inter-band coupling caused by accidental Bloch band crossings. Unlike Bloch states, the polarization defects live and evolve in an unbound momentum space, obeying a local conservation law as a direct consequence of Stokes' theorem, but the total charge number is countless.

Independent manipulation of dual high-Q modes for multifunctionalities

Subwavelength light trapping in periodic structures with high quality (Q) factors is discovered to hold strong light-matter interactions for a variety of applications. Although dual-band or even multiple-band high-Q resonances are applicable to extend the operation range of a nanophotonic device, manipulating the high-Q modes individually is a necessity to implement plural intriguing applications in one system as well as optimize the capabilities across each spectrum. In this work, a novel approach is presented to independently control dual high-Q modes with distinct origins in an all-dielectric metasurface system. The structure consists of hollow nanorod dimers and is found to support a symmetry-protected bound state in the continuum and a guided mode resonance induced by Brillouin-zone-folding effect. Independent and deliberate Q-factor control of these two high-Q optical resonances can be achieved by breaking the disparate mode symmetries. The two modes are found to have distinct polarization properties and Q-factor features across the momentum space. With rich tunable structural parameters, it is possible to develop a multifunctional device meeting specific requirements at each band. This work provides a new method for operating band broadening, performance optimization, and functionality enrichment for nanophotonic devices.

Realization of Merged Topological Corner States in the Continuum in Acoustic Crystals

Merging bound states in the continuum (BICs) has significant promise for wave manipulation since it can provide an ultrahigh Q factor when compared to the isolated BICs. However, the study of merging topological bound states in the continuum (TBICs) remains largely unexplored. In this Letter, we introduce a straightforward structure for crafting the merged higher order TBICs, i.e., the merged topological corner states in the continuum (MTCICs), via a synthetic way. Two identical topological insulators, supporting topological corner states within the bulk band, are mirror stacked. The eigenstates inherited from a single layer experience energy spectrum shifts without hybridization as interlayer couplings change, leading to the emergence of MTCICs. With acoustic crystals, we experimentally identify and characterize the MTCICs. The results evidently confirm the superior energy confinement capabilities of MTCICs over TBICs and gapped topological corner states (TCSs). Our Letter may deepen the understandings of both topological and BIC physics to inspire the development of devices with ultrahigh Q factor and enhanced robustness.

Degenerate merging BICs in resonant metasurfaces

Resonant metasurfaces driven by bound states in the continuum (BIC) offer an intriguing approach to engineering high-Q resonances. Merging multiple BICs in the momentum space could further enhance the Q-factor as well as its robustness to fabrication imperfections. Here, we report the doubly degenerate guided mode resonances (GMR) in a resonant metasurface, whose radiation losses could be totally suppressed due to merging BICs. We show that the GMRs and their associated accidental BICs can evolve into degenerate merging BICs by parametric tuning of the metasurface. Significantly, these two GMRs share the same critical parameter (i.e., lattice constants or thickness) that the merging BICs occur. Interestingly, thanks to the degenerate property of two GMRs, a larger (smaller) period will split one of the merging BICs into eight accidental BICs at an off-Γ point but annihilate the other. Such an exotic phenomenon can be explained by the interaction of GMRs and background Fabry-Perot resonances. Our result provides new, to the best of our knowledge, strategies for engineering high-Q resonances in resonant metasurfaces for light-matter interaction.

Topologically Protected Plasmonic Bound States in the Continuum

Experimental realizations of bound states in the continuum (BICs) with strong robustness and advanced maneuverability in optical loss systems remain a long-standing challenge in nanophotonics. Here, we propose and fabricate a paradigm of diatomic metagratings incorporating the Su-Schrieffer-Heeger model into the design of plasmonic nanocavities to demonstrate optical resonators with a continuous "quasi-BICs (qBICs)-BICs-qBICs" transition. These resonators feature a topological band inversion, making high-quality (Q) resonances immune to the perturbation of incident angles and geometrical parameters. Furthermore, we strive to establish theoretical models to verify the topological nature of BICs-inspired resonances and introduce nonlinear optical probes to quantify strongly enhanced local fields at high-Q resonances. Our findings may provide a simple yet feasible design strategy for facilitating the dissipationless manipulation of surface/interface-enhanced light-matter interactions at the nanoscale, substantially broadening the functional scope of metaphotonics.

Optical moiré bound states in the continuum

Trapping electromagnetic waves within the radiation continuum holds significant implications in the field of optical science and technology. Photonic bound states in the continuum (BICs) present a distinctive approach for achieving this functionality, offering potential applications in laser systems, sensing technologies, and other domains. However, the simultaneous achievement of high Q-factors, flat-band dispersions, and wide-angle responses in photonic BICs has not yet been reported, thereby impeding their practical performance due to laser direction deviation or sample disorder. Here, we theoretically demonstrate the construction of moiré BICs in one-dimensional photonic crystal (PhC) slabs, where high-Q resonances in the entire moiré flat band are achieved. Specifically, we numerically validate that the radiation loss of moiré BICs can be eliminated by aligning multiple topological polarization charges with all diffraction channels, enabling the strong suppression of far-field radiation from the entire moiré band. This leads to a slow decay of Q-factors away from moiré BICs in the momentum space. Moreover, it is found that Q-factors of the moiré flat band can still maintain at a high level with structural disorder. In experiments, we fabricate the designed 1D moiré PhC slab and observe both high-Q resonances and a slow decrease of Q-factors for moiré flat-band Bloch modes. Our findings hold promising implications for designing highly efficient optical devices with wide-angle responses and introduce a novel avenue for exploring BICs in moiré superlattices.

