Bound states in the continuum

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.

In 1929, only three years after the advent of quantum mechanics, von Neumann and Wigner showed that Schrödinger's equation can have bound states above the continuum threshold. These peculiar states, called bound states in the continuum (BICs), manifest themselves as resonances that do not decay. For several decades afterwards the idea lay dormant, regarded primarily as a mathematical curiosity. In 1977, Herrick and Stillinger revived interest in BICs when they suggested that BICs could be observed in semiconductor superlattices. BICs arise naturally from Feshbach's quantum mechanical theory of resonances, as explained by Friedrich and Wintgen, and are thus more physical than initially realized. Recently, it was realized that BICs are intrinsically a wave phenomenon and are thus not restricted to the realm of quantum mechanics. They have since been shown to occur in many different fields of wave physics including acoustics, microwaves and nanophotonics. However, experimental observations of BICs have been limited to passive systems and the realization of BIC lasers has remained elusive. Here we report, at room temperature, lasing action from an optically pumped BIC cavity. Our results show that the lasing wavelength of the fabricated BIC cavities, each made of an array of cylindrical nanoresonators suspended in air, scales with the radii of the nanoresonators according to the theoretical prediction for the BIC mode. Moreover, lasing action from the designed BIC cavity persists even after scaling down the array to as few as 8-by-8 nanoresonators. BIC lasers open up new avenues in the study of light-matter interaction because they are intrinsically connected to topological charges and represent natural vector beam sources (that is, there are several possible beam shapes), which are highly sought after in the fields of optical trapping, biological sensing and quantum information.

Bound states in the continuum (BICs) and circularly polarized points (C points), being well-known momentum-space polarization singularities in photonic crystal (PhC) slabs, have attracted much attention due to their novel properties. The further investigations on the generation and evolution of BICs and C points in momentum space have provided more perspectives to modulate these polarization singularities by tuning parameters. Recently, it was theoretically proposed that starting from a high-order BIC, various tunable evolutions of BICs and C points could be realized by symmetry breaking, offering an effective method to create and modulate polarization singularities in momentum space. To date, there is still no experimental realization of tunable evolution of polarization singularities from a high-order BIC. Here, we experimentally realized tunable evolution of BICs and C points in momentum space by symmetry breaking on purpose. The studied high-order BIC of −2 charge exists in a PhC slab of C6 symmetry. The off-Γ BICs of −1 charge were observed by breaking the C6 symmetry to the C2 symmetry. The at-Γ BIC of +1 charge and off-Γ C points of −12 charge were observed by breaking the C6 symmetry to the C3 symmetry. The symmetry breaking factors and unit-cell configurations were further applied to continuously modulate the movement of polarization singularities in momentum space. Our results can promote the understanding of polarization singularities’ evolution and provide effective approaches of symmetry breaking to on-purpose design BICs and C points in momentum space.

Bound states in the continuum (BICs) have garnered increasing interest for their outstanding ability to enhance wave-matter interactions and provide an infinite quality (Q) factor. However, elastic BICs have not been fully explored due to the complex polarization modes that differ from those of electromagnetic and acoustic waves. In this paper, we theoretically, numerically, and experimentally investigate elastic BICs with multi-polarization hybridization between flexural and longitudinal waves. Based on the hybridization, Friedrich-Wintgen (FW) BICs can be realized by degenerating two different-eigenmode resonances, unlike conventional realizations of two identical ones. Further, we demonstrate that the FW and accidental quasi-BICs can coexist in the multi-polarization elastic system by detuning two flexural resonances and simultaneously modulating the destructive interference. Our study reveals the rich properties of elastic BICs with multi-polarization hybridization and offers a method for achieving perfect mode conversion between flexural and longitudinal waves with a tunable Q factor. Elastic bound states in the continuum (BICs) with multipolarization hybridization, distinct from optical and acoustic cases, remain an open area of investigation. This study demonstrates the coexistence of Friedrich–Wintgen and accidental BICs in a multi-polarization elastic system and achieves perfect mode conversion via these BICs.

Optical bound states in the continuum (BICs) lies in side the continuum and coexists with extended waves, but it remains perfectly confined without any radiation. This unique property of BICs has led to numerous applications, such as highly surface‐sensitive and spectrally sharp resonances for photonic biosensors. However, it remains challenging to experimentally realize the BICs in a single‐particle system, especially for subwavelength structures. This study presents the existence of optical BICs in a subwavelength metallic microstructure, and quasi‐BICs are observed experimentally in a waveguide system with only a single optimized aluminum meta‐particle. This plasmonic BICs is resulting from the destructive interference of two localized surface plasmon modes. Benefiting from its strong localized field confinement and substrate‐free merit of BICs, the experimentally measured quality factor (Q‐factor) of this transmission dip reach to 273. Additionally, this meta‐particle is experimentally verified to show a good sensitivity for both solids and liquids through the spectral shift of the BICs caused transmission dip. This finding extends the optical BICs to a subwavelength scale and opens practical application opportunities for ultrasmall‐quantity detection of biochemical substances.

