Symmetry-protected Bound States In The Continuum Research Articles

Geometry symmetry-free and higher-order optical bound states in the continuum

Geometrical symmetry plays a significant role in implementing robust, symmetry-protected, bound states in the continuum (BICs). However, this benefit is only theoretical in many cases since fabricated samples’ unavoidable imperfections may easily break the stringent geometrical requirements. Here we propose an approach by introducing the concept of geometrical-symmetry-free but symmetry-protected BICs, realized using the static-like environment induced by a zero-index metamaterial (ZIM). We find that robust BICs exist and are protected from the disordered distribution of multiple objects inside the ZIM host by its physical symmetries rather than geometrical ones. The geometric-symmetry-free BICs are robust, regardless of the objects’ external shapes and material parameters in the ZIM host. We further show theoretically and numerically that the existence of those higher-order BICs depends only on the number of objects. By practically designing a structural ZIM waveguide, the existence of BICs is numerically confirmed, as well as their independence on the presence of geometrical symmetry. Our findings provide a way of realizing higher-order BICs and link their properties to the disorder of photonic systems.

Displacement-mediated bound states in the continuum in all-dielectric superlattice metasurfaces

Bound states in the continuum (BICs) are localized states coexisting with extended waves inside the continuous spectrum range, which have infinite lifetimes without any radiation. To extract high-Q quasi-BIC resonances from the symmetry-protected BIC for practical applications, symmetry-breaking approaches are usually exploited, either by slightly breaking the excitation field symmetry or structure symmetry. Here, we introduce an all-dielectric superlattice metasurface that can symmetry-compatibly convert BIC states into high-Q quasi-BIC modes based on the guided-mode resonance coupling by relative displacement tuning. The metasurface is composed of a superlattice of multiple nanobeams, supporting both magnetic mode and toroidal mode with large tunability. Both modes can interact with the incident continuum by mediating the displacement between nanobeams, which empowers dual asymmetric Fano resonances with high Q-factors. The bandwidth of the toroidal mode under y-polarized incidences and that of the magnetic mode under x-polarized incidences can be readily tuned by the local displacement between nanobeams in each unit cell. Such displacement-mediated BIC resonance is promising for various applications such as bio-molecule sensing and low threshold lasing.

Circularly polarized states and propagating bound states in the continuum in a periodic array of cylinders

Bound states in the continuum (BICs) in a periodic structure sandwiched between two homogeneous media have interesting properties and useful applications in photonics. The topological nature of BICs was previously revealed based on a topological charge related to the far-field polarization vector of the surrounding resonant states. Recently, it was established that when symmetry-protected BICs (with a nonzero topological charge) are destroyed by generic symmetry-breaking perturbations, pairs of circularly polarized resonant states (CPSs) emerge and the net topological charge is conserved. A periodic structure can also support propagating BICs with a nonzero wave vector. These BICs are not protected by symmetry in the sense of symmetry mismatch, but they need symmetry for their robust existence. Based on a highly accurate computational method for a periodic array of slightly noncircular cylinders, we show that a propagating BIC is typically destroyed by a structural perturbation that breaks only the in-plane inversion symmetry, and when this happens, a pair of CPSs of opposite handedness emerge so that the net topological charge is conserved. We also study the generation and annihilation of CPSs when a structural parameter is varied. It is shown that two CPSs with opposite topological charge and the same handedness, connected to two BICs or in a continuous branch from one BIC, may collapse and become a CPS with a zero charge. Our study clarifies the important connection between symmetry and topological charge conservation.

Near-Field Excitation of Bound States in the Continuum in All-Dielectric Metasurfaces through a Coupled Electric/Magnetic Dipole Model.