Observation of Ultra-High-Q Resonators in the Ultrasound via Bound States in the Continuum

The confinement of waves in open systems represents a fundamental phenomenon extensively explored across various branches of wave physics. Recently, significant attention is directed toward bound states in the continuum (BIC), a class of modes that are trapped but do not decay in an otherwise unbounded continuum. Here, the theoretical investigation and experimental demonstration of the existence of quasi-bound states in the continuum (QBIC) for ultrasonic waves are achieved by leveraging an elastic Fabry-Pérot metasurface resonator. Several intriguing properties of the ultrasound quasi-bound states in the continuum that are robust to parameter scanning are unveiled, and experimental evidence of a remarkable Q-factor of 350 at ≈1 MHz frequency, far exceeding the state-of-the-art using a fully acoustic underwater system is presented. The findings contribute novel insights into the understanding of BIC for acoustic waves, offering a new paradigm for the design of efficient, ultra-high Q-factor ultrasound devices.

Radiationless optical modes in metasurfaces: recent progress and applications

Non-radiative optical modes attracted enormous attention in optics due to strong light confinement and giant Q-factor at its spectral position. The destructive interference of multipoles leads to zero net-radiation and strong field trapping. Such radiationless states disappear in the far-field, localize enhanced near-field and can be excited in nano-structures. On the other hand, the optical modes turn out to be completely confined due to no losses at discrete point in the radiation continuum, such states result in infinite Q-factor and lifetime. The radiationless states provide a suitable platform for enhanced light matter interaction, lasing, and boost nonlinear processes at the state regime. These modes are widely investigated in different material configurations for various applications in both linear and nonlinear metasurfaces which are briefly discussed in this review.

Quasi-BICs enhanced second harmonic generation from WSe2 monolayer

Quasi-bound states in the continuum (quasi-BICs) offer unique advantages in enhancing nonlinear optical processes and advancing the development of active optical devices. Here, the tunable robust quasi-BICs resonances are experimentally achieved through the engineering of multiple-hole Si-metasurface. Notably, the quasi-BICs mode exhibits flat bands with minimal dispersion at a wide range of incident angles, as demonstrated by the angle-resolved spectroscopy measurements. Furthermore, we demonstrate a giant second-harmonic generation (SHG) enhancement by coupling a WSe2 monolayer to the quasi-BICs hosted in the metasurface. Leveraging the strong local electric field and high state density of the observed quasi-BICs, the SHG from the WSe2 monolayer can be enhanced by more than two orders of magnitude. Our work paves the way for effectively enhancing nonlinear optical processes in two dimensional (2D) materials within the framework of silicon photonics and is expected to be applied in nonlinear optical devices.

Spin-Orbit-Locking Chiral Bound States in the Continuum

Bound states in the continuum (BICs), which are confined optical modes exhibiting infinite quality factors and carrying topological polarization configurations in momentum space, have recently sparked significant interest across both fundamental and applied physics. Here, we show that breaking time-reversal symmetry by an external magnetic field enables a new form of chiral BICs with spin-orbit locking. Applying a magnetic field to a magneto-optical photonic crystal slab lifts doubly degenerate BICs into a pair of chiral BICs carrying opposite pseudospins and orbital angular momenta. Multipole analysis verifies the nonzero angular momenta and reveals the spin-orbital-locking behaviors. In momentum space, we observe ultrahigh quality factors and near-circular polarization surrounding chiral BICs, enabling potential applications in spin-selective nanophotonics. Compared to conventional BICs, the magnetically induced chiral BICs revealed here exhibit distinct properties and origins, significantly advancing the topological photonics of BICs by incorporating broken time-reversal symmetry.

Evolution of topological singularities below the light line in momentum space

Polarization singularities that exist in momentum space have brought new opportunities in various fields such as enhanced optical nonlinearity, structured laser sources, and light field manipulation. However, previous researches have predominantly focused on the polarization singularities above the light line, because they have no leakage and are referred to bound states in the continuum. Here, by extending the polarization fields to Fourier components of the evanescent field on a dielectric metasurface, polarization singularities of different Fourier orders are discovered below the light line. When continuously changing the geometrical parameters of the metasurface, a Fourier order transition process of the polarization singularity is observed through the bandgap closing at the boundary of the Brillouin zone, which finally leads to the annihilation of two singularities with opposite topological charges below the light line. These findings expand the understanding of polarization singularities in the near-field region and may find applications in light field manipulation and light-matter interaction.