We show that a circular periodic array of $N$ dielectric cylinders supports nearly bound states in the continuum (BICs) propagating along the cylinders. These propagating nearly BICs with extremely large $Q$ factors of order $exp(\lambda N)$ are surrounded by resonant modes weakly leaking into the radiation continuum. We present leaky zones in the vicinity of different types of BICs: symmetry protected nearly BICs with the resonant width proportional to the squared propagation constant $\Gamma \sim k_z^2$, non-symmetry protected nearly BICs with finite propagation constant $k_c$ with $\Gamma\sim (k_z-k_c)^2$ and non-symmetry protected nearly BICs with $\Gamma\sim k_z^4$. The latter propagating nearly BICs can serve for transmission of electromagnetic signal paving a way to novel type of optical fibers. We also demonstrate weakly leaking resonant modes which carry orbital angular momentum.

In 1929, von Neumann and Wigner showed that Schrödinger's equation can have, somewhat surprisingly, bound states above the continuum threshold [1]. These bound states represent the limiting case of quasi-bound states with an infinite lifetime, i.e., resonances that do not decay. It was recently realized that bound states in the continuum (BICs) are intrinsically a wave phenomenon and are thus not restricted to quantum mechanics. Since then, they have been shown to occur in many different fields of wave physics such as acoustics and photonics. In photonics' terminology, BICs are eigenmodes of an open system with an infinite radiation quality factor, Qrad. To take advantage of this unique property to design high quality resonant cavities, most investigations have focused on dielectric structures that, unlike their plasmonic counterparts, are not limited by their material quality factor, Qmat [3-5]. To investigate the properties of BICs, various platforms have been used such as 1D gratings [3], waveguide arrays [4], and 2D photonic crystal slabs [5]. In this contribution, we have designed a high quality cavity based on a BIC and harnessed its novel properties to achieve a compact low-threshold nanophotonic laser. [1] J. von Neumann and E. Wigner, "On some peculiar discrete eigenvalues" Phys. Z, 465 (1929). [2] C. Linton et al., "Embedded trapped modes in water waves and acoustics" Wave Motion 45, 16 (2007). [3] D. C. Marinica et al., "Bound states in the continuum in photonics" Phys. Rev. Lett. 100, 183902 (2008). [4] Y. Plotnik et al., "Experimental observation of optical bound states in the continuum" Phys. Rev. Lett. 107, 183901 (2011). [5] C. W. Hsu et al., "Observation of trapped light within the radiation continuum" Nature 499, 188 (2013).

Trapping electromagnetic waves within the radiation continuum holds significant implications in the field of optical science and technology. Photonic bound states in the continuum (BICs) present a distinctive approach for achieving this functionality, offering potential applications in laser systems, sensing technologies, and other domains. However, the simultaneous achievement of high Q-factors, flat-band dispersions, and wide-angle responses in photonic BICs has not yet been reported, thereby impeding their practical performance due to laser direction deviation or sample disorder. Here, we theoretically demonstrate the construction of moiré BICs in one-dimensional photonic crystal (PhC) slabs, where high-Q resonances in the entire moiré flat band are achieved. Specifically, we numerically validate that the radiation loss of moiré BICs can be eliminated by aligning multiple topological polarization charges with all diffraction channels, enabling the strong suppression of far-field radiation from the entire moiré band. This leads to a slow decay of Q-factors away from moiré BICs in the momentum space. Moreover, it is found that Q-factors of the moiré flat band can still maintain at a high level with structural disorder. In experiments, we fabricate the designed 1D moiré PhC slab and observe both high-Q resonances and a slow decrease of Q-factors for moiré flat-band Bloch modes. Our findings hold promising implications for designing highly efficient optical devices with wide-angle responses and introduce a novel avenue for exploring BICs in moiré superlattices.

Bound states in the continuum (BICs), first predicted in the field of quantum physics [1], are localized radiationless states existing in the part of the spectrum that corresponds to radiative modes. BICs are a general wave phenomenon and have recently been found in photonic systems [2]. They are known to exist in photonic structures in almost-pure transverse-electric (TE) or transverse-magnetic (TM) states, at fixed frequencies and propagation directions [3]. More recently, we have shown the existence of fully hybrid BICs alongside pure TE/TM BICs in planar structures containing uniaxial materials in both symmetric and asymmetric geometries [4]. BICs occur when we decouple the radiation mode from the continuum by suppressing the radiation channel. This can happen in anisotropic planar structures due to polarization separation or destructive interference. The fact that interferometric BICs change propagation direction with frequency suggests that the structure gives itself to potential applications as spatial and spectral filters.

