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

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.

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.

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.

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.

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.

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.

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.

Dynamically tunable bound states in the continuum supported by asymmetric Fabry-Pérot resonance

The dynamic regulation of quasi-bound states in the continuum (quasi-BIC) is a research hotspot, such as incident angle, polarization angle, temperature, a medium refractive index, and medium position regulation. In this paper, a dual-band ultra-high absorber composed of upper asymmetric graphene strips and lower graphene nanoribbons can generate a symmetry-protected quasi-BIC and Fabry-Pérot resonance (FPR) mode. The band structure further demonstrates the symmetry-protected BIC. Research shows that the absorption system can withstand a relatively wide range of incidence and polarization angles. Interestingly, the quasi-BIC and FPR modes can be modulated by the Fermi levels of the graphene1 and graphene2, respectively, realizing a multifunctional switch with high modulation depth (MD > 94%), low insertion loss (IL < 0.23 dB), and large dephasing time (DT > 4.35 ps). This work provides a new approach for the dynamic regulation of quasi-BIC and stimulates the development of multifunctional switches in the absorber.

Merging bound states in the continuum by harnessing higher-order topological charges

Bound states in the continuum (BICs) can confine light with a theoretically infinite Q factor. However, in practical on-chip resonators, scattering loss caused by inevitable fabrication imperfection leads to finite Q factors due to the coupling of BICs with nearby radiative states. Merging multiple BICs can improve the robustness of BICs against fabrication imperfection by improving the Q factors of nearby states over a broad wavevector range. To date, the studies of merging BICs have been limited to fundamental BICs with topological charges ±1. Here we show the unique advantages of higher-order BICs (those with higher-order topological charges) in constructing merging BICs. Merging multiple BICs with a higher-order BIC can further improve the Q factors compared with those involving only fundamental BICs. In addition, higher-order BICs offer great flexibility in realizing steerable off-Γ merging BICs. A higher-order BIC at Γ can split into a few off-Γ fundamental BICs by reducing the system symmetry. The split BICs can then be tuned to merge with another BIC, e.g., an accidental BIC, at an off-Γ point. When the in-plane mirror symmetry is further broken, merging BICs become steerable in the reciprocal space. Merging BICs provide a paradigm to achieve robust ultrahigh-Q resonances, which are important in enhancing nonlinear and quantum effects and improving the performance of optoelectronic devices.

Topologically Enabled Ultrahigh-Q Chiroptical Resonances by Merging Bound States in the Continuum

Ultrahigh-Q chiroptical resonance metasurfaces based on merging bound states in the continuum (BICs) are investigated and numerically demonstrated. The destruction of C₂ symmetry results in the leakage of BICs into quasi-BICs, and a chiral quasi-BIC is obtained by oblique incidence or continuous destruction of the mirror symmetry of the structure. Due to the significant topological properties of merging BICs, the Q factor (over 2 × 10⁵) of the chiral resonance peak obtained is much higher than that of the previous work. Moreover, the proposed structure is easy to fabricate because no additional out-of-plane asymmetry is introduced. The proposed scheme is of importance in chiral biosensing applications.

Tailoring Polarization Conversion in Achiral All-Dielectric Metasurfaces by Using Quasi-Bound States in the Continuum

Quasi-bound states in the continuum (quasi-BICs) supported in all-dielectric metasurfaces (MTS) are known for their confinement in real space and the notably high values of the quality factor Q. Recently, the properties of quasi-BICs have been employed to achieve polarization conversion with all-dielectric MTS. However, one of the main disadvantages of the current approaches is the dependence on the chirality of either the meta-atoms or their disposition. We present the possibility of achieving polarization conversion by using all-dielectric MTS with square and rectangular lattices of nano-disks. The precise tuning of the lattice and disks parameters allows to transform linearly polarized light into circularly polarized light with near unity polarization rates while maintaining the high Q values of quasi-BICs. Moreover, by using double accidental BICs it is possible to obtain right and left circularly polarized light on demand just by varying the angle of incidence.

Moiré Quasibound States in the Continuum

The novel physics of twisted bilayer graphene has motivated extensive studies of magic-angle flat bands hosted by moiré structures in electronic, photonic, and acoustic systems. On the other hand, bound states in the continuum (BICs) have also attracted great attention in recent years because of their potential applications in the field of designing superior optical devices. Here, we combine these two independent concepts to construct a new optical state in a twisted bilayer photonic crystal slab, which is called as moiré quasi-BIC, and numerically demonstrate that such an exotic optical state possesses dual characteristics of moiré flat bands and quasi-BICs. To illustrate the mechanism for the formation of moiré flat bands, we develop an effective model at the center of the Brillouin zone and show that moiré flat bands could be fulfilled by balancing the interlayer coupling strength and the twist angle around the band edge above the light line. Moreover, by decreasing the twist angle of moiré photonic crystal slabs with flat bands, it is shown that the moiré flat-band mode at the Brillouin center gradually approaches a perfect BIC, where the total radiation loss from all diffraction channels is significantly suppressed. To clarify the advantage of moiré quasi-BICs, enhanced second-harmonic generation (SHG) is numerically proven with a wide-angle optical source. The efficiency of SHG assisted by designed moiré quasi-BICs can be greatly improved compared with that based on dispersive quasi-BICs with similar quality factors.