Resonant optical modes arising in all-dielectric metasurfaces have attracted much attention in recent years, especially when so-called bound states in the continuum (BICs) with diverging lifetimes are supported. With the aim of studying theoretically the emergence of BICs, we extend a coupled electric and magnetic dipole analytical formulation to deal with the proper metasurface Green function for the infinite lattice. Thereby, we show how to excite metasurface BICs, being able to address their near-field pattern through point-source excitation and their local density of states. We apply this formulation to fully characterize symmetry-protected BICs arising in all-dielectric metasurfaces made of Si nanospheres, revealing their near-field pattern and local density of states, and, thus, the mechanisms precluding their radiation into the continuum. This formulation provides, in turn, an insightful and fast tool to characterize BICs (and any other leaky/guided mode) near fields in all-dielectric (and also plasmonic) metasurfaces, which might be especially useful for the design of planar nanophotonic devices based on such resonant modes.

Accidental and symmetry-protected bound states in the continuum in a photonic-crystal slab: A resonant-state expansion study

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. The high efficiency of the RSE allows us to track the properties of BICs and other high-quality optical modes, covering the full parameter space of the system in a reasonable time frame.

Polarization-selective modulation of supercavity resonances originating from bound states in the continuum

Bound states in the continuum (BICs) are widely studied for their ability to confine light, produce sharp resonances for sensing applications and serve as avenues for lasing action with topological characteristics. Primarily, the formation of BICs in periodic photonic band gap structures are driven by symmetry incompatibility; structural manipulation or variation of incidence angle from incoming light. In this work, we report two modalities for driving the formation of BICs in terahertz metasurfaces. At normal incidence, we experimentally confirm polarization driven symmetry-protected BICs by the variation of the linear polarization state of light. In addition, we demonstrate through strong coupling of two radiative modes the formation of capacitively-driven Freidrich-Wintgen BICs, exotic modes which occur in off-Γ points not accessible by symmetry-protected BICs. The capacitance-mediated strong coupling at 0° polarization is verified to have a normalized coupling strength ratio of 4.17% obtained by the Jaynes-Cummings model. Furthermore, when the polarization angle is varied from 0° to 90° (0° ≤ ϕ < 90°), the Freidrich-Wintgen BIC is modulated until it is completely switched off at 90°.

Nonlinear Bound States in the Continuum of Etchless Lithium Niobate Metasurfaces

Optical bound states in the continuum (BICs) have recently been studied in a wide range of material systems, where light is perfectly confined in the continuous spectrum of radiating modes. In this paper, we reported periodic nonlinear metasurfaces on the etchless LiNbO3 platform, realizing the enhancement of second-order generation (SHG). All-dielectric heterogeneous metasurfaces are constructed by patterning a low-refractive-index polymer on a high refractive-index LiNbO3 film without etching. Due to BICs, light is localized in the LiNbO3 film where the excellent optical second-order nonlinearity is exploited. We demonstrated that with normal incident waves, symmetry-protected BICs are formed at near-infrared wavelength showing a vanishing linewidth in the transmission spectrum. In addition, to manifest the invisible BICs to detectable supercavity resonances at normal incidence, asymmetry is introduced into the system, degrading the symmetry-protected BICs to sharp resonances with a high Q factor. Furthermore, the second harmonic generation (SHG) of the etchless lithium niobate metasurface is studied, predicting that the SHG efficiency can exceed 10−3 with 30 MW/cm2 of the pump intensity. The proposed strategy without facing the fabrication challenge of etching single-crystal LiNbO3 film opens a new avenue for the utilization of BIC in nonlinear optics of all-dielectric heterogeneous metasurfaces.

