Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs

Light-emitting diodes with Ge(Si) nanoislands embedded in photonic crystals

Room temperature lateral p+-i-n+light-emitting diodes (LEDs) with photonic crystals embedded in the i-region were fabricated on structures with Ge(Si) self-assembled islands and their optical properties were investigated. The use of preliminary amorphization and solid phase epitaxy of the implanted p+and n+contact regions made it possible to reduce the impurity activation temperature from 800 °С-1100 °С to 600 °С, which corresponds to the growth temperature of Ge(Si) islands. This resulted in a significant reduction of the detrimental effect of the high-temperature annealing used for diode formation on the intensity and spectral position of the luminescence signal from the islands. It was shown that significant enhancement (more than an order of magnitude) of room temperature electroluminescence of Ge(Si) islands in the spectral range of 1.3-1.55μm can be achieved due to their interaction with different modes of the photonic crystals. The measured radiation power of the obtained diodes in the spectral range of 1.3-1.55μm exceeds 50 pW at a pump current of 8 mA, which is an order of magnitude higher than the previously achieved values for micro-LEDs with Ge(Si) nanoislands. The obtained results open up new possibilities for the realization of silicon-based light emitting devices operating at telecommunication wavelengths.

Polarization states and far-field optical properties in dielectric photonic crystal slabs

We study the role of topological singularities like Bound States in a Continuum (BICs) or Circularly Polarized States (CPSs) in determining ellipticity of the far-field polarization in dielectric metasurfaces. Using finite-difference time-domain as well as rigorous coupled-wave analysis simulations, we determine the behavior of the Stokes parameter S3 in the whole k space above the light cone, with special regard to the region close to the singularities. Moreover, we clarify the relation between the topological singularities and the circular dichroism in reflectivity.

Bound states in the continuum in anisotropic photonic crystal slabs

We investigate the bound states in the continuum (BICs) in photonic crystal slabs composed of alternating anisotropic and isotropic dielectric materials. According to the orientation of optical axis plane, three different configurations are proposed for analyzing various types of BICs, associated with extremely large quality factors and vanishing spectral linewidths. In particular, symmetry-protected (SP) BICs exist at the Brillouin zone center for zero rotation angle of the optical axis, which exhibit antisymmetric field patterns that are decoupled from the symmetric radiating fields. Accidental BICs and Friedrich-Wintgen (FW) BICs also occur at the Brillouin zone center for particular rotation angles of the optical axis. The former emerge on isolated bands with quasi-symmetric or quasi-antisymmetric field patterns, while the latter appear near the avoided crossing between two dispersion bands. At off the Brillouin zone center, SP BICs do not exist while accidental BICs and FW BICs appear at particular optical axis rotation angles, with similar features but somewhat more asymmetric field patterns than those at the Brillouin zone center.

Emission Enhancement of Ge/Si Quantum Dots in Hybrid Structures with Subwavelength Lattice of Al Nanodisks

The effects of resonance interaction of plasmonic and photonic modes in hybrid metal-dielectric structures with square Al nanodisk lattices coupled with a Si waveguide layer were investigated using micro-photoluminescence (micro-PL) spectroscopy. As radiation sources, GeSi quantum dots were embedded in the waveguide. A set of narrow PL peaks superimposed on the broad bands were observed in the range of quantum dot emissions. At optimal parameters of Al nanodisks lattices, almost one order increasing of PL intensity was obtained. The experimental PL spectra are in good agreement with results of theoretical calculations. The realization of high-quality bound states in the continuum was confirmed by a comparative analysis of the experimental spectra and theoretical dispersion dependences. The results demonstrated the perspectives of these type structures for a flat band realization and supporting the slow light.

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.

Brillouin zone folding driven bound states in the continuum

Non-radiative bound states in the continuum (BICs) allow construction of resonant cavities with confined electromagnetic energy and high-quality (Q) factors. However, the sharp decay of the Q factor in the momentum space limits their usefulness for device applications. Here we demonstrate an approach to achieve sustainable ultrahigh Q factors by engineering Brillouin zone folding-induced BICs (BZF-BICs). All the guided modes are folded into the light cone through periodic perturbation that leads to the emergence of BZF-BICs possessing ultrahigh Q factors throughout the large, tunable momentum space. Unlike conventional BICs, BZF-BICs show perturbation-dependent dramatic enhancement of the Q factor in the entire momentum space and are robust against structural disorders. Our work provides a unique design path for BZF-BIC-based silicon metasurface cavities with extreme robustness against disorder while sustaining ultrahigh Q factors, offering potential applications in terahertz devices, nonlinear optics, quantum computing, and photonic integrated circuits.

