Near-zero-index platforms arise as a new opportunity for light manipulation with boosting of optical nonlinearities, transmission properties in waveguides and constant phase distribution. In addition, they represent a solution to impedance mismatch faced in photonic circuitry offering several applications in quantum photonics, communication and sensing. However, their realization is limited to availability of materials that could exhibit such low-index. For materials used in the visible and near-infrared wavelengths, the intrinsic losses annihilate most of near-zero index properties. The design of all-dielectric photonic crystals with specific electromagnetic modes overcame the issue of intrinsic losses while showing effective mode index near-zero. Nonetheless, these modes strongly radiate to the surrounding environment, greatly limiting the devices applications. Here, we explore a novel all-dielectric photonic crystal structure that is able to sustain effective near-zero-index modes coupled to directive bound-states in the continuum in order to decrease radiative losses, opening extraordinary opportunities for radiation manipulation in nanophotonic circuits. Moreover, its relatively simple design and phase stability facilitates integration and reproducibility with other photonic components.
In this paper, we study the radiation from embedded sources in two-dimensional finite-size "photonic-quasicrystal" (PQC) slabs made of dielectric rods arranged according to a 12-fold symmetric aperiodic tiling. The results from our investigation, based on rigorous full-wave simulations, show the possibility of achieving broadside radiation at multiple frequencies, with high-directivity (e.g., 15 dB) and low-sidelobes (e.g., -12 dB). We also show that leaky waves are supported by a PQC slab, and that the beamwidth is directly proportional to the leaky-wave attenuation constant, which provides a…
We investigate the formation of photonic bound states in the continuum (BICs) in photonic crystal slabs from an analytical perspective. Unlike the stationary at-$Γ$ BICs which origin from the geometric symmetry, the tunable off-$Γ$ BICs are due to the weighted destructive via-the-continuum interference in the vicinity of accidental symmetry when the majority of the radiation is pre-canceled. The symmetric compatible nature of the off-$Γ$ BICs leads to a trapping of light that can be tuned through continuously varying the wavevector. With the analytical approach, we explain a reported experimen…
An anisotropic photonic crystal containing two anisotropic defect layers is considered. It is demonstrated that the system under can support a Fabry-Perot bound state in the continuum (FP-BIC). A fully analytic solution of the scattering problem as well as a condition for FP-BIC have been derived in the framework of the temporal coupled-mode theory.
The discovery of the topological nature of free-space light and its quantum chiral behavior has recently raised large attention. This important scientific endeavor features spin-based integrated quantum technologies. Herein, we discuss a novel phenomenon based on a resonantly-enhanced quantum spin-Hall transport of light observed in a dielectric resonator operating near the bound-state-in-continuum (BIC) regime. The BIC mode is characterized by a transverse photonic spin angular momentum density extended on a macroscopic area. As such, the experimental excited mode in near-BIC regime generates…
In this paper we propose a new hypothesis of out of plane band gap formation in all solid photonic band gap (PBG) fibers. At first, one considers the process of the core modes formation as a result of excitation of continuous mode spectrum of single dielectric rod of the cladding. It is shown that the core modes can be considered as transverse resonance of a set of the radiation modes decoupled from the continuum provided that the phase matching condition for the propagation constants are fulfilled. An analogy between the core mode formation in all solid PBG fibers and formation of bound state…
We consider bound states in the continuum (BICs) in a 1D multilayered system of an anisotropic defect layer embedded into an anisotropic photonic crystal. We analytically demonstrate that an anisotropic defect layer embedded into anisotropic photonic crystal supports accidental BICs. These BICs can be transformed to a high-Q resonances by variation of one of the system's parameters. At the same time the BICs are remarkably robust in a sense that a true BIC can be recovered by further tuning any of the other system's parameters leading to tunability of the resonance position.
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 bandgaps 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 non-linear effects and light-matter interactions in structured fibers.