Coherent light-emitting metasurfaces based on bound states in the continuum

An emergent need exists for solid state tunable coherent light emitters in the mid-infrared range for spectroscopy, sensing, and communication applications where current light sources are dominated by spontaneous emitters. This paper demonstrates a distinct class of coherent thermal emitters operating in the mid-infrared wavelength regime. The structure of the light source consists of a dielectric metasurface fabricated on a phononic substrate. In this study, we present the first implementation of off-Γ Friedrich-Wintgen bound states in the continuum at mid-infrared wavelengths suitable for developing the next generation of coherent light emitters. Numerical analysis of the emissivity spectrum reveals the interference of resonances leading to avoided crossings and the formation of Friedrich-Wintgen bound states in the radiation spectrum. Additionally, significant localized field enhancements are observed within the metasurface at operating wavelengths. The emissivity spectra measured by reflectivity and emission experiments exhibit temporally coherent emission peaks in the vicinity of the bound state in the continuum, the first such demonstration in the mid-infrared region for wavelengths longer than 7 µm. These results represent a new approach for significant advancement in realizing mid-infrared coherent light emitters with promising implications for future technologies.

Bound states in the continuum in divided triangular hole metasurfaces

We investigate the bound states in the continuum (BICs) in dielectric metasurfaces consisting of a two-part divided triangular hole in the unit cell of a square lattice, with emphasis on the generation, splitting, and merging of BICs. At the smallest height ratio between the upper triangular and the lower trapezoidal holes, the accidental BIC with an extremely large quality factor emerges on an isolated dispersion band at the Brillouin zone center, which is recognized as a polarization singularity (V point) with an integer topological charge. As the height ratio increases, the accidental BIC is split into a pair of circularly polarized states, which are polarization singularities (C points) with half-integer topological charges. The two states depart from each other to a maximum distance, and then approach each other as the height ratio continues to change. They finally merge to another polarization singularity (V point) with an integer topological charge, which is identified as the Friedrich-Wintgen BIC that occurs near the avoided crossing between two interacting dispersion bands.

Design of an ultrafast plasmonic nanolaser for high-intensity broadband emission operating at room temperature

We propose a plasmonic nanolaser based on a metal-insulator-semiconductor-insulator-metal (MISIM) structure, which effectively confines light on a subwavelength scale (∼λ/14). As the pump power increases, the proposed plasmonic nanolaser exhibits broadband output characteristics of 20 nm, and the maximum output power can reach 20 µW. Furthermore, the carrier lifetime at the upper energy level in our proposed structure is measured to be about 400 fs using a double pump-probe excitation. The ultrafast characteristic is attributed to the inherent Purcell effect of plasmonic systems. Our work paves the way toward deep-subwavelength mode confinement and ultrafast femtosecond plasmonic lasers in spaser-based interconnected, eigenmode engineering of plasmonic nanolasers, nano-LEDs, and spontaneous emission control.

Super Bound States in the Continuum on a Photonic Flatband: Concept, Experimental Realization, and Optical Trapping Demonstration

In this Letter, we theoretically propose and experimentally demonstrate the formation of a super bound state in a continuum (BIC) on a photonic crystal flat band. This unique state simultaneously exhibits an enhanced quality factor and near-zero group velocity across an extended region of the Brillouin zone. It is achieved at the topological transition when a symmetry-protected BIC pinned at k=0 merges with two Friedrich-Wintgen quasi-BICs, which arise from the destructive interference between lossy photonic modes of opposite symmetries. As a proof of concept, we employ the ultraflat super BIC to demonstrate three-dimensional optical trapping of individual particles. Our findings present a novel approach to engineering both the real and imaginary components of photonic states on a subwavelength scale for innovative optoelectronic devices.

Merging diverse bound states in the continuum: from intrinsic to extrinsic scenarios

Bound states in the continuum (BICs) in photonic crystal slabs are characterized as vortex centers in far-field polarization and infinite quality (Q) factors, which can be dynamically manipulated in momentum space to construct the singularity configurations with functionalities such as merging BICs for further suppress scattering loss of nearby resonance. However, the vast majority of research focuses on two types of intrinsic BICs for simplicity, because these polarization singularities affect each other, and are even prone to annihilation. Here, we introduce the extrinsic (Fabry-Pérot) BICs and combine them with the intrinsic BICs to merge diverse BICs in momentum space. The extrinsic BICs can move independently of the intrinsic BICs, providing an unprecedented degree of freedom to reduce the complexity of constructing merging BIC configurations. Interestingly, an interaction of oppositely charged BICs that is collision beyond annihilation is revealed, which only exchanges the topological charge of BICs but not affect their existence. Following the proposed strategy, four-types-BICs merging and steerable three-types merging are achieved at the Γ and off-Γ points, further boosting the Q factor scaling rule up to Q∝k x-14 and Q∝k x-6 respectively. Our findings suggest a systematic route to arrange abundant BICs, may facilitate some applications including beam steering, optical trapping and enhancing the light-matter interactions.