Selection rules for quasibound states in the continuum

Photonic crystal slabs (PCSs) are a well-studied class of devices known to support optical Fano resonances for light normally incident to the slab, useful for narrowband filters, modulators, and nonlinear photonic devices. In shallow-etched PCSs the linewidth of the resonances is easily controlled by tuning the etching depth. This design strength comes at the cost of large device footprint due to the poor in-plane localization of optical energy. In fully-etched PCSs realized in high index contrast material systems, the in-plane localization is greatly improved, but the command over linewidth suffers. This disadvantage in fully-etched PCSs, also known as high contrast gratings (HCGs), can be overcome by accessing symmetry-protected Bound States in the Continuum (BICs). By perturbing an HCG, the BIC may be excited from the free space with quality factor showing an inverse squared dependence on the magnitude of the perturbation, while inheriting the excellent in-plane localization of their unperturbed counterparts. Here, we report an exhaustive catalog of the selection rules (if and to which free space polarization coupling occurs) of symmetry-protected BICs controlled by in-plane symmetry breaking in six types of two-dimensional PCS lattices. The chosen lattices allow access to the three highest symmetry mode classes of unperturbed square and hexagonal PCSs. The restriction to in-plane symmetry breaking allows for manufacturing devices with simple lithographic fabrication techniques in comparison to out-of-plane symmetry breaking, useful for practical applications. The approach reported provides a high-level roadmap for designing PCSs supporting controllable sharp spectral features with minimal device footprints using a mature fabrication platform.

Bound states in the continuum in symmetric and asymmetric photonic crystal slabs

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. Thanks to the semi-analyticity of the model, we investigate the dynamics of BICs with the slab thickness in symmetric and asymmetric photonic crystal slabs. We evidence that the symmetry-protected BICs that exist in symmetric structures at the {\Gamma}-point of the dispersion diagram can still exist when the horizontal mirror symmetry is broken, but only for particular values of the slab thickness.

Symmetry-protected bound states in the continuum supported by all-dielectric metasurfaces

Symmetry-protected bound states in the continuum (BICs) are nonradiative states with infinite lifetime and perfect confinement of energy even though lying in the radiation continuum due to the symmetry incompatibility. Herein, we study the symmetry-protected BIC supported by metasurfaces composed of silicon nanodisks. Through adding or removing parts of the nanodisks from the edge, a sharp Fano resonance emerges and demonstrates the excitation of quasi-BIC. Their $Q$ factors exhibit the same dependence on the asymmetry degree with these two opposite operations. Furthermore, from both qualitative and quantitative perspectives, analysis on far-field contributions from multipole moments along different directions combining with near-field distributions explains the evolution from BIC to quasi-BIC. The dominant contributor to the quasi-BIC is illustrated to be the electric quadrupole in the $x\ensuremath{-}y$ plane. Finally, the topological charge carried by the BIC is calculated to be $\ensuremath{-}1$, demonstrating the topological characteristics of our design. Such metasurfaces are robust in nanofabrication. Our results may provide a route for resonators with better performance applied in sensing, switching, nonlinear optics, and so on.

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.

Experimental observation of a symmetry-protected bound state in the continuum in a chain of dielectric disks

Existence of bound states in the continuum (BIC) manifests a general wave phenomenon firstly predicted in quantum mechanics in 1929 by J. von Neumann and E. Wigner. Today it is being actively explored in photonics, radiophysics, acoustics, and hydrodynamics. In this paper, we report the first experimental observation of electromagnetic bound state in the radiation continuum in 1D array of dielectric particles. By measurement of the transmission spectra of the ceramic disk chain at GHz frequencies we demonstrate how a resonant state in the vicinity of the center of the Brillouin zone turns into a symmetry-protected BIC with increase the number of the disks. We estimate a number of the disks when the radiation losses become negligible in comparison to material absorption and, therefore, the chain could be considered practically as infinite. The presented analysis is supplemented by measurements of the near fields of the symmetry protected BIC. All measurements are in a good agreement with the results of numerical simulation and analytical model based on tight-binding approximation. The obtained results provide useful guidelines for practical implementations of structures with bound states in the continuum that opens up new horizons for the development of optical and radiofrequency metadevices.

