Topological Bound States in the Continuum in Arrays of Dielectric Spheres

Million-Q free space meta-optical resonator at near-visible wavelengths

High-quality (Q)-factor optical resonators with extreme temporal coherence are of both technological and fundamental importance in optical metrology, continuous-wave lasing, and semiconductor quantum optics. Despite extensive efforts in designing high-Q resonators across different spectral regimes, the experimental realization of very large Q-factors at visible wavelengths remains challenging due to the small feature size that is sensitive to fabrication imperfections, and thus is typically implemented in integrated photonics. In the pursuit of free-space optics with the benefits of large space-bandwidth product and massive parallel operations, here we design and fabricate a near-visible-wavelength etch-free metasurface with minimized fabrication defects and experimentally demonstrate a million-scale ultrahigh-Q resonance. A new laser-scanning momentum-space-resolved spectroscopy technique with extremely high spectral and angular resolution is developed to characterize the record-high Q-factor as well as the dispersion of the million-Q resonance in free space. By integrating monolayer WSe2 into our ultrahigh-Q meta-resonator, we further demonstrate laser-like highly unidirectional and narrow-linewidth exciton emission, albeit without any operating power density threshold. Under continuous-wave laser pumping, we observe pump-power-dependent linewidth narrowing at room temperature, indicating the potential of our meta-optics platform in controlling coherent quantum light-sources. Our result also holds great promise for applications like optical sensing, spectral filtering, and few-photon nonlinear optics.

Mode-Symmetry-Assisted Optical Pulling by Bound States in the Continuum

Aside from optical pushing and trapping that have been implemented successfully, the transportation of objects backward to the source by the optical pulling forces (OPFs) has attracted tremendous attention, which was usually achieved by increasing the forward momentum of light. However, the limited momentum transfer between light and object greatly constrains the amplitudes of OPFs. Here, we present a mechanism to generate strong interactions between object and background through the bound states in the continuums, which can generate large OPFs without increasing the forward momentum of light. The underlying physics is the extraction of momentum from the designed background lattice units assisted by mode symmetry. This work paves the way for extraordinary optical manipulations and shows great potential for exploring the momenta of light in media.

Observation of tunable accidental bound state in the continuum in silicon nanodisk array

We experimentally demonstrate the tuning of accidental bound states in the continuum (A-BICs) in silicon nanodisk arrays. The A-BIC emerges of the destructive interference of multipoles, which are the dominating out-of-plane electric dipole and in-plane magnetic dipole, and weak electric quadrupole and magnetic quadrupole. We further show that the spectral and angular position of the A-BIC can be conveniently tuned by varying the nanodisk size or the lattice period. Remarkably, the angular position can be tuned even to 0°, suggesting an interesting transition of the A-BIC from an off-Γ-BIC to an at-Γ-BIC. Our work provides a new strategy for light trapping with high quality factors, and the obtained tunable A-BICs can find potential applications in low-threshold lasing, enhanced nonlinear optics, and optical sensing.

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.

Surface acoustic waves in the continuous spectrum of Bloch waves in piezoelectric one-dimensional phononic crystals

This paper theoretically investigates surface acoustic waves (SAWs) which emerge within the continuous spectrum of bulk Bloch waves in piezoelectric one-dimensional phononic crystals. Accordingly, these SAWs may be treated as an example of the bound states in the continuum (BIC). The equations which determine the existence of such BIC-SAWs have been derived. Unlike SAWs in the frequency intervals forbidden for bulk Bloch waves, BIC-SAWs are governed not by a single purely real dispersion equation but by sets of equations, so BIC-SAWs prove to be robust only to a consistent change of a definite number of free parameters characterizing the wave propagation. The form of the derived equations allows the establishment of the conditions on the frequency and other parameters under which the BIC-SAW exists. The number of conditions depends on the number of bulk waves in the frequency interval under consideration. In the case of generic crystallographic symmetry, there are three, five, and seven conditions which have to be fulfilled for a BIC-SAWs to coexist with one pair, two pairs, and three pairs of bulk Bloch waves, respectively. It is shown that the crystallographic symmetry may reduce the number of conditions to two, three and four, respectively. Numerical computations confirm analytic results.

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.