Ultra-high Q resonances based on zero group-velocity modes accompanied by bound states in the continuum in 2D photonic crystal slabs

Optical resonators made of 2D photonic crystal (PhC) slabs provide efficient ways to manipulate light at the nanoscale through small group-velocity modes with low radiation losses. The resonant modes in periodic photonic lattices are predominantly limited by nonleaky guided modes at the boundary of the Brillouin zone below the light cone. Here, we propose a mechanism for ultra-high Q resonators based on the bound states in the continuum (BICs) above the light cone that have zero-group velocity (ZGV) at an arbitrary Bloch wavevector. By means of the mode expansion method, the construction and evolution of avoided crossings and Friedrich-Wintgen BICs are theoretically investigated at the same time. By tuning geometric parameters of the PhC slab, the coalescence of eigenfrequencies for a pair of BIC and ZGV modes is achieved, indicating that the waveguide modes are confined longitudinally by small group-velocity propagation and transversely by BICs. Using this mechanism, we engineer ultra-high Q nanoscale resonators that can significantly suppress the radiative losses, despite the operating frequencies above the light cone and the momenta at the generic k point. Our work suggests that the designed devices possess potential applications in low-threshold lasers and enhanced nonlinear effects.

Merging toroidal dipole bound states in the continuum without up-down symmetry in Lieb lattice metasurfaces

The significance of bound states in the continuum (BICs) lies in their potential for theoretically infinite quality factors. However, their actual quality factors are limited by imperfections in fabrication, which lead to coupling with the radiation continuum. In this study, we present a novel approach to address this issue by introducing a merging BIC regime based on a Lieb lattice. By utilizing this approach, we effectively suppress the out-of-plane scattering loss, thereby enhancing the robustness of the structure against fabrication artifacts. Notably, unlike previous merging systems, our design does not rely on the up-down symmetry of metasurfaces. This characteristic grants more flexibility in applications that involve substrates and superstrates with different optical properties, such as microfluidic devices. Furthermore, we incorporate a lateral band gap mirror into the design to encapsulate the BIC structure. This mirror serves to suppress the in-plane radiation resulting from finite-size effects, leading to a remarkable ten-fold improvement in the quality factor. Consequently, our merged BIC metasurface, enclosed by the Lieb lattice photonic crystal mirror, achieves an exceptionally high-quality factor of 105 while maintaining a small footprint of 26.6 × 26.6 μm. Our findings establish an appealing platform that capitalizes on the topological nature of BICs within compact structures. This platform holds great promise for various applications, including optical trapping, optofluidics, and high-sensitivity biodetection, opening up new possibilities in these fields.

Bifurcation of bound states in the continuum in periodic structures

In lossless dielectric structures with a single periodic direction, a bound state in the continuum (BIC) is a special resonant mode with an infinite quality factor (Q factor). The Q factor of a resonant mode near a typical BIC satisfies Q∼1/(β-β ∗)2, where β and β ∗ are the Bloch wavenumbers of the resonant mode and the BIC, respectively. However, for some special BICs with β ∗=0 (referred to as super-BICs by some authors), the Q factor satisfies Q ∼ 1/β6. Although super-BICs are usually obtained by merging a few BICs through tuning a structural parameter, they can be precisely characterized by a mathematical condition. In this Letter, we consider arbitrary perturbations to structures supporting a super-BIC. The perturbation is given by δF(r), where δ is the amplitude and F(r) is the perturbation profile. We show that for a typical F(r), the BICs in the perturbed structure exhibit a pitchfork bifurcation around the super-BIC. The number of BICs changes from one to three as δ passes through zero. However, for some special profiles F(r), there is no bifurcation, i.e., there is only a single BIC for δ around zero. In that case, the super-BIC is not associated with a merging process for which δ is the parameter.

Topological Nature of Radiation Asymmetry in Bilayer Metagratings

Manipulating radiation asymmetry of photonic structures is of particular interest in many photonic applications such as directional optical antenna, high efficiency on-chip lasers, and coherent light control. Here, we proposed a term of pseudopolarization to reveal the topological nature of radiation asymmetry in bilayer metagratings. Robust pseudopolarization vortex with an integer topological charge exists in P-symmetry metagrating, allowing for tunable directionality ranging from -1 to 1 in synthetic parameter space. When P-symmetry breaking, such vortex becomes pairs of C points due to the conservation law of charge, leading to the phase difference of radiation asymmetry from π/2 to 3π/2. Furthermore, topologically enabled coherent perfect absorption is robust with customized phase difference at will between two counterpropagating external light sources. This Letter can not only enrich the understanding of two particular topological photonic behaviors, i.e., bound state in the continuum and unidirectional guided resonance, but also provide a topological view on radiation asymmetry, opening an unexplored avenue for asymmetric light manipulation in on-chip laser, light-light switch, and quantum emitters.

Realizing high-efficiency third harmonic generation via accidental bound states in the continuum

The bound states in the continuum (BICs) have attracted much attention in designing metasurface due to their high Q-factor and effectiveness in suppressing radiational loss. Here we report on the realization of the third harmonic generation (THG) at a near-ultraviolet wavelength (343 nm) via accidental BICs in a metasurface. The absolute conversion efficiency of the THG reaches 1.13 × 10-5 at a lower peak pump intensity of 0.7 GW/cm2. This approach allows the generation of an unprecedentedly high nonlinear conversion efficiency with simple structures.

