Compact surface Fano states embedded in the continuum of waveguide arrays

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.

Multibranch Elastic Bound States in the Continuum

Constructing a highly localized wave field by means of bound states in the continuum (BICs) promotes enhanced wave-matter interaction and offers approaches to high-sensitivity devices. Elastic waves can carry complex polarizations and thus differ from electromagnetic waves and other scalar mechanical waves in the formation of BICs, which is yet to be fully explored and exploited. Here, we report the investigation of local resonance modes supported by a Lamb waveguide side-branched with two pairs of resonant pillars and show the emergence of two groups of elastic BICs with different polarizations or symmetries. Particularly, the two groups of BICs exhibit distinct responses to external perturbations, based on which a label-free sensing scheme with enhanced-sensitivity is proposed. Our study reveals the rich properties of BICs arising from the complex wave dynamics in elastic media and demonstrates their unique functionality for sensing and detection.

Topological corner state localized bound states in continuum in photonic crystals

In the field of optics, bound states in the continuum (BICs) are of significant practical importance as they can trap electromagnetic waves spatially, even though their frequency lies within the continuous spectrum. Previous research, however, has shown that BICs localized in optical cavities are highly sensitive to geometric and environmental changes. This sensitivity implies that slight variations can lead to the loss of BICs, necessitating extreme precision in manufacturing, which poses a challenge for practical implementation. To overcome this issue, this study employs topological photonic crystals (PhCs) to engineer topological corner states (TCS) within PhCs. By doing so, it establishes a method for creating topological BICs that are inherently robust against disturbances, thereby enhancing their suitability for real-world applications.

Bound-state-in-continuum guided modes in a multilayer electro-optically active photonic integrated circuit platform

In many physical systems, the interaction with an open environment leads to energy dissipation and reduced coherence, making it challenging to control these systems effectively. In the context of wave phenomena, such lossy interactions can be specifically controlled to isolate the system, a condition known as a bound-state-in-continuum (BIC). Despite the recent advances in engineered BICs for photonic waveguiding, practical implementations are still largely polarization- and geometry-specific, and the underlying principles remain to be systematically explored. Here, we theoretically and experimentally study low loss BIC photonic waveguiding within a two-layer heterogeneous electro-optically active integrated photonic platform. We show that coupling to the slab wave continuum can be selectively suppressed for guided modes with different polarizations and spatial structure. We demonstrate a low-loss same-polarization quasi-BIC guided mode enabling a high extinction Mach-Zehnder electro-optic amplitude modulator within a single Si3N4 ridge waveguide integrated with an extended LiNbO3 slab layer. By elucidating the broad BIC waveguiding principles and demonstrating them in an industry-relevant photonic configuration, this work may inspire innovative approaches to photonic applications such as switching and filtering. The broader impact of this work extends beyond photonics, influencing research in other wave dynamics disciplines, including microwave and acoustics.

Robust and non-robust bound states in the continuum in rotationally symmetric periodic waveguides

A fiber grating and a one-dimensional (1D) periodic array of spheres are examples of rotationally symmetric periodic (RSP) waveguides. It is well known that bound states in the continuum (BICs) may exist in lossless dielectric RSP waveguides. Any guided mode in an RSP waveguide is characterized by an azimuthal index m, the frequency ω, and Bloch wavenumber β. A BIC is a guided mode, but for the same m, ω and β, cylindrical waves can propagate to or from infinity in the surrounding homogeneous medium. In this paper, we investigate the robustness of nondegenerate BICs in lossless dielectric RSP waveguides. The question is whether a BIC in an RSP waveguide with a reflection symmetry along its axis z, can continue its existence when the waveguide is perturbed by small but arbitrary structural perturbations that preserve the periodicity and the reflection symmetry in z. It is shown that for m = 0 and m ≠ 0, generic BICs with only a single propagating diffraction order are robust and non-robust, respectively, and a non-robust BIC with m ≠ 0 can continue to exist if the perturbation contains one tunable parameter. The theory is established by proving the existence of a BIC in the perturbed structure mathematically, where the perturbation is small but arbitrary, and contains an extra tunable parameter for the case of m ≠ 0. The theory is validated by numerical examples for propagating BICs with m ≠ 0 and β ≠ 0 in fiber gratings and 1D arrays of circular disks.

Permittivity-Asymmetric Quasi-Bound States in the Continuum

Breaking the in-plane geometric symmetry of dielectric metasurfaces allows us to access a set of electromagnetic states termed symmetry-protected quasi-bound states in the continuum (qBICs). Here we demonstrate that qBICs can also be accessed by a symmetry breaking in the permittivity of the comprising materials. While the physical size of atoms imposes a limit on the lowest achievable geometrical asymmetry, weak permittivity modulations due to carrier doping, and electro-optical Pockels and Kerr effects, usually considered insignificant, open the possibility of infinitesimal permittivity asymmetries for on-demand, dynamically tunable resonances of extremely high quality factors. As a proof-of-principle, we probe the excitation of permittivity-asymmetric qBICs (ε-qBICs) using a prototype Si/TiO₂ metasurface, in which the asymmetry in the unit cell is provided by the permittivity contrast of the materials. ε-qBICs are also numerically demonstrated in 1D gratings, where quality-factor enhancement and tailored interference phenomena of qBICs are shown via the interplay of geometrical and permittivity asymmetries.