Ultrahigh-Q guided mode resonances in an All-dielectric metasurface

High quality(Q) factor optical resonators are indispensable for many photonic devices. While very large Q-factors can be obtained theoretically in guided-mode settings, free-space implementations suffer from various limitations on the narrowest linewidth in real experiments. Here, we propose a simple strategy to enable ultrahigh-Q guided-mode resonances by introducing a patterned perturbation layer on top of a multilayer-waveguide system. We demonstrate that the associated Q-factors are inversely proportional to the perturbation squared while the resonant wavelength can be tuned through material or structural parameters. We experimentally demonstrate such high-Q resonances at telecom wavelengths by patterning a low-index layer on top of a 220 nm silicon on insulator substrate. The measurements show Q-factors up to 2.39 × 10⁵, comparable to the largest Q-factor obtained by topological engineering, while the resonant wavelength is tuned by varying the lattice constant of the top perturbation layer. Our results hold great promise for exciting applications like sensors and filters.

Topological Metamaterials

The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

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.

Automatic optimization of miniaturized bound states in the continuum cavity

Bound states in the continuum (BICs) provide, what we believe to be, a novel and efficient way for light trapping. However, using BICs to confine the light into a three-dimensional compact volume remains a challenging task, since the energy leakage at the lateral boundaries dominates the cavity loss when its footprint shrinks to considerably small, and hence, sophisticated boundary designs turn out to be inevitable. Conventional design methods fail in solving the lateral boundary problem because a large number of degree-of-freedoms (DOFs) are involved. Here, we propose a fully automatic optimization method to promote the performance of lateral confinement for a miniaturized BIC cavity. Briefly, we combine a random parameter adjustment process with a convolutional neural network (CNN), to automatically predict the optimal boundary design in the parameter space that contains a number of DOFs. As a result, the quality factor that is accounted for lateral leakage increases from 4.32 × 10⁴ in the baseline design to 6.32 × 10⁵ in the optimized design. This work confirms the effectiveness of using CNNs for photonic optimization and will motivate the development of compact optical cavities for on-chip lasers, OLEDs, and sensor arrays.

Morphology-dependent resonance induced optical forces in a multiple-sphere system

Optical fields and forces can be greatly enhanced for a microparticle when the whispering gallery modes (WGMs) are excited. In this paper, by solving the scattering problem using the generalized Mie theory, the morphology-dependent resonances (MDRs) and resonant optical forces derived from the coherent coupling of WGMs are investigated in multiple-sphere systems. When the spheres approach each other, the bonding and antibonding modes of MDRs emerge and correspond to the attractive and repulsive forces, respectively. More importantly, the antibonding mode is good at propagating light forward, while the optical fields decay rapidly for the bonding mode. Moreover, the bonding and antibonding modes of MDRs in the PT-symmetric system can persist only when the imaginary part of the refractive index is small enough. Interestingly, it is also shown that for a PT-symmetric structure, only a minor imaginary part of the refractive index is required to generate a significant pulling force at MDRs, making the whole structure move against the light propagation direction. Our work deepens the understanding of the collective resonance behavior of multiple spheres and paves the way for potential applications in particle transportation, non-Hermitian systems, integrated optical devices, etc.

Arbitrarily polarized bound states in the continuum with twisted photonic crystal slabs

Arbitrary polarized vortex beam induced by polarization singularity offers a new platform for both classical optics and quantum entanglement applications. Bound states in the continuum (BICs) have been demonstrated to be associated with topological charge and vortex polarization singularities in momentum space. For conventional symmetric photonic crystal slabs (PhCSs), BIC is enclosed by linearly polarized far fields with winding angle of 2π, which is unfavorable for high-capacity and multi-functionality integration-optics applications. Here, we show that by breaking σ_z-symmetry of the PhCS, asymmetry in upward and downward directions and arbitrarily polarized BIC can be realized with a bilayer-twisted PhCS. It exhibits elliptical polarization states with constant ellipticity angle at every point in momentum space within the vicinity of BIC. The topological nature of BIC reflects on the orientation angle of polarization state, with a topological charge of 1 for any value of ellipticity angle. Full coverage of Poincaré sphere (i.e., [Formula: see text] and [Formula: see text]) and higher-order Poincaré sphere can be realized by tailoring the twist angles. Our findings may open up new avenues for applications in structured light, quantum optics, and twistronics for photons.