Governance of Friedrich-Wintgen bound states in the continuum by tuning the internal coupling of meta-atoms

Bound state in the continuum (BIC) is a phenomenon that describes the perfect confinement of electromagnetic waves despite their resonant frequencies lying in the continuous radiative spectrum. BICs can be realized by introducing a destructive interference between distinct modes, referred to as Friedrich-Wintgen BICs (FW-BICs). Herein, we demonstrate that FW-BICs can be derived from coupled modes of individual split-ring resonators (SRR) in the terahertz band. The eigenmode results manifest that FW-BICs are in the center of the far-field polarization vortices. Quasi-BIC-I keeps an ultrahigh quality factor (Q factor) in a broad momentum range along the Γ-X direction, while the Q factor of the quasi-BIC-II drops rapidly. Our results can facilitate the design of devices with high-Q factors with extreme robustness against the incident angle.

Three-Dimensional Reconfigurable Optical Singularities in Bilayer Photonic Crystals

Metasurfaces and photonic crystals have revolutionized classical and quantum manipulation of light and opened the door to studying various optical singularities related to phases and polarization states. However, traditional nanophotonic devices lack reconfigurability, hindering the dynamic switching and optimization of optical singularities. This paper delves into the underexplored concept of tunable bilayer photonic crystals (BPhCs), which offer rich interlayer coupling effects. Utilizing silicon nitride-based BPhCs, we demonstrate tunable bidirectional and unidirectional polarization singularities, along with spatiotemporal phase singularities. Leveraging these tunable singularities, we achieve dynamic modulation of bound-state-in-continuum states, unidirectional guided resonances, and both longitudinal and transverse orbital angular momentum. Our work paves the way for multidimensional control over polarization and phase, inspiring new directions in ultrafast optics, optoelectronics, and quantum optics.

Directive giant upconversion by supercritical bound states in the continuum

Photonic bound states in the continuum (BICs), embedded in the spectrum of free-space waves1,2 with diverging radiative quality factor, are topologically non-trivial dark modes in open-cavity resonators that have enabled important advances in photonics3,4. However, it is particularly challenging to achieve maximum near-field enhancement, as this requires matching radiative and non-radiative losses. Here we propose the concept of supercritical coupling, drawing inspiration from electromagnetically induced transparency in near-field coupled resonances close to the Friedrich-Wintgen condition2. Supercritical coupling occurs when the near-field coupling between dark and bright modes compensates for the negligible direct far-field coupling with the dark mode. This enables a quasi-BIC field to reach maximum enhancement imposed by non-radiative loss, even when the radiative quality factor is divergent. Our experimental design consists of a photonic-crystal nanoslab covered with upconversion nanoparticles. Near-field coupling is finely tuned at the nanostructure edge, in which a coherent upconversion luminescence enhanced by eight orders of magnitude is observed. The emission shows negligible divergence, narrow width at the microscale and controllable directivity through input focusing and polarization. This approach is relevant to various physical processes, with potential applications for light-source development, energy harvesting and photochemical catalysis.

Non-generic bound states in the continuum in waveguides with lateral leakage channels

For optical waveguides with a layered background which itself is a slab waveguide, a guided mode is a bound state in the continuum (BIC), if it coexists with slab modes propagating outwards in the lateral direction; i.e., there are lateral leakage channels. It is known that generic BICs in optical waveguides with lateral leakage channels are robust in the sense that they still exist if the waveguide is perturbed arbitrarily. However, the theory is not applicable to non-generic BICs which can be defined precisely. Near a BIC, the waveguide supports resonant and leaky modes with a complex frequency and a complex propagation constant, respectively. In this paper, we develop a perturbation theory to show that the resonant and leaky modes near a non-generic BIC have an ultra-high Q factor and ultra-low leakage loss, respectively. Recently, many authors studied merging-BICs in periodic structures through tuning structural parameters. It has been shown that resonant modes near a merging-BIC have an ultra-high Q factor. However, the existing studies on merging-BICs are concerned with specific examples and specific parameters. Moreover, we analyze an arbitrary structural perturbation given by δF(r) to waveguides supporting a non-generic BIC, where F(r) is the perturbation profile and δ is the amplitude, and show that the perturbed waveguide has two BICs for δ > 0 (or δ < 0) and no BIC for δ < 0 (or δ > 0). This implies that a non-generic BIC can be regarded as a merging-BIC (for almost any perturbation profile F) when δ is considered as a parameter. Our study indicates that non-generic BICs have interesting special properties that are useful in applications.

Photonic Bound States in the Continuum in Nanostructures

Bound states in the continuum (BIC) have garnered considerable attention recently for their unique capacity to confine electromagnetic waves within an open or non-Hermitian system. Utilizing a variety of light confinement mechanisms, nanostructures can achieve ultra-high quality factors and intense field localization with BIC, offering advantages such as long-living resonance modes, adaptable light control, and enhanced light-matter interactions, paving the way for innovative developments in photonics. This review outlines novel functionality and performance enhancements by synergizing optical BIC with diverse nanostructures, delivering an in-depth analysis of BIC designs in gratings, photonic crystals, waveguides, and metasurfaces. Additionally, we showcase the latest advancements of BIC in 2D material platforms and suggest potential trajectories for future research.