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.

Label-Free Bound-States-in-the-Continuum Biosensors

Bound states in the continuum (BICs) have attracted considerable attentions for biological and chemical sensing due to their infinite quality (Q)-factors in theory. Such high-Q devices with enhanced light-matter interaction ability are very sensitive to the local refractive index changes, opening a new horizon for advanced biosensing. In this review, we focus on the latest developments of label-free optical biosensors governed by BICs. These BICs biosensors are summarized from the perspective of constituent materials (i.e., dielectric, metal, and hybrid) and structures (i.e., grating, metasurfaces, and photonic crystals). Finally, the current challenges are discussed and an outlook is also presented for BICs inspired biosensors.

Topological Floquet bound states in the continuum

A honeycomb array of helical waveguides with zigzag-zigzag edges and a refractive index gradient orthogonal to the edges may support Floquet bound states in the continuum (BICs). The gradient of the refractive index leads to strong asymmetry of the Floquet-Bloch spectrum. The mechanism of creation of such Floquet BICs is understood as emergence of crossings and avoided crossings of the branches supported by spatially limited stripe array. The whole spectrum of a finite array is split into the bulk branches being a continuation of the edge states in the extended zone revealing multiple self-crossings and bulk modes disconnected from the gap states by avoided crossings. Nearly all states in the system are localized due to the gradient, but topological edge states manifest much stronger localization than other states. Such strongly localized Floquet BICs coexist with localized Wannier-Stark-like bulk modes. Robustness of the edge Floquet states is confirmed by their passage through a localized edge defect in the form of a missing waveguide.

Recent Advances in Tunable Metasurfaces: Materials, Design, and Applications

Metasurfaces, a two-dimensional (2D) form of metamaterials constituted by planar meta-atoms, exhibit exotic abilities to tailor electromagnetic (EM) waves freely. Over the past decade, tremendous efforts have been made to develop various active materials and incorporate them into functional devices for practical applications, pushing the research of tunable metasurfaces to the forefront of nanophotonics. Those active materials include phase change materials (PCMs), semiconductors, transparent conducting oxides (TCOs), ferroelectrics, liquid crystals (LCs), atomically thin material, etc., and enable intriguing performances such as fast switching speed, large modulation depth, ultracompactness, and significant contrast of optical properties under external stimuli. Integration of such materials offers substantial tunability to the conventional passive nanophotonic platforms. Tunable metasurfaces with multifunctionalities triggered by various external stimuli bring in rich degrees of freedom in terms of material choices and device designs to dynamically manipulate and control EM waves on demand. This field has recently flourished with the burgeoning development of physics and design methodologies, particularly those assisted by the emerging machine learning (ML) algorithms. This review outlines recent advances in tunable metasurfaces in terms of the active materials and tuning mechanisms, design methodologies, and practical applications. We conclude this review paper by providing future perspectives in this vibrant and fast-growing research field.

Bound states in the continuum in waveguide arrays within a symmetry classification scheme

We study a photonic implementation of a modified Fano-Anderson model - a waveguide array with two additional waveguides and by using the coupled mode theory we calculate its spectral and scattering properties. We classify eigenmodes according to vertical symmetry of the structure given by self-coupling coefficients of the additional waveguides and establish the conditions for bound states in the continuum (BIC) existence. The main predictions drawn from the theoretical model are verified by rigorous full-wave simulations of realistic structures. We use the Weierstrass factorization theorem and interpret the scattering spectra of the systems with broken symmetry in terms of the eigenmodes. The Fano resonance related with excitation of quasi-BIC is explained as arising from the interference between this mode and another leaky mode.

Quasi-BIC-Based High-Q Perfect Absorber with Decoupled Resonant Wavelength and Q Factor

The Q factor in a quasi-BIC-based optical device can approach infinity and has therefore been attracting the attention of many researchers in recent years. However, this mode is barely applied to absorbers since it mainly tunes the radiative loss. The resonant wavelength of quasi-BICs normally couples with the Q factor, and it is difficult to independently tune one of them while maintaining the other, which weakens the flexibility of tuning. In this work, a quasi-BIC-based high-Q perfect absorber with some unique features is proposed. It shows a decoupled relationship between the resonant wavelength and the Q factor such that these two properties can be independently tuned by changing different structure parameters. In addition, both radiative and resistive losses are tunable. An easy method is proposed to design a perfect absorber with different resonant wavelengths and different Q factors, and a near-infrared perfect absorber with a Q factor as high as 5.13 × 105 is designed. This work proposes a method to tune the quasi-BIC mode, thereby introducing a new paradigm for the design of a high-Q perfect absorber.