Observation of multiple bulk bound states in the continuum modes in a photonic crystal cavity

Obtaining bound states in the continuum (BICs) in photonic crystals gives rise to the realization of resonances with high quality factors for lasing and nonlinear applications. For BIC cavities in finite-size photonic crystals, the bulk resonance band turns into discrete modes with different mode profiles and radiation patterns. Here, photonic-crystal BIC cavities encircled by the photonic bandgap of lateral heterostructures are designed. The mirror-like photonic bandgap exhibits strong side leakage suppression to confine the mode profile in the designed cavity. Multiple bulk quantized modes are observed both in simulation and experiment. After exciting the BIC cavity at different positions, different resonance peaks are observed. The physical origin of the dependence between the resonance peak and the illuminating position is explained by analyzing the mode profile distribution and further verified by numerical simulations. Our findings have potential applications regarding the mode selectivity in BIC devices to manipulate the lasing mode in photonic-crystal surface-emitting lasers or the radiation pattern in nonlinear optics.

Nonlinear optical heating of all-dielectric super-cavity: efficient light-to-heat conversion through giant thermorefractive bistability

Optical heating of resonant nanostructures is one of the key issues in modern nanophotonics, being either harmful or desirable effect depending on the applications. Despite a linear regime of light-to-heat conversion being well-studied both for metal and semiconductor resonant systems is generalized as a critical coupling condition, the clear strategy to optimize optical heating upon high-intensity light irradiation is still missing. This work proposes a simple analytical model for such a problem, taking into account material properties changes caused by the heating. It allows us to derive a new general critical coupling condition for the nonlinear case, requiring a counterintuitive initial spectral mismatch between the pumping light frequency and the resonant one. Based on the suggested strategy, we develop an optimized design for efficient nonlinear optical heating, which employs a cylindrical nanoparticle supporting the quasi bound state in the continuum mode (quasi-BIC or so-called 'super-cavity mode') excited by the incident azimuthal vector beam. Our approach provides a background for various nonlinear experiments related to optical heating and bistability, where self-action of the intense laser beam can change resonant properties of the irradiated nanostructure.

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.

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.

Use of transmission and reflection complex time delays to reveal scattering matrix poles and zeros: Example of the ring graph

We identify the poles and zeros of the scattering matrix of a simple quantum graph by means of systematic measurement and analysis of Wigner, transmission, and reflection complex time delays. We examine the ring graph because it displays both shape and Feshbach resonances, the latter of which arises from an embedded eigenstate on the real frequency axis. Our analysis provides a unified understanding of the so-called shape, Feshbach, electromagnetically induced transparency, and Fano resonances on the basis of the distribution of poles and zeros of the scattering matrix in the complex frequency plane. It also provides a first-principles understanding of sharp resonant scattering features and associated large time delay in a variety of practical devices, including photonic microring resonators, microwave ring resonators, and mesoscopic ring-shaped conductor devices. Our analysis involves use of the reflection time difference, as well as a comprehensive use of complex time delay, to analyze experimental scattering data.

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.

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.

Strong optomechanical coupling in chain-like waveguides of silicon nanoparticles with quasi-bound states in the continuum

We propose and demonstrate that strong optomechanical coupling can be achieved in a chain-like waveguide consisting of silicon nanorods. By employing quasi-bound states in the continuum and mechanical resonances at a frequency around 10 GHz, the optomechanical coupling rate can be above 2 MHz and surpass most microcavities. We have also studied cases with different optical wave numbers and size parameters of silicon, and a robust coupling rate has been verified, benefiting the experimental measurements and practical applications. The proposed silicon chain-like waveguide of strong optomechanical coupling may pave new ways for research on photon-phonon interaction with microstructures.

Optical super-resonance in a customized P T-symmetric system of hybrid interaction

We investigate the optical resonances in coupled meta-atoms with hybrid interaction pathways. One interaction pathway is the directly near-field coupling between the two meta-atoms. The other interaction pathway is via the continuum in a waveguide functioned as a common bus connecting them. We show that by properly introducing gain or loss into the meta-atoms, the hybrid optical system becomes parity-time (P T) symmetric, in which the effective coupling rate can be customized by manipulating the length of the waveguide. At the exact phase of the customized P T symmetry, the coupled meta-atoms support discrete super-resonant modes that can be observed from the transmission spectra as extremely sharp peaks. At an exception point where the eigenmodes coalesce, albeit the transmission curve is flat, a high-Q factor of the localized field in the meta-atoms can be obtained. Similarities of the super-resonance with the bound states in the continuum (BICs) are discussed. This investigation promotes our understanding about the ways in realizing high-Q optical resonance especially by manipulating the distributions of loss and gain via the concepts of P T and BICs. Many attractive applications are expected.