Optical bound state in the continuum (BIC) is characterized by infinitely high quality factor resulting in drastic enhancement of light-matter interaction phenomena. We study the optical response of a one-dimensional photonic crystal slab with Kerr focusing nonlinearity in the vicinity of BIC analytically and numerically. We predict a strong nonlinear response including multistable behaviour, self-tuning of BIC to the frequency of incident wave, and breaking of symmetry protected BIC. We show that all of these phenomena can be observed in silicon photonic structure at the pump power of several…
We develop a semi-analytical model to describe bound states in the continuum (BICs) in photonic crystal slabs. We model leaky modes supported by photonic crystal slabs as a transverse Fabry-Perot resonance composed of a few propagative Bloch waves bouncing back and forth vertically inside the slab. This multimode Fabry-Perot model accurately predicts the existence of BICs and their positions in the parameter space. We show that, regardless of the slab thickness, BICs cannot exist below a cut-off frequency, which is related to the existence of the second-order Bloch wave in the photonic crystal…
When two nonorthogonal resonances are coupled to the same radiation channel, avoided crossing arises and a bound state in the continuum (BIC) appears in parametric space. This paper presents numerical and analytical results on the properties of avoided crossing and BIC due to the coupled guided-mode resonances in one-dimensional leaky-mode photonic lattices with slab geometry. In symmetric photonic lattices with up-down mirror symmetry, Friedrich-Wintgen BICs with infinite lifetime are accompanied by avoided crossings due to the coupling between two guided modes with the same transverse parity…
We develop a formalism, based on the mode expansion method, to describe the guided resonances and bound states in the continuum (BICs) in photonic crystal slabs with one-dimensional periodicity. This approach provides analytic insights to the formation mechanisms of these states: the guided resonances arise from the transverse Fabry-Pérot condition, and the divergence of the resonance lifetimes at the BICs is explained by a destructive interference of radiation from different propagating components inside the slab. We show BICs at the center and on the edge of the Brillouin zone protected by s…
Bound states in the continuum (BICs) in photonic crystal slabs represent the resonances with an infinite quality(Q)-factor, occurring above the light line for an infinitely periodic structure. We show that a set of BICs can turn into quasi-BICs with a very high Q-factor even for two or three unit cell structures. They are explained by a viewpoint of BICs originating from the tight binding of individual resonances of each unit cell as in semiconductors. Combined with a reciprocal-space matching technique, the microcavities based on quasi-BICs can achieve a Q-factor as high as defect-based PhC m…
We present a new resonant behavior based on bound states in the continuum in a guided wave silicon platform. The continuum has the form of a collimated beam of light which is confined vertically in a TE mode of a silicon slab. The bound state is a discrete TM mode of a ridge on the silicon slab. The coupling between the slab and ridge modes results in a single sharp resonance at the wavelength where they phase match. We experimentally demonstrate this phenomenon on a silicon photonic chip using foundry compatible parameters and interface it on-chip to standard single mode silicon nanowire wave…
We consider a one-dimensional photonic crystal composed of alternating layers of isotropic and anisotropic dielectric materials. Such a system has different band structures for different polarizations of light. We demonstrate that if an anisotropic defect layer is inserted into the structure, the crystal can support an optical bound state in the continuum. By tilting the principle dielectric axes of the defect layer relative to those of the photonic crystal we observe a long-lived resonance in the transmission spectrum. We derive an analytical expression for the decay rate of the resonance tha…
Germanium self-assembled nanoislands and quantum dots are very prospective for CMOS-compatible optoelectronic integrated circuits but their luminescence intensity is still insufficient for many practical applications. Here, we demonstrate experimentally that photoluminescence of Ge nanoislands in silicon photonic crystal slab with hexagonal lattice can be dramatically enhanced due to the involvement in the emission process of the bounds states in the continuum. We experimentally demonstrate more than two orders of magnitude peak photoluminescence enhancement and more than one order of magnitud…
A bound state in the continuum (BIC) is a localized state of an open structure with access to radiation channels, yet it remains highly confined with, in theory, infinite lifetime and quality factor. There have been many realizations of such exceptional states in dielectric systems without loss. However, realizing BICs in systems with losses such as plasmonics remains a challenge. In this Letter, we explore the possibility of realizing BICs in a hybrid plasmonic-photonic structure consisting of a plasmonic grating coupled to a dielectric optical waveguide. The plasmonic-photonic system support…
Bound states in the continuum (BICs) have been extensively studied in various systems since its first proposal in quantum mechanics. Photonic BICs can enable optical mode confinement and provide field enhancement for nonlinear optics, but they have rarely been explored in nonlinear integrated photonic waveguides. Applying BICs in photonic integrated circuits enables low-loss light guidance and routing in low-refractive-index waveguides on high-refractive-index substrates, which is suitable for integrated photonics with nonlinear materials. Here, we report experimental demonstration of second-h…