Guiding-mode-assisted double-BICs in an all-dielectric metasurface

The electromagnetically induced transparency (EIT) effect realized in a metasurface is potential for slow light applications for its extreme dispersion variation in the transparency window. Herein, we propose an all-dielectric metasurface to generate a double resonance-trapped quasi bound states in the continuum (BICs) in the form of EIT or Fano resonance through selectively exciting the guiding modes with the grating. The group delay of the EIT is effectively improved up to 2113 ps attributing to the ultrahigh Q-factor resonance carried by the resonance-trapped quasi-BIC. The coupled harmonic oscillator model and a full multipole decomposition are utilized to analyze the physical mechanism of EIT-based quasi-BIC. In addition, the BIC based on Fano and EIT resonance can simultaneously exist at different wavelengths. These findings provide a new feasible platform for slow light devices in the near-infrared region.

Investigation of bound states in the continuum in dual-band perfect absorbers

Enhancing the light-matter interaction of two-dimensional materials in the visible and near-infrared regions is highly required in optical devices. In this paper, the optical bound states in the continuum (BICs) that can enhance the interaction between light and matter are observed in the grating-graphene-Bragg mirror structure. The system can generate a dual-band perfect absorption spectrum contributed by guided-mode resonance (GMR) and Tamm plasmon polarition (TPP) modes. The optical switch can also be obtained by switching the TE-TM wave. The dual-band absorption response is analyzed by numerical simulation and coupled-mode theory (CMT), with the dates of each approach displaying consistency. Research shows that the GMR mode can be turned into the Fabry-Pérot BICs through the transverse resonance principle (TRP). The band structures and field distributions of the proposed loss system can further explain the BIC mechanism. Both static (grating pitch P) and dynamic parameters (incident angle θ) can be modulated to generate the Fabry-Pérot BICs. Moreover, we explained the reason why the strong coupling between the GMR and TPPs modes does not produce the Friedrich-Wintgen BIC. Taken together, the proposed structure can not only be applied to dual-band perfect absorbers and optical switches but also provides guidance for the realization of Fabry-Pérot BICs in lossy systems.

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.

Nanoscale mapping of optically inaccessible bound-states-in-the-continuum

Bound-states-in-the-continuum (BIC) is an emerging concept in nanophotonics with potential impact in applications, such as hyperspectral imaging, mirror-less lasing, and nonlinear harmonic generation. As true BIC modes are non-radiative, they cannot be excited by using propagating light to investigate their optical characteristics. In this paper, for the 1st time, we map out the strong near-field localization of the true BIC resonance on arrays of silicon nanoantennas, via electron energy loss spectroscopy with a sub-1-nm electron beam. By systematically breaking the designed antenna symmetry, emissive quasi-BIC resonances become visible. This gives a unique experimental tool to determine the coherent interaction length, which we show to require at least six neighboring antenna elements. More importantly, we demonstrate that quasi-BIC resonances are able to enhance localized light emission via the Purcell effect by at least 60 times, as compared to unpatterned silicon. This work is expected to enable practical applications of designed, ultra-compact BIC antennas such as for the controlled, localized excitation of quantum emitters.

BIC in waveguide arrays

We propose a simple theoretical model based on the coupled-mode theory which allows to calculate the spectral properties and transmittance of the one-dimensional waveguide structures. The model was verified on the common coupled-waveguide array in which the existence of the symmetry-protected bound state in the continuum (BIC) was confirmed experimentally by Plotnik et al. [Phys. Rev. Lett. 107, 28-31 (2011)]. The method can be extended to topologically nontrivial lattices to explore the properties of the BICs protected by time-reversal symmetry.

Metasurface-Driven Optically Variable Devices

Optically variable devices (OVDs) are in tremendous demand as optical indicators against the increasing threat of counterfeiting. Conventional OVDs are exposed to the danger of fraudulent replication with advances in printing technology and widespread copying methods of security features. Metasurfaces, two-dimensional arrays of subwavelength structures known as meta-atoms, have been nominated as a candidate for a new generation of OVDs as they exhibit exceptional behaviors that can provide a more robust solution for optical anti-counterfeiting. Unlike conventional OVDs, metasurface-driven OVDs (mOVDs) can contain multiple optical responses in a single device, making them difficult to reverse engineered. Well-known examples of mOVDs include ultrahigh-resolution structural color printing, various types of holography, and polarization encoding. In this review, we discuss the new generation of mOVDs. The fundamentals of plasmonic and dielectric metasurfaces are presented to explain how the optical responses of metasurfaces can be manipulated. Then, examples of monofunctional, tunable, and multifunctional mOVDs are discussed. We follow up with a discussion of the fabrication methods needed to realize these mOVDs, classified into prototyping and manufacturing techniques. Finally, we provide an outlook and classification of mOVDs with respect to their capacity and security level. We believe this newly proposed concept of OVDs may bring about a new era of optical anticounterfeit technology leveraging the novel concepts of nano-optics and nanotechnology.