Adjustable converter of bound state in the continuum basing on metal-graphene hybrid metasurfaces

The bound state in the continuum (BIC) is widely applied to metamaterial study in order to obtain robust resonance and high quality (Q) factor. In this paper, we propose a metallic metasurface structure that can support double types of BICs, and acquire quasi-BIC state by restructuring each type with a specific approach. Electric field distribution is investigated to explore the physic mechanism behind the evolution of BICs. Moreover, we substitute structured graphene with corresponding metal counterparts. The promoted design is able to switch freely between BIC and quasi-BIC state even after the fabrication, as the graphene would convert from semiconductor-like to metal-like when increasing the Fermi level. Further exploration on electric field distribution demonstrates the metallicity difference between graphene and gold, which leads to the exotic phenomenon emerge on the proposed metal-graphene structure. Finally, the proposed metal-graphene structure is applied to a digital coding display through Fermi level regulating. Therefore, our work provides deep insights to the BIC metasurface investigation, and introduces a desirable improvement for current BIC metasurface design to achieve the free conversion between BIC and quasi-BIC states.

Bound states in the continuum based on the total internal reflection of Bloch waves

A photonic-crystal slab can support bound states in the continuum (BICs) that have infinite lifetimes but are embedded into the continuous spectrum of optical modes in free space. The formation of BICs requires a total internal reflection (TIR) condition at both interfaces between the slab and the free space. Here, we show that the TIR of Bloch waves can be directly obtained based on the generalized Fresnel equations proposed. If each of these Bloch waves picks up a phase with integer multiples of 2π for traveling a round trip, light can be perfectly guided in the slab, namely forming a BIC. A BIC solver with low computational complexity and fast convergence speed is developed, which can also work efficiently at high frequencies beyond the diffraction limit where multiple radiation channels exist. Two examples of multi-channel BICs are shown and their topological nature in momentum space is also revealed. Both can be attributed to the coincidence of the topological charges of far-field radiations from different radiation channels. The concept of the generalized TIR and the TIR-based BIC solver developed offer highly effective approaches for explorations of BICs that could have many potential applications in guided-wave optics and enhanced light-matter interactions.

Observation of bound states in the continuum embedded in symmetry bandgaps

In the past decade, symmetry-protected bound states in the continuum (BICs) have proven to be an important design principle for creating and enhancing devices reliant upon states with high-quality (Q) factors, such as sensors, lasers, and those for harmonic generation. However, as we show, current implementations of symmetry-protected BICs in photonic crystal slabs can only be found at the center of the Brillouin zone and below the Bragg diffraction limit, which fundamentally restricts their use to single-frequency applications. By microprinting a three-dimensional (3D) photonic crystal structure using two-photon polymerization, we demonstrate that this limitation can be overcome by altering the radiative environment surrounding the slab to be a 3D photonic crystal. This allows for the protection of a line of BICs by embedding it in a symmetry bandgap of the crystal. This concept substantially expands the design freedom available for developing next-generation devices with high-Q states.

Dynamics of Topological Polarization Singularity in Momentum Space

The polarization singularity in momentum space has recently been discovered as a new class of topological signatures of Bloch modes in photonic crystal slabs concerning the far-field radiations, beyond its near-field description with widely explored topological band theory. Bound states in the continuum (BICs) in photonic crystal slabs are demonstrated as vortex eigenpolarization singularities in momentum space and the circular polarization points (C points) are also obtained based on BICs, opening up more possibilities for exotic light scattering and various topological phenomena of singular optics. Here, focusing on the nondegenerate bands, we report the generation to annihilation of two pairs of C points in momentum space in the photonic crystal slabs with inversion symmetry but broken up-down mirror symmetry. Interestingly, as the C points evolve with the structure parameter, we find two merging processes of C points, where an accidental at-Γ BIC and unidirectional radiative resonances with leaky channels of drastically different radiative lifetime emerge. The whole evolution is governed by the global charge conservation and the sum of topological charges equals to zero. Our findings suggest a novel recipe for dynamic generation and manipulation of various polarization singularities in momentum space and might shed new light to control the resonant and topological properties of light-matter interactions.

High-quality-factor dual-band Fano resonances induced by dual bound states in the continuum using a planar nanohole slab

In photonics, it is essential to achieve high-quality (Q)-factor resonances to improve optical devices' performances. Herein, we demonstrate that high-Q-factor dual-band Fano resonances can be achieved by using a planar nanohole slab (PNS) based on the excitation of dual bound states in the continuum (BICs). By shrinking or expanding the tetramerized holes of the superlattice of the PNS, two symmetry-protected BICs can be induced to dual-band Fano resonances and their locations as well as their Q-factors can be flexibly tuned. Physical mechanisms for the dual-band Fano resonances can be interpreted as the resonant couplings between the electric toroidal dipoles or the magnetic toroidal dipoles based on the far-field multiple decompositions and the near-field distributions of the superlattice. The dual-band Fano resonances of the PNS possess polarization-independent feature, and they can be survived even when the geometric parameters of the PNS are significantly altered, making them more suitable for potential applications.