Bound States in the Continuum through Environmental Design

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.

Quasi-guided modes resulting from the band folding effect in a photonic crystal slab for enhanced interactions of matters with free-space radiations

We elucidate that guided modes supported by a regular photonic crystal slab structure composed of a square lattice of air holes in a silicon slab will transition into quasi-guided (leaky) modes when the radius of every second column of air holes is changed slightly. This intentional geometric perturbation will lead to a doubling of the period in one direction and the corresponding shrinkage of the first Brillouin zone. Because of the translational symmetry in the k-space, leaky waves inheriting the spatial dispersion of the original guided modes, which do not interact with external radiation, will appear with the dispersion curves above the light cone. Our results show that ultrahigh Q-factor resonances with large operating bandwidth can be achieved. Interestingly, the perturbation in only one direction of the photonic lattice will lead to an in-plane wave number-dependent resonance characteristic in both directions. Our numerical results demonstrate a local enhancement of the electric field magnitude by the order of 10², which is even more significant than those in most plasmonic structures. These quasi-guided modes with superior properties will provide a new platform for efficient light-matter interactions.

Photonic flatband resonances for free-electron radiation

Flatbands have become a cornerstone of contemporary condensed-matter physics and photonics. In electronics, flatbands entail comparable energy bandwidth and Coulomb interaction, leading to correlated phenomena such as the fractional quantum Hall effect and recently those in magic-angle systems. In photonics, they enable properties including slow light1 and lasing2. Notably, flatbands support supercollimation-diffractionless wavepacket propagation-in both systems3,4. Despite these intense parallel efforts, flatbands have never been shown to affect the core interaction between free electrons and photons. Their interaction, pivotal for free-electron lasers5, microscopy and spectroscopy6,7, and particle accelerators8,9, is, in fact, limited by a dimensionality mismatch between localized electrons and extended photons. Here we reveal theoretically that photonic flatbands can overcome this mismatch and thus remarkably boost their interaction. We design flatband resonances in a silicon-on-insulator photonic crystal slab to control and enhance the associated free-electron radiation by tuning their trajectory and velocity. We observe signatures of flatband enhancement, recording a two-order increase from the conventional diffraction-enabled Smith-Purcell radiation. The enhancement enables polarization shaping of free-electron radiation and characterization of photonic bands through electron-beam measurements. Our results support the use of flatbands as test beds for strong light-electron interaction, particularly relevant for efficient and compact free-electron light sources and accelerators.

Enhanced bound states in the continuum in a DBR-assisted photonic crystal slab

Bound states in the continuum (BICs) are perfectly confined resonances within the radiation continuum. The novel characteristics of single BICs have been studied in great detail in various wave systems, including electromagnetic waves, acoustic waves, water waves, and elastic waves in solids. In practice, the performance of BICs is limited by the finite size of the structure, while the combination of multiple BICs can further improve the localization of resonances. In this study, we experimentally demonstrate the combination of Fabry-Perot and symmetry-protected BICs at near infrared wavelengths by employing a compound photonic crystal system composed of a photonic crystal slab and a distributed Bragg reflector, resulting in an enhanced high quality factor.

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.

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

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

Observation of bound states in the continuum embedded in symmetry bandgaps

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

Strongly Enhanced Second Harmonic Generation in a Thin Film Lithium Niobate Heterostructure Cavity

Boosting second-order optical nonlinear frequency conversion over subwavelength thickness has long been pursued through optical resonance in micro- and nanophotonics. However, the availability of thin film materials with high second-order nonlinearity is limited to III-V semiconductors, which have low transparency in the visible. Here, we experimentally demonstrated strongly enhanced second harmonic generation in one-dimensional heterostructure cavities on thin film lithium niobate. A guided-mode resonance resonator and distributed Bragg reflectors are combined for both efficient coupling and electromagnetic field localization. Over 1200 times second harmonic generation enhancement is experimentally realized compared with flat thin film lithium niobate through optimizing the trade-off between quality factor and mode volume, leading to a record high normalized conversion efficiency of 2.03×10^{-5}  cm^{2}/GW under 1.92  MW/cm^{2} pump intensity. Our approach could inspire the miniaturization and integration of compact resonant nonlinear photonic devices on thin film lithium niobate.

Point-Defect-Localized Bound States in the Continuum in Photonic Crystals and Structured Fibers

We show that point defects in two-dimensional photonic crystals can support bound states in the continuum (BICs). The mechanism of confinement is a symmetry mismatch between the defect mode and the Bloch modes of the photonic crystal. These BICs occur in the absence of band gaps and therefore provide an alternative mechanism to confine light. Furthermore, we show that such BICs can propagate in a fiber geometry and exhibit arbitrarily small group velocity which could serve as a platform for enhancing nonlinear effects and light-matter interactions in structured fibers.

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.

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.

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.

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.

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.

Circularly Polarized States Spawning from Bound States in the Continuum

Bound states in the continuum in periodic photonic systems like photonic crystal slabs are proved to be accompanied by vortex polarization singularities on the photonic bands in the momentum space. The winding structures of polarization states not only widen the field of topological physics but also show great potential that such systems could be applied in polarization manipulating. In this Letter, we report the phenomenon that by in-plane inversion (C_{2}) symmetry breaking, pairs of circularly polarized states could spawn from the eliminated bound states in the continuum. Along with the appearance of the circularly polarized states as the two poles of the Poincaré sphere together with linearly polarized states covering the equator, full coverage on the Poincaré sphere could be realized. As an application, ellipticity modulation of linear polarization is demonstrated in the visible frequency range. This phenomenon provides a new degree of freedom in modulating polarization. The C points could also find applications in light-matter interactions. Further studying and manipulating the reported polarization singularities may lead to novel phenomena and physics in radiation modulating and topological photonics.