Unveiling the Symmetry Protection of Bound States in the Continuum with Terahertz Near-Field Imaging

Bound states in the continuum (BICs) represent a new paradigm in photonics due to the full suppression of radiation losses. However, this suppression has also hampered the direct observation of them. By using a double terahertz (THz) near-field technique that allows the local excitation and detection of the THz amplitude, we are able to map for the first time the electromagnetic field amplitude and phase of BICs over extended areas, unveiling the field-symmetry protection that suppresses the far-field radiation. This investigation, done for metasurfaces of dimer scatterers, reveals the in-plane extension and formation of BICs with antisymmetric phases, in agreement with coupled-dipole calculations. By displacing the scatterers, we show experimentally that a mirror symmetry is not a necessary condition for a BIC formation. Only π-rotation symmetry is required, making BICs exceptionally robust to structural changes. This work makes the local field of BICs experimentally accessible, which is crucial for the engineering of cavities with infinite lifetimes.

Quantum superposition demonstrated higher-order topological bound states in the continuum

Higher-order topological insulators, as newly found non-trivial materials and structures, possess topological phases beyond the conventional bulk-boundary correspondence. In previous studies, in-gap boundary states such as the corner states were regarded as conclusive evidence for the emergence of higher-order topological insulators. Here, we present an experimental observation of a photonic higher-order topological insulator with corner states embedded into the bulk spectrum, denoted as the higher-order topological bound states in the continuum. Especially, we propose and experimentally demonstrate a new way to identify topological corner states by exciting them separately from the bulk states with photonic quantum superposition states. Our results extend the topological bound states in the continuum into higher-order cases, providing an unprecedented mechanism to achieve robust and localized states in a bulk spectrum. More importantly, our experiments exhibit the advantage of using the time evolution of quantum superposition states to identify topological corner modes, which may shed light on future exploration between quantum dynamics and higher-order topological photonics.

Quantum-Well Bound States in Graphene Heterostructure Interfaces

We present experimental evidence of electronic and optical interlayer resonances in graphene van der Waals heterostructure interfaces. Using the spectroscopic mode of a low-energy electron microscope (LEEM), we characterized these interlayer resonant states up to 10 eV above the vacuum level. Compared with nontwisted, AB-stacked bilayer graphene (AB BLG), an ≈0.2  Å increase was found in the interlayer spacing of 30° twisted bilayer graphene (30°-tBLG). In addition, we used Raman spectroscopy to probe the inelastic light-matter interactions. A unique type of Fano resonance was found around the D and G modes of the graphene lattice vibrations. This anomalous, robust Fano resonance is a direct result of quantum confinement and the interplay between discrete phonon states and the excitonic continuum.

Sound trapping in an open resonator

The ability of sound energy confinement with high-quality factor resonance is of vital importance for acoustic devices requiring high intensity and hypersensitivity in biological ultrasonics, enhanced collimated sound emission (i.e. sound laser) and high-resolution sensing. However, structures reported so far have been experimentally demonstrated with a limited quality factor of acoustic resonances, up to several tens in an open resonator. The emergence of bound states in the continuum makes it possible to realize high quality factor acoustic modes. Here, we report the theoretical design and experimental demonstration of acoustic bound states in the continuum supported by a single open resonator. We predicted that such an open acoustic resonator could simultaneously support three types of bound states in the continuum, including symmetry protected bound states in the continuum, Friedrich-Wintgen bound states in the continuum induced by mode interference, as well as a new type-mirror symmetry induced bound states in the continuum. We also experimentally demonstrated their existence with quality factor up to one order of magnitude greater than the highest quality factor reported in an open resonator.

On the robustness of bound states in the continuum in waveguides with lateral leakage channels

Bound states in the continuum (BICs) are trapped or guided modes with frequencies in radiation continua. They are associated with high-quality-factor resonances that give rise to strong local field enhancement and rapid variations in scattering spectra, and have found many valuable applications. A guided mode of an optical waveguide can also be a BIC, if there is a lateral structure supporting compatible waves propagating in the lateral direction; i.e., there is a channel for lateral leakage. A BIC is typically destroyed (becomes a resonant or a leaky mode) if the structure is slightly perturbed, but some BICs are robust with respect to a large family of perturbations. In this paper, we show (analytically and numerically) that a typical BIC in optical waveguides with a left-right mirror symmetry and a single lateral leakage channel is robust with respect to any structural perturbation that preserves the left-right mirror symmetry. Our study improves the theoretical understanding on BICs and can be useful when applications of BICs in optical waveguides are explored.

Rabi oscillations of bound states in the continuum

Photonic bound states in the continuum (BICs) are special localized and non-decaying states of a photonic system with a frequency embedded into the spectrum of scattered states. The simplest photonic structure displaying a single BIC is provided by two waveguides side-coupled to a common waveguide lattice, where the BIC is protected by symmetry. Here we consider such a simple photonic structure and show that by breaking mirror symmetry and allowing for non-nearest neighbor couplings, a doublet of quasi-BIC states can be sustained, enabling weakly damped embedded Rabi oscillations of photons between the waveguides.