The question of how to continuously manipulate a photonic system between a radiating state and a bound state is an important challenge in photonics, as its solution promises broad technological relevance for optical sensors, modulators, switches and displays. Existing approaches utilise the inherent wave-nature of electromagnetic fields to their advantage, and are commonly identified as bound states in the continuum (BICs), as they resemble singular bound states embedded in a band of radiating states. Although quasi-BICs have been demonstrated for numerous symmetric periodic photonic crystals,…
The resonant-state expansion (RSE) provides a precise and computationally cheap tool to find resonant states in complex systems using the optical modes of a simpler system as a basis. We apply the RSE to a photonic crystal slab in order to identify and analyze its bound states in the continuum (BICs). We show that the RSE is a useful and reliable method for not only finding the BICs but also for differentiating between accidental and symmetry-protected BICs, as well as for understanding their formation from the basis modes and evolution with structural and material parameters of the system. Th…
Bound states in the continuum (BICs) are radiationless localized states embedded in the part of the parameter space that otherwise corresponds to radiative modes. Many decades after their original prediction and early observations in acoustic systems, such states have been demonstrated recently in photonic structures with engineered geometries. Here, we put forward a mechanism, based on waveguiding structures that contain anisotropic birefringent materials, that affords the existence of BICs with fundamentally new properties. In particular, anisotropy-induced BICs may exist in symmetric as wel…
Nonlinearity is a powerful determinant of physical systems. Controlling nonlinearity leads to interesting states of matter and new applications. In optics, diverse families of continuous and discrete states arise from balance of nonlinearity and group-velocity dispersion (GVD). Moreover, the dichotomy of states with locally enhanced or diminished field intensity depends critically on the relative sign of nonlinearity and either anomalous or normal GVD. Here, we introduce a resonator with unconditionally normal GVD and a single defect mode that supports both dark, reduced-intensity states and b…
Recently emerged dielectric resonators and metasurfaces offer a low-loss platform for efficient manipulation of electromagnetic waves from microwave to visible. Such flat meta-optics can focus electromagnetic waves, generate structured beams and vortices, enhance local fields for sensing as well as provide additional functionalities for advanced MRI machinery. Recent advances are associated with exotic optical modes called bound states in the continuum, which can give rise to extremely large quality factors and supercavity lasing. Here, we experimentally demonstrate subwavelength active superc…
Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to a HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. …
Metasurfaces based on resonant subwavelength photonic structures enable novel ways of wavefront control and light focusing, underpinning a new generation of flat-optics devices. Recently emerged all-dielectric metasurfaces exhibit high-quality resonances underpinned by the physics of bound states in the continuum that drives many interesting concepts in photonics. Here we suggest a novel approach to explain the physics of bound photonic states embedded into the radiation continuum. We study dielectric metasurfaces composed of planar periodic arrays of Mie-resonant nanoparticles ("meta-atoms") …
Bound states in the continuum (BICs) and Fano resonances in planar photonic lattices, including metasurfaces and photonic crystal slabs, have been studied extensively in recent years. Typically, the BICs and Fano resonances are associated with the second stop bands open at the second-order Gamma ($Γ$) point. This paper address the fundamental properties of the fourth stop band accompanied by BICs at the third-order $Γ$ point in one-dimensional (1D) leaky-mode photonic lattices. At the fourth stop band, one band edge mode suffers radiation loss, thereby generating a Fano resonance, while the ot…
Conventional photonic lattices, such as metamaterials and photonic crystals, exhibit various interesting physical properties that are attributed to periodic modulations in lattice parameters. In this study, we introduce novel types of photonic lattices, namely Fourier-component-engineered metasurfaces, that do not possess the first Fourier harmonic component in the lattice parameters. We demonstrate that these metasurfaces support the continuous high-$Q$ bound states near second stop bands. The concept of engineering Fourier harmonic components in periodic modulations provides a new method to …
Photonic time crystals assisted by quasi-bound states in the continuum
National and Kapodistrian University of Athens（雅典国立卡波迪斯特里阿斯大学）；NCSR “Demokritos”（德谟克利特国家科学研究中心）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Harbin Engineering University（哈尔滨工程大学）；University of Eastern Finland（东芬兰大学）；Aalto University（阿尔托大学）