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.

Unidirectional guided resonances in anisotropic waveguides

We show that anisotropic planar anti-guiding waveguide structures with two radiation channels toward the surrounding cladding materials can support unidirectional guided resonances (UGRs), where radiation is canceled in one of the radiation channels and redirected into the other. Their formation is subtle as it requires breaking the so-called polar anisotropy-symmetry of the structures. Then, UGRs appear at specific wavelengths and light propagation directions, are robust, and are characterized by phase singularities in the channel in which radiation is canceled. The mechanism we describe allows for ready selection of the radiation direction, as well as tuning of the wavelength and the propagation angle at which UGRs occur.

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.

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.

Evolution and global charge conservation for polarization singularities emerging from non-Hermitian degeneracies

Core concepts in singular optics, especially the polarization singularities, have rapidly penetrated the surging fields of topological and non-Hermitian photonics. For open photonic structures with non-Hermitian degeneracies in particular, polarization singularities would inevitably encounter another sweeping concept of Berry phase. Several investigations have discussed, in an inexplicit way, connections between both concepts, hinting at that nonzero topological charges for far-field polarizations on a loop are inextricably linked to its nontrivial Berry phase when degeneracies are enclosed. In this work, we reexamine the seminal photonic crystal slab that supports the fundamental two-level non-Hermitian degeneracies. Regardless of the invariance of nontrivial Berry phase (concerning near-field Bloch modes defined on the momentum torus) for different loops enclosing both degeneracies, we demonstrate that the associated far polarization fields (defined on the momentum sphere) exhibit topologically inequivalent patterns that are characterized by variant topological charges, including even the trivial scenario of zero charge. Moreover, the charge carried by the Fermi arc actually is not well defined, which could be different on opposite bands. It is further revealed that for both bands, the seemingly complex evolutions of polarizations are bounded by the global charge conservation, with extra points of circular polarizations playing indispensable roles. This indicates that although not directly associated with any local charges, the invariant Berry phase is directly linked to the globally conserved charge, physical principles underlying which have all been further clarified by a two-level Hamiltonian with an extra chirality term. Our work can potentially trigger extra explorations beyond photonics connecting Berry phase and singularities.

Plasmonic nanocavity for obtaining bound state in the continuum in silicon waveguides

Bound states in the continuum (BICs) have become a new trend in the area of metaoptics and nanophotonics. Strong interactions in electromagnetic fields are analogous to electron transitions in atoms, giving rise to BICs with vanishing radiative losses. However, it is still a great challenge to realize BICs in the lossy plasmonic systems. For this problem, we propose a supercavity-like plasmonic nanocavity consisting of an Au nanorod deposited inside an Au symmetric split ring, and explore the possibility of exciting quasi-BICs that own finite but high quality (Q) factors. In such hybrid configuration, the excited resonances can be easily engineered by modifying the rotation angle or the length of the Au nanorod. With the integration of such nanocavity in silicon (Si) waveguides, sharp transmission spectra could be achieved with fiber-chip in-parallel excitations and detections. Besides, the ultracompact geometry of this plasmonic nanocavity provides a route to boost enhanced electric fields, thus improving sensing performances significantly. Our study not only offers a novel platform for the realization of chip-scale quasi-BICs, but extends functionalities of photonic-plasmonic hybrid circuits.

Critical coupling vortex with grating-induced high Q-factor optical Tamm states

We investigate optical Tamm states supported by a dielectric grating placed on top of a distributed Bragg reflector. It is found that under certain conditions the Tamm state may become a bound state in the continuum. The bound state, in its turn, induces the effect of critical coupling with the reflectance amplitude reaching an exact zero. We demonstrate that the critical coupling point is located in the core of a vortex of the reflection amplitude gradient in the space of the wavelength and angle of incidence. The emergence of the vortex is explained by the coupled mode theory.