Observation of the bound states in the continuum supported by mode coupling in a terahertz metasurface

Metasurface supporting bound states in the continuum (BIC) provides a unique approach for the realization of intense near-field enhancement and high quality factor (Q-factor) resonance, which promote the advancement of various applications. Here we experimentally demonstrate a Friedrich-Wintgen BIC based on the mode coupling in the terahertz metasurface, which produces BIC by the coupling of the LC mode and dipole mode resonances. The transition from ideal BIC to quasi-BIC is caused by the mismatch of the coupling, and the mode decay rate during this process is analyzed by temporal coupled mode theory. The Q-factor and the electric field enhancement of the quasi-BIC resonance are significantly increased, which provides enormous potential in sensing, nonlinear optics, and topological optics.

Passive nonreciprocal transmission and optical bistability based on polarization-independent bound states in the continuum

Free-space nonreciprocal transmission is a crucial aspect of modern optics devices. The implementation of nonreciprocal optical devices through optical nonlinearity has been demonstrated. However, due to the weak nonlinearity of traditional materials, most self-biased nonreciprocal devices are heavily dependent on the high Q strong resonances. In general, these resonances are frequently polarization sensitive. In this work, we propose ultrathin optical metasurface embedding Kerr nonlinearities to achieve nonreciprocal transmission and optical bistability for free-space propagation based on symmetry-protected bound states in the continuum (BICs). Since the structure of the metasurface retains C4ν symmetry, the symmetry-protected BIC is polarization-independent. It is also shown that the nonreciprocal intensity range could be largely tuned by the structure parameters. The demonstrated devices merge the field of nonreciprocity with ultrathin metasurface technologies making this design an exciting prospect for an optical switch, routing, and isolator with optimal performance.

Bound states in the continuum in anisotropic photonic crystal slabs

We investigate the bound states in the continuum (BICs) in photonic crystal slabs composed of alternating anisotropic and isotropic dielectric materials. According to the orientation of optical axis plane, three different configurations are proposed for analyzing various types of BICs, associated with extremely large quality factors and vanishing spectral linewidths. In particular, symmetry-protected (SP) BICs exist at the Brillouin zone center for zero rotation angle of the optical axis, which exhibit antisymmetric field patterns that are decoupled from the symmetric radiating fields. Accidental BICs and Friedrich-Wintgen (FW) BICs also occur at the Brillouin zone center for particular rotation angles of the optical axis. The former emerge on isolated bands with quasi-symmetric or quasi-antisymmetric field patterns, while the latter appear near the avoided crossing between two dispersion bands. At off the Brillouin zone center, SP BICs do not exist while accidental BICs and FW BICs appear at particular optical axis rotation angles, with similar features but somewhat more asymmetric field patterns than those at the Brillouin zone center.

General Bound States in the Continuum in Momentum Space

Polarization singularities including bound states in the continuum (BICs) and circularly polarized states have provided promising opportunities in the manipulation of light waves. Previous studies show that BICs in photonic crystal slabs are protected by C_{2}T symmetry and hence normally exist on the high-symmetry lines of momentum space. Here, we propose an approach based on graph theory to study these polarization singularities in momentum space, especially in the region off the high-symmetry lines. With a polarization graph, it is demonstrated for the first time that BICs can stably exist off the high-symmetry lines of momentum space for both one-dimensional and two-dimensional photonic crystal slabs. Furthermore, two kinds of interesting processes, including the merging involved with this newly found BICs both on and off the high-symmetry lines, are observed by changing the geometrical parameters of photonic crystal slabs while keeping their symmetry. Our findings provide a new perspective to explore polarization singularities in momentum space and render their further applications in light-matter interaction and light manipulation.

Bound chiral magnonic polariton states for ideal microwave isolation

Bound states in the continuum (BICs) present a unique solution for eliminating radiation loss. So far, most reported BICs are observed in transmission spectra, with only a few exceptions being in reflection spectra. The correlation between reflection BICs (r-BICs) and transmission BICs (t-BICs) remains unclear. Here, we report the presence of both r-BICs and t-BICs in a three-mode cavity magnonics. We develop a generalized framework of non-Hermitian scattering Hamiltonians to explain the observed bidirectional r-BICs and unidirectional t-BICs. In addition, we find the emergence of an ideal isolation point in the complex frequency plane, where the isolation direction can be switched by fine frequency detuning, thanks to chiral symmetry protection. Our results demonstrate the potential of cavity magnonics and also extend the conventional BICs theory through the application of a more generalized effective Hamiltonians theory. This work offers an alternative idea for designing functional devices in general wave optics.