Waves that are perfectly confined in the continuous spectrum of radiating waves without interaction with them are known as bound states in the continuum (BICs). Despite recent discoveries of BICs in nanophotonics, full routing and control of BICs are yet to be explored. Here, we experimentally demonstrate BICs in a fundamentally new photonic architecture by patterning a low-refractive-index material on a high-refractive-index substrate, where dissipation to the substrate continuum is eliminated by engineering the geometric parameters. Pivotal BIC-based photonic components are demonstrated, inc…
Robust Unidirectional Edge States in the Continuum in non-Topological Floquet Photonic Crystals
School of Physics, Beijing Institute of Technology（北京理工大学物理学院）；MOE & Guangxi Key Laboratory of Processing for Non-Ferrous Metals and Featured Materials, School of Physical Science and Technology, Guangxi University（广西大学物理科学与技术学院、有色金属及特色材料加工教育部与广西重点实验室）
Bound states in the continuum provide a remarkable example of how a simple problem solved about a century ago in quantum mechanics can drive the research on a whole spectrum of resonant phenomena in wave physics. Due to their huge radiative lifetime, bound states in the continuum have found multiple applications in various areas of physics devoted to wave processes, including hydrodynamics, atomic physics, and acoustics. In this review paper, we present a comprehensive description of bound states in the continuum and related effects, focusing mainly on photonic dielectric structures. We review…
Light trapping is a constant pursuit in photonics because of its importance in science and technology. Many mechanisms have been explored, including the use of mirrors made of materials or structures that forbid outgoing waves, and bound states in the continuum that are mirror-less but based on topology. Here we report a compound method, combing mirrors and bound states in the continuum in an optimized way, to achieve a class of on-chip optical cavities that have high quality factors and small modal volumes. Specifically, light is trapped in the transverse direction by the photonic band gap of…
Elusive features in photonic and electronic devices can be detected by means of advanced, time-domain spectroscopic techniques. In this letter we introduce a novel kind of modulation spectroscopy, based on the optomechanical interaction of photonic and mechanical modes. Applying the technique to a Si metasurface and its drum-like mechanical modes, we detect narrow-band quasi-Bound-State-in-the-Continuum (q-BIC) modes close to normal incidence, where their measurement can be hindered by a high symmetry protection and undesired background modes. Showing a visibility enhancement of more than one …
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 work, 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 appea…
Recently, optical bound states in continuum in various passive photonic crystals have been identified and similar structures incorporated with optical gain have been reported to exhibit lasing. However, no explicit control over the type of lasing BIC has been reported. In this work, we utilize all four fundamental BICs related to the lowest energy Gamma-point of a square photonic crystal lattice. We identify the associated topological charges from experimentally obtained dispersions, finite element method simulations, as well as from spherical decomposition method based on the microscopic pola…
The realization of lossless metasurfaces with true chirality crucially requires the fabrication of three-dimensional structures, constraining their feasibility for experiments and hampering practical implementations. Even though the three-dimensional assembly of metallic nanostructures has been demonstrated previously, the resulting plasmonic resonances suffer from high intrinsic and radiative losses. The concept of photonic bound states in the continuum (BICs) is instrumental for tailoring radiative losses in diverse geometries, especially when implemented using lossless dielectrics, but appl…
Photonic nanostructures simultaneously maximizing spectral and spatial overlap between fundamental and second-harmonic confined modes are highly desirable for enhancing second-order nonlinear effects in nonlinear media. These conditions have thus far remained challenging to satisfy in photonic crystal cavities because of the difficulty in designing a band gap at the second-harmonic frequency. Here, we solve this issue by using instead a bound state in the continuum at that frequency, and we design a doubly-resonant photonic crystal slab cavity with strongly improved figures of merit for nonlin…
The photonic bound state in the continuum (BIC) is discovered in a hybrid photonic circuit with low refractive index waveguide on a high refractive index thin membrane, where the optical dissipation is forbidden because of the destructive interference of different leakage channels. Based on the photonic BIC, the low mode area in a hybrid waveguide and high quality factor in a microresonator can be applied to enhance the light-matter interaction. Taking the fabrication-friendly polymer structure on diamond membrane as an example, those excellent optical performances can exist in a wide range of…
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, 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 betw…
Metamaterials with an effective zero refractive index associated to their electromagnetic response are sought for a number of applications in communications and nonlinear optics. A promising way that this can be achieved in all-dielectric photonic crystals is through the design of a Dirac cone at zero Bloch wave-vector in the photonic band structure. In the optical frequency range, the natural way to implement this design is through the use of a photonic crystal slab. In the existing implementation, however, the zero-index photonic modes also radiate strongly into the environment due to intrin…