We show that lattices with higher-order topology can support corner-localized bound states in the continuum (BICs). We propose a method for the direct identification of BICs in condensed matter settings and use it to demonstrate the existence of BICs in a concrete lattice model. Although the onset for these states is given by corner-induced filling anomalies in certain topological crystalline phases, additional symmetries are required to protect the BICs from hybridizing with their degenerate bulk states. We demonstrate the protection mechanism for BICs in this model and show how breaking this mechanism transforms the BICs into higher-order topological resonances. Our work shows that topological states arising from the bulk-boundary correspondence in topological phases are more robust than previously expected, expanding the search space for crystalline topological phases to include those with boundary-localized BICs or resonances.

High-quality factor optical modes with a low dispersion in the momentum space are highly desirable for applications such as low-threshold lasers, strong light-matter interactions, and optical trapping. Bound states in the continuum (BICs) have recently gained attention as a promising optical cavity concept due to their theoretically infinite quality factors. However, their quality factor decreases exponentially when deviating from the BIC singularity in the momentum space, which limits their practical use. Here, we present a design concept and experimental realization of flatband BICs in a rectangular array of titanium dioxide nanopillars. By precisely engineering the interaction between four counterpropagating guided modes in the array, a nondispersive BIC band can be obtained. The flatband BIC exhibits an enhanced quality factor near the Γ-point by 2 orders of magnitude compared to that of the symmetry-protected BIC mode in a square array, along with an exceptionally high optical density of states. As a result, we achieve room-temperature lasing at the flatband BIC with a quality factor of ∼9100 and a threshold 4 times lower than that of the symmetry-protected BIC. The flatband-BIC lasing properties, such as directionality and topological charge, are also studied in detail. The concept and outstanding lasing performance of the flatband BICs presented in our work mark an important step toward efficient optical cavities and microlasers and hold great potential for advanced photonic and optoelectronic devices.

A second-order topological insulator is designed on a platform of a two-dimensional (2D) square lattice with all coupling coefficients having the same sign. Simulated results show the existence of two types of nontrivial corner states in this system, with one type being identified as bound states in the continuum (BIC). The non-BIC corner states are also found by surrounding a nontrivial sample by a trivial one, and interestingly, these perfectly confined corner states can be gradually delocalized and merge into edge states by tuning the intersystem coupling coefficient. Both BIC and non-BIC corner states originate from bulk dipole moments rather than quantized quadrupole moments, with the corresponding topological invariant being the 2D Zak phase. Full wave simulations based on realistic acoustic waveguide structures are demonstrated. Our proposal provides an experimentally feasible platform for the study of the interplay between BIC and a high-order topological insulator, and the evolution from corner states to edge states.

The radiation mode of the interaction between electromagnetic waves and materials has always been a research hotspot in nanophotonics, and bound states in the continuum (BICs) belong to one of the nonradiative modes. Owing to their high-quality factor characteristics, BICs are extensively employed in nonlinear harmonic generators and sensors. Here, the influence of structural parameters on radiation modes has been systematically analyzed using band theory; the mechanisms of quasi-BIC mode and BIC mode were also analyzed through multipole decomposition of scattered power and near-field distribution. Notably, this study presents the discovery that the toroidal dipole-BIC (TD-BIC) arises from the interference and cancellation of electric and toroidal dipoles. The research results indicate that the structure, which supports symmetry-protected BICs, is sensitive to variations in the concentration of NaCl solution in its surroundings, making it applicable for liquid detection in miniaturized metal sensors. The proposed scheme broadens the applicability of BIC-based sensors and provides a prospective platform for biological and chemical sensing.

Optical bound states in the continuum (BICs) are capable of manipulating the polarization, confinement, and coupling of light with infinitely high-quality factor. The emerging design based on photonic crystal (PhC) slabs has led to the realization of novel platforms with strong light–matter interaction, but these structures usually are sensitive to the polarization of light. Here, we report theoretically that both transverse-electric (TE) and transverse-magnetic (TM) polarized BICs at telecommunication wavelengths can be simultaneously constructed based on one-dimensional dielectric PhC slabs. By means of the mode expansion method, the essential characteristics of these BICs are systematically investigated in this structure, including the formation and modulation of the symmetry-protected and non-symmetry-protected BICs for different polarizations. It is derived that these BICs can be achieved independent of the incident polarization and for a broad range of propagating constants. These results can provide potential applications for efficient biosensing and perfectly filtering as well as to study various nonlinear phenomena.

Bound states in the continuum (BICs) are a type of waves that are perfectly confined in the continuous spectrum of radiating waves without interaction with them. Here, we fabricated, with CMOS-compatible processes on a silicon chip, a wheel-shaped optomechanical microresonator, in which we experimentally observed the BIC in the micromechanical domain. The BIC results from destructive interference between two dissipative mechanical modes of the microresonator under broken azimuthal symmetry. Such BICs can be obtained from devices with large and robust supporting structures with variable sizes, which substantially reduces fabrication difficulty and allows for versatile application environments. Our results open a new way of phonon trapping in micromechanical structures with dissipation channels, and produce long phonon lifetimes that are desired in many mechanical applications such as mechanical oscillators, sensors, and quantum information processors.