Fluorescence enhancement of PbS colloidal quantum dots from silicon metasurfaces sustaining bound states in the continuum

PbS colloidal quantum dots (CQDs) can be considered a promising lighting material, but their emission performance is mired by defect sites, strong photo-induced activity, and interaction with the environment. Here, we utilize periodic silicon metasurface sustaining a symmetry-protected bound state in the continuum to enhance the near-infrared emission of PbS CQDs at room temperature. In the experimental investigation, it is observed that the fluorescence of the coated PbS CQDs is enhanced by 10 times by the fabricated metasurface, and the emission peak has a quality factor up to 251 at wavelength 1408 nm. Meanwhile, the potential of this work in sensing is demonstrated by showing that the enhanced emission is disturbed by the introduction of sparse gold nanoparticles. In all, this work confirms that dielectric metasurfaces sustaining bound states in the continuum can be adopted to efficiently improve the emission performance of PbS CQDs which may find various practical applications including on-chip silicon-based optical sources and integrated sensors.

Multiple symmetry protected BIC lines in two dimensional synthetic parameter space

Bound states in the continuum (BICs) have attracted significant interest in recent years due to their unique optical properties, such as infinite quality factor and wave localization. In order to improve the optical performance of BICs based devices, more degrees of freedom are required to tune BICs in high-dimension parameter space for practical applications. To effectively tune more BICs, we form a 2D synthetic parameter space based on a nanohole metasurface array. Multiple symmetry protected BIC modes with high Q factors can be achieved at high-order symmetry point. Through manipulating asymmetry parameters, BIC lines formed by a series of BIC modes can be found in the 2D synthetic parameter space. Moreover, the electric field distributions are investigated to demonstrate the generation and evolution of BICs. By measuring the absorption spectra, the tuning of multiple BICs with synthetic asymmetry parameters is experimentally explored, which agrees well with theoretical results. Therefore, our design can provide new insight for a variety of on-chip applications, such as nonlinear devices, integrated nanolasing array, and high-resolution sensors for infrared molecular detection.

Brillouin zone folding driven bound states in the continuum

Non-radiative bound states in the continuum (BICs) allow construction of resonant cavities with confined electromagnetic energy and high-quality (Q) factors. However, the sharp decay of the Q factor in the momentum space limits their usefulness for device applications. Here we demonstrate an approach to achieve sustainable ultrahigh Q factors by engineering Brillouin zone folding-induced BICs (BZF-BICs). All the guided modes are folded into the light cone through periodic perturbation that leads to the emergence of BZF-BICs possessing ultrahigh Q factors throughout the large, tunable momentum space. Unlike conventional BICs, BZF-BICs show perturbation-dependent dramatic enhancement of the Q factor in the entire momentum space and are robust against structural disorders. Our work provides a unique design path for BZF-BIC-based silicon metasurface cavities with extreme robustness against disorder while sustaining ultrahigh Q factors, offering potential applications in terahertz devices, nonlinear optics, quantum computing, and photonic integrated circuits.

Perfect linear polarization wave generator based on quasi-bound states in the continuum

Quasi-bound states in the continuum (q-BICs) in optical metasurfaces have been found to carry special radiation polarization properties. Herein, we have studied the relationship between the radiation polarization state of a q-BIC and the polarization state of the output wave, and theoretically proposed a perfect linear polarization wave generator controlled by the q-BIC. The proposed q-BIC has an x-polarized radiation state, and the y co-polarized output wave is completely eliminated by introducing additional resonance at the q-BIC frequency. Finally, a perfect x-polarized transmission wave with very low background scattering is obtained, and the transmission polarization state is not limited by the incident polarization state. The device can be used to efficiently obtain narrowband linearly polarized waves from non-polarized waves, and can also be used for polarization-sensitive high-performance spatial filtering.

Quasi-bound states in the continuum with a stable resonance wavelength in dimer dielectric metasurfaces

Symmetry-protected bound states in the continuum (SP-BICs) are one of the most intensively studied BICs. Typically, SP-BICs must be converted into quasi-BICs (QBICs) by breaking the unit cell's symmetry so that they can be accessed by the external excitation. The symmetry-broken usually results in a varied resonance wavelength of QBICs which are also highly sensitive to the asymmetry parameters. In this work, we demonstrate that QBICs with a stable resonance wavelength can be realized by breaking translational symmetry in an all-dielectric metasurface. The unit cell of metasurface is made of a silicon nanodisk dimer. The Q-factor of QBICs is precisely tuned by changing the interspacing of two nanodisks while their resonance wavelength is quite stable against the interspacing. We also find that such BICs show weak dependence on the shape of the nanodisk. Multiple decompositions indicate that the toroidal dipole dominates this type of QBIC. The resonance wavelengths of QBICs can be tuned only by changing either the lattice constants or the radius of nanodisk. Finally, we present experimental demonstrations on such a QBIC with a stable resonance wavelength. The highest measured Q-factor of QBICs is >3000. Our results may find promising applications in enhancing light-matter interaction.