Ultra-low threshold continuous-wave quantum dot mini-BIC lasers

Highly compact lasers with ultra-low threshold and single-mode continuous wave (CW) operation have been a long sought-after component for photonic integrated circuits (PICs). Photonic bound states in the continuum (BICs), due to their excellent ability of trapping light and enhancing light-matter interaction, have been investigated in lasing configurations combining various BIC cavities and optical gain materials. However, the realization of BIC laser with a highly compact size and an ultra-low CW threshold has remained elusive. We demonstrate room temperature CW BIC lasers in the 1310 nm O-band wavelength range, by fabricating a miniaturized BIC cavity in an InAs/GaAs epitaxial quantum dot (QD) gain membrane. By enabling effective trapping of both light and carriers in all three dimensions, ultra-low threshold of 12 μW (0.052 kW cm^-2) is achieved at room temperature. Single-mode lasing is also realized in cavities as small as only 5 × 5 unit cells (~2.5 × 2.5 μm² cavity size) with a mode volume of 1.16(λ/n)³. The maximum operation temperature reaches 70 °C with a characteristic temperature of T₀ ~93.9 K. With its advantages in terms of a small footprint, ultra-low power consumption, and adaptability for integration, the mini-BIC lasers offer a perspective light source for future PICs aimed at high-capacity optical communications, sensing and quantum information.

Permittivity-Asymmetric Quasi-Bound States in the Continuum

Breaking the in-plane geometric symmetry of dielectric metasurfaces allows us to access a set of electromagnetic states termed symmetry-protected quasi-bound states in the continuum (qBICs). Here we demonstrate that qBICs can also be accessed by a symmetry breaking in the permittivity of the comprising materials. While the physical size of atoms imposes a limit on the lowest achievable geometrical asymmetry, weak permittivity modulations due to carrier doping, and electro-optical Pockels and Kerr effects, usually considered insignificant, open the possibility of infinitesimal permittivity asymmetries for on-demand, dynamically tunable resonances of extremely high quality factors. As a proof-of-principle, we probe the excitation of permittivity-asymmetric qBICs (ε-qBICs) using a prototype Si/TiO₂ metasurface, in which the asymmetry in the unit cell is provided by the permittivity contrast of the materials. ε-qBICs are also numerically demonstrated in 1D gratings, where quality-factor enhancement and tailored interference phenomena of qBICs are shown via the interplay of geometrical and permittivity asymmetries.

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.

Large-area silicon photonic crystal supporting bound states in the continuum and optical sensing formed by nanoimprint lithography

Optical bound states in the continuum (BIC) are found in various dielectric, plasmonic and hybrid photonic systems. The localized BIC modes and quasi-BIC resonances can result in a large near-field enhancement and a high-quality factor with low optical loss. They represent a very promising class of ultrasensitive nanophotonic sensors. Usually, such quasi-BIC resonances can be carefully designed and realized in the photonic crystal that is precisely sculptured by electron beam lithography or interference lithography. Here, we report quasi-BIC resonances in large-area silicon photonic crystal slabs formed by soft nanoimprinting lithography and reactive ion etching. Such quasi-BIC resonances are extremely tolerant to fabrication imperfections while the optical characterization can be performed over macroscopic area by simple transmission measurements. By introducing lateral and vertical dimension changes during the etching process, the quasi-BIC resonance can be tuned over a wide range with the highest experimental quality factor of 136. We observe an ultra-high sensitivity of 1703 nm per RIU and a figure-of-merit of 65.5 for refractive index sensing. A good spectral shift is observed for detecting glucose solution concentration changes and adsorption of monolayer silane molecules. Our approach involves low-cost fabrication and easy characterization process for large-area quasi-BIC devices, which might enable future realistic optical sensing applications.

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.

Perturbation approach to improve the angular tolerance of high-Q resonances in metasurfaces

The interest in high quality factor (high-Q) resonances in metasurfaces has been rekindled with the rise of the bound states in the continuum (BIC) paradigm, which describes resonances with apparently limitlessly high quality-factors (Q-factors). The application of BICs in realistic systems requires the consideration of the angular tolerance of resonances, however, which is an issue that has not yet been addressed. Here, we develop an ab-initio model, based on temporal coupled mode theory, to describe the angular tolerance of distributed resonances in metasurfaces that support both BICs and guided mode resonances (GMRs). We then discuss the idea of a metasurface with a perturbed unit cell, similar to a supercell, as an alternative approach for achieving high-Q resonances and we use the model to compare the two. We find that, while sharing the high-Q advantage of BIC resonances, perturbed structures feature higher angular tolerance due to band planarization. This observation suggests that such structures offer a route toward high-Q resonances that are more suitable for applications.