Observation of Supercavity Modes in Subwavelength Dielectric Resonators

Electromagnetic response of dielectric resonators with high refractive index is governed by optically induced electric and magnetic Mie resonances facilitating confinement of light with the amplitude enhancement. Traditionally, strong subwavelength trapping of light was associated only with plasmonic or epsilon-near-zero structures, which however suffer from material losses. Recently, an alternative localization mechanism was proposed allowing the trapping of light in individual subwavelength optical resonators with a high quality factor in the regime of a supercavity mode. Here, the experimental observation of the supercavity modes in subwavelength ceramic resonators in the radio-frequency range is presented. It is experimentally demonstrated that the regime of supercavity modes can be achieved via precise tuning of the resonator's dimensions. A huge growth of the unloaded quality factor is achieved with experimental values up to 1.25 × 10⁴ , limited only by material losses of ceramics. It is revealed that the supercavity modes can be excited efficiently both in the near- and far-field. In both cases, the supercavity mode manifests itself explicitly as a Fano resonance with characteristic peculiarities of spectral shape and radiation pattern. A comparison of supercavities made of diversified materials for the visible, infrared, THz, and radio-frequency regimes is provided.

Rotational symmetry of photonic bound states in the continuum

The bound states in the continuum (BICs) have been investigated by simulating the optical reflectivity of a tri-layer photonic crystal slab. We found that optical BICs can occur in a class of photonic crystal systems with [Formula: see text], [Formula: see text] or [Formula: see text] rotational symmetries, which are constructed by three identical photonic crystal slabs. By applying the two mode coupled model, we obtain the reflectivity formula to fit the numerical data and evaluate the lifetime of radiation decay. In vicinity of BIC, the lifetime diverges as a power law form, when approaching the BIC point. The infinity life time of [Formula: see text] in the tri-layer structure indicate that it is a true BIC. The [Formula: see text] occurs robustly in tri-layer structures, but the resonance frequency of the BICs is dependent on the permittivity of slab, air-hole size and hole shape.

Unconventional Singularity in Anti-Parity-Time Symmetric Cavity Magnonics

By engineering an anti-parity-time (anti-PT) symmetric cavity magnonics system with precise eigenspace controllability, we observe two different singularities in the same system. One type of singularity, the exceptional point (EP), is produced by tuning the magnon damping. Between two EPs, the maximal coherent superposition of photon and magnon states is robustly sustained by the preserved anti-PT symmetry. The other type of singularity, arising from the dissipative coupling of two antiresonances, is an unconventional bound state in the continuum (BIC). At the settings of BICs, the coupled system exhibits infinite discontinuities in the group delay. We find that both singularities coexist at the equator of the Bloch sphere, which reveals a unique hybrid state that simultaneously exhibits the maximal coherent superposition and slow light capability.

Bound States in the Continuum in Anisotropic Plasmonic Metasurfaces

The concept of optical bound states in the continuum (BICs) currently drives the field of dielectric resonant nanophotonics, providing an important physical mechanism for engineering high-quality (high-Q) optical resonances in high-index dielectric nanoparticles and structured dielectric metasurfaces. For structured metallic metasurfaces, realization of BICs remains a challenge associated with strong dissipative losses of plasmonic materials. Here, we suggest and realize experimentally anisotropic plasmonic metasurfaces supporting high-Q resonances governed by quasi-BIC collective resonant modes. Our metasurfaces are composed of arrays of vertically oriented double-pillar meta-molecules covered by a thin layer of gold. We engineer quasi-BIC modes and observe experimentally sharp resonances in mid-IR reflectance spectra. Our work suggests a direct route to boost the resonant field enhancement in plasmonic metasurfaces via combining a small effective mode volume of plasmonic systems with engineered high-Q resonances provided by the BIC physics, with multiple applications to enhance light-matter interaction for nano-optics and quantum photonics.

Coexistence of a new type of bound state in the continuum and a lasing threshold mode induced by PT symmetry

Some photonic systems support bound states in the continuum (BICs) that have infinite lifetimes, although their frequencies and momenta are matched to vacuum modes. Using a prototypical system that can be treated analytically, we show that each of these BICs always splits into a pair of new type BIC and lasing threshold mode when a parity-time (PT)-symmetric perturbation is introduced. The radiation loss at the lasing threshold is exactly balanced by the net gain of the particles. These PT symmetry-induced BICs are different from ordinary BICs, as they can be excited by an external source but do not radiate, and they carry a different quality factor divergence rate from that of the ordinary BICs. While most of the attention of PT-symmetric systems is captured by the coalescence of modes at exceptional points, the splitting of ordinary BICs is a new phenomenon that illustrates the rich physics embedded in PT-symmetric systems.