Photonic spin-selective perfect absorptance on planar metasurfaces driven by chiral quasi-bound states in the continuum

Optical metasurfaces with high-quality-factor resonances and selective chirality simultaneously are desired for nanophotonics. Here, an all-dielectric planar chiral metasurface is theoretically proposed and numerically proved to support the astonishing symmetry-protected bound state in the continuum (BIC), due to the preserved π rotational symmetry around the z axis and up-down mirror symmetry simultaneously. Importantly, such BIC is a vortex polarization singularity enclosed by elliptical eigenstate polarizations with non-vanishing helicity, owing to the broken in-plane mirror symmetry. Under the oblique incidence, companied by the BIC transforming into a quasi-BIC (Q-BIC), the strong extrinsic chirality manifests. Assisted by the single-port critical coupling, the planar metasurface can selectively and near-perfectly absorb one circularly polarized light but non-resonantly reflect its counterparts. The circular dichroism (CD) approaching 0.812 is achieved. Intriguingly, the sign of CD (namely, the handedness of the chiral metasurface) can be flexibly manipulated only via varying the azimuthal angle of incident light, due to the periodic helicity sign flip in eigen polarizations around the BIC. Numerical results are consistent with the coupled-mode theory and multipole decomposition method. The spin-selective metasurface absorber empowered by the physics of chiral Q-BICs undoubtedly may promise various applications such as optical filters, polarization detectors, and chiral imaging.

Universal Mirror-Stacking Approach for Constructing Topological Bound States in the Continuum

Bound states in the continuum (BICs) are counterintuitive localized states with eigenvalues embedded in the continuum of extended states. Recently, nontrivial band topology is exploited to enrich the BIC physics, resulting in topological BICs (TBICs) with extraordinary robustness against perturbations or disorders. Here, we propose a simple but universal mirror-stacking approach to turn nontrivial bound states of any topological monolayer model into TBICs. Physically, the mirror-stacked bilayer Hamiltonian can be decoupled into two independent subspaces of opposite mirror parities, each of which directly inherits the energy spectrum information and band topology of the original monolayer. By tuning the interlayer couplings, the topological bound state of one subspace can move into and out of the continuum of the other subspace continuously without hybridization. As representative examples, we construct one-dimensional first-order and two-dimensional higher-order TBICs, and demonstrate them unambiguously by acoustic experiments. Our findings will expand the research implications of both topological materials and BICs.

Polarization multiplexing multichannel high-Q terahertz sensing system

Terahertz functional devices with high-Q factor play an important role in spectral sensing, security imaging, and wireless communication. The reported terahertz devices based on the electromagnetic induction transparency (EIT) effect cannot meet the needs of high-Q in practical applications due to the low-Q factor. Therefore, to increase the Q-factor of resonance, researchers introduced the concept of bound state in the continuum (BIC). In the quasi-BIC state, the metasurface can be excited by the incident wave and provide resonance with a high-Q factor because the condition that the resonant state of the BIC state is orthogonal is not satisfied. The split ring resonator (SRR) is one of the most representative artificial microstructures in the metasurface field, and it shows great potential in BIC. In this paper, based on the classical single-SRR array structure, we combine the large and small SRR and change the resonance mode of the inner and outer SRR by changing the outer radius of the inner SRR. The metasurface based on parameter-tuned BIC verified that the continuous modulation of parameters in a system could make a pair of resonant states strongly coupled, and the coherent cancellation of the resonant states will cause the linewidth of one of the resonant states to disappear, thus forming BIC. Compared with the single-SRR array metasurface based on symmetry-protected BIC, the dual-SRR array metasurface designed in this paper has multiple accidental BICs and realizes multichannel multiplexing of X-polarization and Y-polarization. It provides a brilliant platform for high-sensitivity optical sensor array, low threshold laser and efficient optical harmonic generation.

Exploiting extraordinary topological optical forces at bound states in the continuum

Polarization singularities and topological vortices in photonic crystal slabs centered at bound states in the continuum (BICs) can be attributed to zero amplitude of polarization vectors. We show that such topological features are also observed in optical forces within the vicinity of BIC, around which the force vectors wind in the momentum space. The topological force carries force topological charge and can be used for trapping and repelling nanoparticles. By tailoring asymmetry of the photonic crystal slab, topological force will contain spinning behavior and shifted force zeros, which can lead to three-dimensional asymmetric trapping. Several off-Γ BICs generate multiple force zeros with various force distribution patterns. Our findings introduce the concepts of topology to optical force around BICs and create opportunities to realize optical force vortices and enhanced reversible forces for manipulating nanoparticles and fluid flow.

Spin Hall Effect of Light via Momentum-Space Topological Vortices around Bound States in the Continuum

Optical bound states in the continuum (BICs) are exotic topological defects in photonic crystal slabs, carrying polarization topological vortices in momentum space. The topological vortex configurations not only topologically protect the infinite radiation lifetime of BICs, but also intrinsically contain many unexploited degrees of freedom for light manipulation originating from BICs. Here, we theoretically propose and experimentally demonstrate the spin Hall effect of light in photonic crystal slabs via momentum-space topological vortices around BICs. The strong spin-orbit interactions of light are induced by using the topological vortices around BICs, introducing both wave-vector-dependent Pancharatnam-Berry phase gradients and cross-polarized resonant phase gradients to the spinning light beam, which lead to spin-dependent in-plane-oblique lateral light beam shifts. Our work reveals intriguing spin-related topological effects around BICs, opening an avenue toward applications of BICs in integrated spin-optical devices and information processing.