High- Q resonant modes in a finite array of dielectric particles

We trace the $Q$ factor of the resonant modes which are limited to bound states in the continuum (BICs) for $N=\ensuremath{\infty}$ in the finite array of $N$ dielectric spheres and disks. For the symmetry-protected BICs we observe the quadratic dependence of the $Q$ factor on $N$ for high-refractive-index particles, while for low-refractive-index particles there is an interplay between the quadratic and cubic dependencies. The $Q$ factor of accidental BICs grows cubically with $N$. We show that a plane wave can excite these quasi-BICs for tuning of the angle of incidence.

Resonances and bound states in the continuum on periodic arrays of slightly noncircular cylinders

Optical bound states in the continuum (BICs), especially those on periodic structures, have interesting properties and potentially important applications. Existing theoretical and numerical studies for optical BICs are mostly for idealized structures with simple and perfect geometric features, such as circular holes, rectangular cylinders and spheres. Since small distortions are always present in actual fabricated structures, we perform a high accuracy numerical study for BICs and resonances on a simple periodic structure with small distortions, i.e., periodic arrays of slightly noncircular cylinders. Our numerical results confirm that symmetries are important not only for the so-called symmetry-protected BICs, but also for the majority of propagating BICs which do not have a symmetry mismatch with the outgoing radiation waves. Typically, the BICs continue to exist if the small distortions keep the relevant symmetries, and they become resonant modes with finite quality factors if the small distortions break a required symmetry.

Strong resonances on periodic arrays of cylinders and optical bistability with weak incident waves

A one-dimensional periodic array of circular dielectric cylinders surrounded by air is a simple structure on which guided modes above the light line, also called bound states in the continuum (BICs), may exist. Recent studies reveal that such an array supports not only antisymmetric standing waves which are symmetry-protected BICs, but also propagating Bloch BICs and symmetric standing waves. Near a BIC, there is a family of resonant modes (depending on the Bloch wave number $\ensuremath{\beta}$) with arbitrarily large quality factors. Using a perturbation method, we show that the quality factor of the resonant mode typically depends on $\ensuremath{\beta}$ like $1/{(\ensuremath{\beta}\ensuremath{-}{\ensuremath{\beta}}_{*})}^{2}$, where ${\ensuremath{\beta}}_{*}$ is the Bloch wave number of the BIC, but near a symmetric standing wave $({\ensuremath{\beta}}_{*}=0)$, the quality factor blows up like $1/{\ensuremath{\beta}}^{4}$. This indicates that strong resonances can be more easily induced near a symmetric standing wave. As an application, we numerically study optical bistability for the periodic array assuming the cylinders have a Kerr nonlinearity. With the nonlinear effects enhanced by the resonances, it is possible to have optical bistability for weak incident waves. The numerical results confirm that the weakest incident wave for optical bistability is realized through the resonances near the symmetric standing waves.

Tunable optical bound states in the continuum beyond in-plane symmetry protection

The formation of tunable bound states in the continuum (BICs) within photonic crystal (PC) slabs has been investigated by using a semianalytical coupled-wave theory framework. An analytic expression of the radiative wave has been derived in order to depict the condition of BICs. As a result, in addition to well-known symmetry-protected BICs, a novel type of vertical-cancellation BIC can be realized through continuously varying a given parameter to eliminate radiative waves at the boundaries. We investigated one-dimensional and two-dimensional (2D) periodic structures, and found that such tunable BICs can occur for a wide range of wave vectors by the selection of appropriate slab thicknesses. For a 2D PC slab, a ring of high-$Q$ modes is predicted and confirmed by numerical simulation.

Topological nature of optical bound states in the continuum.

Optical bound states in the continuum (BICs) have recently been realized in photonic crystal slabs, where the disappearance of out-of-plane radiation turns leaky resonances into guided modes with infinite lifetimes. We show that such BICs are vortex centers in the polarization directions of far-field radiation. They carry conserved and quantized topological charges, defined by the winding number of the polarization vectors, which ensure their robust existence and govern their generation, evolution, and annihilation. Our findings connect robust BICs in photonics to a wide range of topological physical phenomena.