Highly Controllable Etchless Perovskite Microlasers Based on Bound States in the Continuum

Lead halide perovskites have been promising materials for lasing applications. Despite that a series of perovskite microlasers have been reported, their lasing modes are confined by either the as-grown morphology or the etched boundary. The first one is quite random and incompatible with integration, whereas the latter one strongly spoils the laser performances. Herein, we propose and experimentally demonstrate a robust and generic mechanism to realize well-controlled perovskite microlasers without the etching process. By patterning a one-dimensional polymer grating onto a perovskite film, we show that the symmetry-protected bound states in the continuum (BICs) can be formed in it. The intriguing properties of BICs including a widely spread mode profile and high Q factor, associated with the exceptional gain of perovskite, produce single-mode microlasers with high repeatability, controllability, directionality, and a polarization vortex. This mechanism can also be extended to two-dimensional nanostructures, enabling BIC lasers with different topological charges.

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

Bound states in the continuum (BICs) confine resonances embedded in a continuous spectrum by eliminating radiation loss. Merging multiple BICs provides a promising approach to further reduce the scattering losses caused by fabrication imperfections. However, to date, BIC merging has been limited to only the Γ point, which constrains potential application scenarios such as beam steering and directional vector beams. Here, we propose a new scheme to construct merging BICs at almost an arbitrary point in reciprocal space. Our approach utilizes the topological features of BICs on photonic crystal slabs, and we merge a Friedrich-Wintgen BIC and an accidental BIC. The Q factors of the resulting merging BIC are enhanced for a broad wave vector range compared with both the original Friedrich-Wintgen BIC and the accidental BIC. Since Friedrich-Wintgen BICs and accidental BICs are quite common in the band structure, our proposal provides a general approach to realize off-Γ merging BICs with superhigh Q factors that can substantially enhance nonlinear and quantum effects and boost the performance of on-chip photonic devices.

Chiral excitation and effective bandwidth enhancement in tilted waveguide lattices

Light escape from an optical waveguide side-coupled to a waveguide lattice provides a photonic analogue of the spontaneous emission process of an excited two-level atom in a one-dimensional array of cavities. According to the Fermi golden rule, the decay process is prevented when the atomic resonance frequency falls in a stop band of the lattice, while time-reversal symmetry ensures that the spontaneously emitted photon has equal probability to propagate in opposite directions of the array. This scenario is drastically modified when the quantum emitter drifts along the lattice. In the waveguide optics analogue, the atomic drift is emulated by the introduction of a slight geometric tilt of the waveguide axis from the lattice axis. In this setting, light excitation in the array is chiral, i.e., light propagates in a preferred direction of the lattice, and coupling is allowed even though the waveguide is far detuned from the tight-binding lattice band.

Observation of a Higher-Order Topological Bound State in the Continuum

Higher-order topological insulators are a recently discovered class of materials that can possess zero-dimensional localized states regardless of the dimension of the system. Here, we experimentally demonstrate that the topological corner-localized modes of higher-order topological systems can be symmetry-protected bound states in the continuum; these states do not hybridize with the surrounding bulk states of the lattice even in the absence of a bulk band gap. This observation expands the scope of bulk-boundary correspondence by showing that protected boundary-localized states can be found within topological bands, in addition to being found in between them.

Strong coupling of single quantum dots with low-refractive-index/high-refractive-index materials at room temperature

Strong coupling between a cavity and transition dipole moments in emitters leads to vacuum Rabi splitting. Researchers have not reported strong coupling between a single emitter and a dielectric cavity at room temperature until now. In this study, we investigated the photoluminescence (PL) spectra of colloidal quantum dots on the surface of a SiO₂/Si material at various collection angles at room temperature. We measured the corresponding reflection spectra for the SiO₂/Si material and compared them with the PL spectra. We observed PL spectral splitting and regarded it as strong coupling between colloidal quantum dots and the SiO₂/Si material. Upper polaritons and lower polaritons exhibited anticrossing behavior. We observed Rabi splitting from single-photon emission in the dielectric cavity at room temperature. Through analysis, we attributed the Rabi splitting to strong coupling between quantum dots and bound states in the continuum in the low-refractive-index/high-refractive-index hybrid material.

Photonic simulation of giant atom decay

Spontaneous emission of an excited atom in a featureless continuum of electromagnetic modes is a fundamental process in quantum electrodynamics associated with an exponential decay of the quantum emitter to its ground state accompanied by an irreversible emission of a photon. However, such a simple scenario is deeply modified when considering a "giant" atom, i.e., an atom whose dimension is larger than the wavelength of the emitted photon. In such an unconventional regime, non-Markovian effects and strong deviations from an exponential decay are observed owing to interference effects arising from nonlocal light-atom coupling. Here we suggest a photonic simulation of non-Markovian giant atom decay, based on light escape dynamics in an optical waveguide nonlocally coupled to a waveguide lattice. Major effects, such as nonexponential decay, enhancement, or slowing down of the decay, and formation of atom-field dark states can be emulated in this system.