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.

Ultrafast control of vortex microlasers

The development of classical and quantum information-processing technology calls for on-chip integrated sources of structured light. Although integrated vortex microlasers have been previously demonstrated, they remain static and possess relatively high lasing thresholds, making them unsuitable for high-speed optical communication and computing. We introduce perovskite-based vortex microlasers and demonstrate their application to ultrafast all-optical switching at room temperature. By exploiting both mode symmetry and far-field properties, we reveal that the vortex beam lasing can be switched to linearly polarized beam lasing, or vice versa, with switching times of 1 to 1.5 picoseconds and energy consumption that is orders of magnitude lower than in previously demonstrated all-optical switching. Our results provide an approach that breaks the long-standing trade-off between low energy consumption and high-speed nanophotonics, introducing vortex microlasers that are switchable at terahertz frequencies.

Self-Assembled Binary Photonic Crystals under the Active Confinement and Their Light Trapping

The self-assembly of oppositely charged colloidal ellipsoids and spheres under active confinement is first proposed to achieve long-range ordered photonic crystals. Compared with the conventional passive confinement, a characteristic of the active confinement is that boundaries are movable. Our Brownian dynamics simulations show that dynamic steady structures, similar to quasi-2D colloidal crystals, can be obtained under the strong confinement when the two boundaries periodically oscillate together. The in-plane structures can be regulated by changing the charge ratio of the two kinds of particles. These dynamic steady structures are determined by the minimum electrostatic energy with the aid of increased mobility of confined particles, which are not available in equilibrium. Numerical simulations verify that light can be perfectly confined in this dielectric binary photonic slab without any radiation, which corresponds to a typical optical bound state with divergent lifetime and ultrasharp spectral profile. Given the changeable geometry of this photonic slab, the trapped optical field might be applicable to enhanced light-matter interactions. In addition, for thicker layers, layer-by-layer ordered structures occur spontaneously, driven by the active confinement, while no global order occurs in the passive confinement. Our results show that the boundary motion can become an important factor affecting self-assembled structure and function.

Topological photonic crystals: a review

The field of topological photonic crystals has attracted growing interest since the inception of optical analog of quantum Hall effect proposed in 2008. Photonic band structures embraced topological phases of matter, have spawned a novel platform for studying topological phase transitions and designing topological optical devices. Here, we present a brief review of topological photonic crystals based on different material platforms, including all-dielectric systems, metallic materials, optical resonators, coupled waveguide systems, and other platforms. Furthermore, this review summarizes recent progress on topological photonic crystals, such as higherorder topological photonic crystals, non-Hermitian photonic crystals, and nonlinear photonic crystals. These studies indicate that topological photonic crystals as versatile platforms have enormous potential applications in maneuvering the flow of light.

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.