Lanthanide Ion Resonance-Driven Rayleigh Scattering of Nanoparticles for Dual-Modality Interferometric Scattering Microscopy

Light scattering from nanoparticles is significant in nanoscale imaging, photon confinement. and biosensing. However, engineering the scattering spectrum, traditionally by modifying the geometric feature of particles, requires synthesis and fabrication with nanometre accuracy. Here it is reported that doping lanthanide ions can engineer the scattering properties of low-refractive-index nanoparticles. When the excitation wavelength matches the ion resonance frequency of lanthanide ions, the polarizability and the resulted scattering cross-section of nanoparticles are dramatically enhanced. It is demonstrated that these purposely engineered nanoparticles can be used for interferometric scattering (iSCAT) microscopy. Conceptually, a dual-modality iSCAT microscopy is further developed to identify different nanoparticle types in living HeLa cells. The work provides insight into engineering the scattering features by doping elements in nanomaterials, further inspiring exploration of the geometry-independent scattering modulation strategy.

Structurally engineered colloidal quantum dot phosphor using TiO2 photonic crystal backbone

Photonic crystal (PhC) phosphor, in which the phosphor material is periodically modulated for an enhancement in color-conversion efficiency via resonant absorption of excitation photons, is a paradigm-shifting structural phosphor platform. Two-dimensional (2D) square-lattice PhC phosphor is currently considered the most advanced platform because of not only its high efficiency, but also its immunity to excitation polarization. In the present study, two major modifications are made to further improve the performance of the 2D PhC phosphor: increasing the refractive index contrast and planarizing the surface. The index contrast is improved by replacing the PhC backbone material with TiO₂ whereas the surface planarization is achieved by removing excessive colloidal quantum dots from the surface. In comparison with the reference phosphor, the upgraded PhC phosphor exhibits ~59 times enhanced absorption (in simulations) and ~7 times enhanced emission (in experiments), both of which are unprecedentedly high. Our results not only brighten the viability and applicability of the PhC phosphor but also spur the phosphor development through structural engineering of phosphor materials.

Engineering Electromagnetic Field Distribution and Resonance Quality Factor Using Slotted Quasi-BIC Metasurfaces

Dielectric metasurfaces governed by bound states in the continuum (BIC) are actively investigated for achieving high-quality factors and strong electromagnetic field enhancements. Traditional approaches reported for tuning the performance of quasi-BIC metasurfaces include tuning the resonator size, period, and structure symmetry. Here we propose and experimentally demonstrate an alternative approach through engineering slots within a zigzag array of elliptical silicon resonators. Through analytical theory, three-dimensional electromagnetic modeling, and infrared spectroscopy, we systematically investigate the spectral responses and field distributions of the slotted metasurface in the mid-IR. Our results show that by introducing slots, the electric field intensity enhancement near the apex and the quality factor of the quasi-BIC resonance are increased by a factor of 2.1 and 3.3, respectively, in comparison to the metasurface without slots. Furthermore, the slotted metasurface also provides extra regions of electromagnetic enhancement and confinement, which holds enormous potential in particle trapping, sensing, and emission enhancement.

Graphene-based fine tuning of Fano resonance transmission of quasi-bound states in the continuum

Quasi-bound state in the continuum (BIC) has significant potential because it supports an ultra-high quality factor (Q-factor). Here, we propose a graphene-embedded subwavelength grating that supports quasi-BIC for tuning very sharp Fano resonance transmission. The strongly enhanced light-graphene interaction from the quasi-BIC enables fine variation of the transmission at the resonant wavelength. The Q-factor of quasi-BIC significantly decreases as the Fermi level of graphene increases. We also propose a low-energy consumption THz-wave modulator using this scheme. The designed modulator shows approximately 100% modulation depth with a Fermi level shift of only E_F = 90 meV.