Near-field analysis of bound states in the continuum in photonic crystal slabs

Bound states in the continuum (BICs) can be derived from a generalized waveguide condition in which the total internal reflection is substituted by coherent perfect reflection. Coherent perfect reflection can occur in the truncated photonic crystal (PhC) due to the interference of different Bloch modes. Based on the coherent reflection, BICs can be constructed by the bulk Bloch modes of PhC slabs. In contrast to the determination of BICs from the topological vortices of far-field radiation, this interpretation from coherent reflection can give the spatial field profile in detail in the near field. We show that the BICs can be characterized by the indices (or number of nodes) of their constituent Bloch modes. Moreover, all the guided resonances in addition to BICs can also be labelled by these mode indices. It is found that for the guided resonances the mode indices can change suddenly on the same frequency band. Our results may have potential applications in guided-wave optics and enhanced light-matter interaction.

High-dimensional communication on etchless lithium niobate platform with photonic bound states in the continuum

Photonic bound states in the continuum (BICs) have been exploited in various systems and found numerous applications. Here, we investigate high-order BICs and apply BICs on an integrated photonic platform to high-dimensional optical communication. A four-channel TM mode (de)multiplexer using different orders of BICs on an etchless lithium niobate (LiNbO₃) platform where waveguides are constructed by a low-refractive-index material on a high-refractive-index substrate is demonstrated. Low propagation loss of the TM modes in different orders and phase-matching conditions for efficient excitation of the high-order TM modes are simultaneously achieved. A chip consisting of four-channel mode (de)multiplexers was fabricated and measured with data transmission at 40 Gbps/channel. All the channels have insertion loss <4.0 dB and crosstalk <-9.5 dB in a 70-nm wavelength band. Therefore, the demonstrated mode (de)multiplexing and high-dimensional communication on LiNbO₃ platform can meet the increasing demand for high capacity in on-chip optical communication.

Acousto-optic modulation of photonic bound state in the continuum

Photonic bound states in the continuum (BICs) have recently been studied in various systems and have found wide applications in sensors, lasers, and filters. Applying BICs in photonic integrated circuits enables low-loss light guidance and routing in low-refractive-index waveguides on high-refractive-index substrates, which opens a new avenue for integrated photonics with functional single-crystal materials. Here, we demonstrate high-quality integrated lithium niobate microcavities inside which the photonic BIC modes circulate and further modulate these BIC modes acousto-optically by using piezoelectrically actuated surface acoustic waves at microwave frequencies. With a high acousto-optic modulation frequency, the acousto-optic coupling is well situated in the resolved-sideband regime. This leads to coherent coupling between microwave and optical photons, which is exhibited by the observed electro-acousto-optically induced transparency and absorption. Therefore, our devices serve as a paradigm for manipulating and controlling photonic BICs on a chip, which will enable many other applications of photonic BICs in the areas of microwave photonics and quantum information processing.

Engineering zero modes, Fano resonance, and Tamm surface states in the waveguide-array realization of the modified Su-Schrieffer-Heeger model

In this article, we developed a generalized coupled-mode theory for mixing an isolated state with a continuum having an intrinsic energy gap, which dubbed as "the bound states in the gapped continuum" (BIGC). We investigated the mixture interaction by mimicking the Su-Schrieffer-Heeger model in an optical coupled waveguide array (WA), and presented a unified engineering mechanism for topologically-protected zero modes, Fano resonance, and Tamm surface states, even though those phenomena are diverse in topological insulators, atomic physics and semiconductors, respectively. By tuning the on-site potential and coupling strength of the isolated state, we found the unified operating characteristics for zero modes, Fano resonance, and Tamm states, with demonstrating their localization, transmission spectra, and distinct evolution dynamics explicitly. As an extension for triple-modes coupling, two special sandwich-like configurations are studied: the isolated-continuous-isolated and continuous-isolated-continuous configurations lead to adiabatic eliminations and domain walls, respectively, revealing possible applications and wide connections in many fields of physics and optics.

Dynamic Nonlinear Image Tuning through Magnetic Dipole Quasi-BIC Ultrathin Resonators

Dynamical tuning of the nonlinear optical wavefront allows for a specific spectral response of predefined profiles, enabling various applications of nonlinear nanophotonics. This study experimentally demonstrates the dynamical switching of images generated by an ultrathin silicon nonlinear metasurface supporting a high-quality leaky mode, which is formed by partially breaking a bound-state-in-the-continuum (BIC) generated by the collective magnetic dipole (MD) resonance excited in the subdiffractive periodic systems. Such a quasi-BIC MD state can be excited directly under normal plane wave incidence and leads to a strong near-field enhancement to further boost the nonlinear process, resulting in a 500-fold enhancement of the third-harmonic emission experimentally. Due to sharp spectral features and asymmetry of the unit cell, it allows for effective tailoring of the nonlinear emissions over spectral or polarization responses. Dynamical nonlinear image tuning is experimentally demonstarted via polarization and wavelength control. The results pave the way for nanophotonics applications such as tunable displays, nonlinear holograms, tunable nanolaser, and ultrathin nonlinear nanodevices with various functionalities.