Geometric Nanophotonics: Light Management in Single Nanowires through Morphology

Comprehensive control of light-matter interactions at the nanoscale is increasingly important for the development of miniaturized light-based technologies that have applications ranging from information processing to sensing. Control of light in nanoscale structures-the realm of nanophotonics-requires precise control of geometry on a few-nanometer length scale. From a chemist's perspective, bottom-up growth of nanoscale materials from chemical precursors offers a unique opportunity to design structures atom-by-atom that exhibit desired properties. In this Account, we describe our efforts to create chemically and morphologically precise Si nanowires (NWs) with designed nanophotonic properties using a vapor-liquid-solid (VLS) growth process. A synthetic technique termed "Encoded Nanowire Growth and Appearance through VLS and Etching" (ENGRAVE) combines optimized VLS growth, dopant modulation, and dopant-dependent wet-chemical etching to produce NWs with precisely designed diameter modulations, yielding lithographic-like morphological control that can vary from sinusoids to fractals. The ENGRAVE NWs thus provide a versatile playground for coupling, trapping, and directing light in a nanoscale geometry. Previously, the nanophotonic functionality of NWs primarily relied on uniform-diameter structures that exhibit Mie scattering resonances and longitudinally oriented guided modes, two key photonic properties that typically cannot be utilized simultaneously due to their orthogonality. However, when the NW diameter is controllably modulated along the longitudinal axis on a scale comparable to the wavelength of light-a geometry we term a geometric superlattice (GSL)-we found that NWs can exhibit a much richer and tunable set of nanophotonic properties, as described herein. To understand these unique properties, we first summarize the basic optical properties of uniform-diameter NWs using Mie scattering theory and dispersion relations, and we describe both conventional and relatively new microscopy methods that experimentally probe the optical properties of single NWs. Next, delving into the properties of NW GSLs, we summarize their ability to couple a Mie resonance with a guided mode at a select wavevector (or wavelength) dictated by their geometric pitch. The coupling forms a bound guided state (BGS) with a standing wave profile, which allows a NW GSL to serve as a spectrally selective light coupler and to act as optical switch or sensor. We also summarize the capacity of a GSL to trap light by serving as an ultrahigh (theoretically infinite) quality factor optical cavity with an optical bound state in the continuum (BIC), in which destructive interference prevents coupling to and from the far field. Finally, we discuss a future research outlook for using ENGRAVE NWs for nanoscale light control. For instance, we highlight research avenues that could yield light-emitting devices by interfacing a NW-based BIC with emissive materials such as quantum dots, 2D materials, and hybrid perovskite. We also discuss the design of photonic band gaps, generation of high-harmonics with quasi-BIC structures, and the possibility for undiscovered nanophotonic properties and phenomena through more complex ENGRAVE geometric designs.

Collective lattice resonances in arrays of dielectric nanoparticles: a matter of size

Collective lattice resonances (CLRs) in finite-sized $ 2D $2D arrays of dielectric nanospheres have been studied via the coupled dipole approximation. We show that even for sufficiently large arrays, up to $ 100 \times 100 $100×100 nanoparticles (NPs), electric or magnetic dipole CLRs may differ significantly from the ones calculated for infinite arrays with the same NP sizes and interparticle distances. The discrepancy is explained by the existence of a sufficiently strong cross-interaction between electric and magnetic dipoles induced at NPs in finite-sized lattices, which is ignored for infinite arrays. We support this claim numerically and propose an analytic model to estimate a spectral width of CLRs for finite-sized arrays. Given that most of the current theoretical and numerical researches on collective effects in arrays of dielectric NPs rely on modeling infinite structures, the reported findings may contribute to thoughtful and optimal design of inherently finite-sized photonic devices.

Brewster quasi bound states in the continuum in all-dielectric metasurfaces from single magnetic-dipole resonance meta-atoms

Bound states in the continuum (BICs) are ubiquitous in many areas of physics, attracting special interest for their ability to confine waves with infinite lifetimes. Metasurfaces provide a suitable platform to realize them in photonics; such BICs are remarkably robust, being however complex to tune in frequency-wavevector space. Here we propose a scheme to engineer BICs and quasi-BICs with single magnetic-dipole resonance meta-atoms. Upon changing the orientation of the magnetic-dipole resonances, we show that the resulting quasi-BICs, emerging from the symmetry-protected BIC at normal incidence, become transparent for plane-wave illumination exactly at the magnetic-dipole angle, due to a Brewster-like effect. While yielding infinite Q-factors at normal incidence (canonical BIC), these are termed Brewster quasi-BICs since a transmission channel is always allowed that slightly widens resonances at oblique incidences. This is demonstrated experimentally through reflectance measurements in the microwave regime with high-refractive-index mm-disk metasurfaces. Such Brewster-inspired configuration is a plausible scenario to achieve quasi-BICs throughout the electromagnetic spectrum inaccessible through plane-wave illumination at given angles, which could be extrapolated to other kind of waves.

Angular control of anisotropy-induced bound states in the continuum

Radiation of leaky modes existing in anisotropic waveguides can be cancelled by destructive interference at special propagation directions relative to the optical axis orientation, resulting in fully bound states surrounded by radiative modes. Here we study the variation of the loci of such special directions in terms of the waveguide constitutive parameters. We show that the angular loci of the bound states are sensitive to several design parameters, allowing bound states to exist for a broad range of angular directions and wavelengths and suggesting applications in filtering and sensing.

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.