Bound States in the Continuum through Environmental Design

We propose a new paradigm for realizing bound states in the continuum (BICs) by engineering the environment of a system to control the number of available radiation channels. Using this method, we demonstrate that a photonic crystal slab embedded in a photonic crystal environment can exhibit both isolated points and lines of BICs in different regions of its Brillouin zone. Finally, we demonstrate that the intersection between a line of BICs and a line of leaky resonances can yield exceptional points connected by a bulk Fermi arc. The ability to design the environment of a system opens up a broad range of experimental possibilities for realizing BICs in three-dimensional geometries, such as in 3D-printed structures and the planar grain boundaries of self-assembled systems.

Optical Bound States in the Continuum with Nanowire Geometric Superlattices

Perfect trapping of light in a subwavelength cavity is a key goal in nanophotonics. Perfect trapping has been realized with optical bound states in the continuum (BIC) in waveguide arrays and photonic crystals; yet the formal requirement of infinite periodicity has limited the experimental realization to structures with macroscopic planar dimensions. We characterize BICs in a silicon nanowire (NW) geometric superlattice (GSL) that exhibits one-dimensional periodicity in a compact cylindrical geometry with a subwavelength diameter. We analyze the scattering behavior of NW GSLs by formulating temporal coupled mode theory to include Lorenz-Mie scattering, and we show that GSL-based BICs can trap electromagnetic energy for an infinite lifetime and exist over a broad range of geometric parameters. Using synthesized NW GSLs tens of microns in length and with variable pitch, we demonstrate the progressive spectral shift and disappearance of Fano resonances in experimental single-NW extinction spectra as a manifestation of BIC GSL modes.

Nonlinear response from optical bound states in the continuum

We consider nonlinear effects in scattering of light by a periodic structure supporting optical bound states in the continuum. In the spectral vicinity of the bound states the scattered electromagnetic field is resonantly enhanced triggering optical bistability. Using coupled mode approach we derive a nonlinear equation for the amplitude of the resonant mode associated with the bound state. We show that such an equation for the isolated resonance can be easily solved yielding bistable solutions which are in quantitative agreement with the full-wave solutions of Maxwell’s equations. The coupled mode approach allowed us to cast the the problem into the form of a driven nonlinear oscillator and analyze the onset of bistability under variation of the incident wave. The results presented drastically simplify the analysis nonlinear Maxwell’s equations and, thus, can be instrumental in engineering optical response via bound states in the continuum.

Compact localized states of open scattering media: a graph decomposition approach for an ab initio design

We study the compact localized scattering resonances of periodic and aperiodic chains of dipolar nanoparticles by combining the powerful equitable partition theorem (EPT) of a graph theory with the spectral dyadic Green's matrix formalism for the engineering of embedded quasi-modes in non-Hermitian open scattering systems in three spatial dimensions. We provide the analytical and numerical design of the spectral properties of compact localized states in electromagnetically coupled chains and establish a connection with the distinctive behavior of bound states in the continuum. Our results extend the concept of compact localization to the scattering resonances of open systems with an arbitrary aperiodic order beyond tight-binding models, and are relevant for the efficient design of novel photonic and plasmonic metamaterial architectures for enhanced light-matter interaction.

Extreme Huygens' Metasurfaces Based on Quasi-Bound States in the Continuum

We introduce the concept of and a generic approach to realizing extreme Huygens' metasurfaces by bridging the concepts of Huygens' conditions and optical bound states in the continuum. This novel paradigm allows the creation of Huygens' metasurfaces with quality factors that can be tuned over orders of magnitude, generating extremely dispersive phase modulation. We validate this concept with a proof-of-concept experiment at the near-infrared wavelengths, demonstrating all-dielectric Huygens' metasurfaces with different quality factors. Our study points out a practical route for controlling the radiative decay rate while maintaining the Huygens' condition, complementing existing Huygens' metasurfaces whose bandwidths are relatively broad and complicated to tune. This novel feature can provide new insight for various applications, including optical sensing, dispersion engineering and pulse shaping, tunable metasurfaces, metadevices with high spectral selectivity, and nonlinear meta-optics.

Nearly complete survival of an entangled biphoton through bound states in continuum in disordered photonic lattices

Bound states in the continuum (BICs) of periodic lattices have been the recent focus in a variety of photonic nanostructures. Motivated by the recent results about the photons evolving in BIC structures, we investigate the quantum decay of entangled biphotons through disordered photonic lattices. We report that the persistence of bound states in disordered photonic lattices leads to an interplay between the BIC and disorder-induced Anderson localized states. We reveal a novel effect resulting from such an interplay: a nearly complete quantum survival for the entangled biphoton respecting the antisymmetric exchange symmetry. This is in contrast to the complete vanishment in a periodic photonic lattice.

Observation of Polarization Vortices in Momentum Space

The vortex, a fundamental topological excitation featuring the in-plane winding of a vector field, is important in various areas such as fluid dynamics, liquid crystals, and superconductors. Although commonly existing in nature, vortices were observed exclusively in real space. Here, we experimentally observed momentum-space vortices as the winding of far-field polarization vectors in the first Brillouin zone of periodic plasmonic structures. Using homemade polarization-resolved momentum-space imaging spectroscopy, we mapped out the dispersion, lifetime, and polarization of all radiative states at the visible wavelengths. The momentum-space vortices were experimentally identified by their winding patterns in the polarization-resolved isofrequency contours and their diverging radiative quality factors. Such polarization vortices can exist robustly on any periodic systems of vectorial fields, while they are not captured by the existing topological band theory developed for scalar fields. Our work provides a new way for designing high-Q plasmonic resonances, generating vector beams, and studying topological photonics in the momentum space.

Bound states in the continuum in a two-dimensional PT-symmetric system

We address a 2D parity-time (PT)-symmetric structure built as a chain of waveguides, where all waveguides except for the central one are conservative, while the central one is divided into two halves with gain and losses. We show that such a system admits bound states in the continuum (BICs) whose properties vary drastically with the orientation of the line separating amplifying and absorbing domains, which sets the direction of internal energy flow. When the flow is perpendicular to the chain of the waveguides, narrow BICs emerge when the standard defect mode, which is initially located in the finite gap, collides with another mode in a standard symmetry breaking scenario, and its propagation constant enters the continuous spectrum upon increase of the strength of gain/losses. In contrast, when the energy flow is parallel to the chain of the waveguides, the symmetry gets broken even for a small strength of the gain/losses. In that case, the most rapidly growing mode emerges inside the continuous spectrum and realizes a weakly localized BIC. All BICs found here are the most rapidly growing modes; therefore, they can be excited from noisy inputs and, importantly, should dominate the beam dynamics in experiments.

Bound states in the continuum on periodic structures: perturbation theory and robustness

On periodic structures, a bound state in the continuum (BIC) is a standing or propagating Bloch wave with a frequency in the radiation continuum. Some BICs (e.g., antisymmetric standing waves) are symmetry protected, since they have incompatible symmetry with outgoing waves in the radiation channels. The propagating BICs do not have this symmetry mismatch, but they still crucially depend on the symmetry of the structure. In this Letter, a perturbation theory is developed for propagating BICs on two-dimensional periodic structures. The Letter shows that these BICs are robust against structural perturbations that preserve the symmetry, indicating that these BICs, in fact, are implicitly protected by symmetry.

Topological Bound States in the Continuum in Arrays of Dielectric Spheres

We consider Bloch bound states in the radiation continuum in periodic arrays of dielectric spheres. It is demonstrated that the bound states are associated with phase singularities of the quasimode coupling strength. That makes the bound states topologically protected and, therefore, robust against any variation of parameters preserving the periodicity and rotational symmetry about the array axis. It is shown that under variation of parameters the bound states can only be destroyed by either annihilation of the topological charge or by migration to the sector of the parametric space where the second radiation channel is open.

Light enhancement by quasi-bound states in the continuum in dielectric arrays

The article reports on light enhancement by structural resonances in linear periodic arrays of identical dielectric elements. As the basic elements both subwavelength spheres and rods with circular cross section have been considered. In either case it has been demonstrated numerically that high-Q structural resonant modes originated from bound states in the continuum enable near-field amplitude enhancement by factor of 10-25 in the red-to-near infrared range in lossy silicon. The asymptotic behavior of the Q-factor with the number of elements in the array is explained theoretically by analyzing quasi-bound states propagation bands.

Propagating Bloch bound states with orbital angular momentum above the light line in the array of dielectric spheres

We present propagating Bloch bound states in the radiation continuum with orbital angular momentum in an infinite linear periodical array of dielectric spheres. The bound states in the continuum demonstrate a giant Poynting vector spiraling around the array. They can be excited by a plane wave with incident linear polarization with a small tilt relative to the axis of the array.

Topological Subspace-Induced Bound State in the Continuum

We propose and experimentally realize a new kind of bound states in the continuum (BICs) in a class of systems constructed by coupling multiple identical one-dimensional chains, each with inversion symmetry. In such systems, a specific separation of the Hilbert space into a topological and a nontopological subspace exists. Bulk-boundary correspondence in the topological subspace guarantees the existence of a localized interface state which can lie in the continuum of extended states in the nontopological subspace, forming a BIC. Such a topological BIC is observed experimentally in a system consisting of coupled acoustic resonators.