Interaction of Ge(Si) Self-Assembled Nanoislands with Different Modes of Two-Dimensional Photonic Crystal

The interaction of Ge(Si)/SOI self-assembled nanoislands with modes of photonic crystal slabs (PCS) with a hexagonal lattice is studied in detail. Appropriate selection of the PCS parameters and conditions for collecting the photoluminescence (PL) signal allowed to distinguish the PCS modes of different physical nature, particularly the radiative modes and modes associated to the bound states in the continuum (BIC). It is shown that the radiative modes with relatively low Q-factors could provide a increase greater than an order of magnitude in the integrated PL intensity in the wavelength range of 1.3-1.55 µm compared to the area outside of PCS at room temperature. At the same time, the interaction of Ge(Si) islands emission with the BIC-related modes provides the peak PL intensity increase of more than two orders of magnitude. The experimentally measured Q-factor of the PL line associated with the symmetry-protected BIC mode reaches the value of 2600.

All-dielectric high saturation structural colors enhanced by multipolar modulated metasurfaces

A visible light depth modulation based on a metasurface consisting of TiO₂ nanorings and SiO₂ substrate is proposed to significantly enhance the saturation and structural colors' gamut. Compared with the nanostructure of the TiO₂ nanodisks, the developed TiO₂ nanorings can enhance monochromatic excitation by inhibiting the multipole mode, particularly electric quadrupole (EQ) mode at a shorter wavelength. Furthermore, when TiO₂ nanorings are combined with a refractive index matching layer - water, reflection bandwidth, and background reflection are reduced, and the brightness and color purity are significantly enhanced. The novel and unique nanostructures developed can generate a significant gamut of 140% sRGB and 103% Adobe RGB. Additionally, the color structure based on the TiO₂ nanoring metasurface is sensitive to the surrounding medium's refractive index and can be employed in sensor display and other fields, as well as to amplify color information in high resolution display and imaging applications.

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.

Tunable high-quality-factor absorption in a graphene monolayer based on quasi-bound states in the continuum

A tunable graphene absorber, composed of a graphene monolayer and a substrate spaced by a subwavelength dielectric grating, is proposed and investigated. Strong light absorption in the graphene monolayer is achieved due to the formation of embedded optical quasi-bound states in the continuum in the subwavelength dielectric grating. The physical origin of the absorption with high quality factor is examined by investigating the electromagnetic field distributions. Interestingly, we found that the proposed absorber possesses high spatial directivity and performs similar to an antenna, which can also be utilized as a thermal emitter. Besides, the spectral position of the absorption peak can not only be adjusted by changing the geometrical parameters of dielectric grating, but it is also tunable by a small change in the Fermi level of the graphene sheet. This novel scheme to tune the absorption of graphene may find potential applications for the realization of ultrasensitive biosensors, photodetectors, and narrow-band filters.

Evolution of optical harmonic generation near bound-states in the continuum in hybrid plasmonic-photonic structures

We investigate the nonlinear optical harmonic generation behaviors near the bound-states in the continuum (BICs) in hybrid plasmonic-photonic structures. The hybrid structures are designed to consist of a plasmonic grating covered with a nonlinear dielectric waveguide layer, which support two distinct groups of BICs, i.e. the symmetry-protected BICs and Friedrich-Wintgen BICs. The evolution of second- and third-harmonic generation (SHG and THG) near the two groups of BICs was studied. The high dependence of nonlinear response on the local field distribution and tensor components of susceptibility of nonlinear materials was determined. Especially, there exists optimized angles of incidence for efficient SHG and THG response due to the interaction of photonic and plasmonic modes. The results are important to understand the nonlinear response behaviors in hybrid plasmonic-photonic structures and to design the nonlinear photonic devices.

Adjustable converter of bound state in the continuum basing on metal-graphene hybrid metasurfaces

The bound state in the continuum (BIC) is widely applied to metamaterial study in order to obtain robust resonance and high quality (Q) factor. In this paper, we propose a metallic metasurface structure that can support double types of BICs, and acquire quasi-BIC state by restructuring each type with a specific approach. Electric field distribution is investigated to explore the physic mechanism behind the evolution of BICs. Moreover, we substitute structured graphene with corresponding metal counterparts. The promoted design is able to switch freely between BIC and quasi-BIC state even after the fabrication, as the graphene would convert from semiconductor-like to metal-like when increasing the Fermi level. Further exploration on electric field distribution demonstrates the metallicity difference between graphene and gold, which leads to the exotic phenomenon emerge on the proposed metal-graphene structure. Finally, the proposed metal-graphene structure is applied to a digital coding display through Fermi level regulating. Therefore, our work provides deep insights to the BIC metasurface investigation, and introduces a desirable improvement for current BIC metasurface design to achieve the free conversion between BIC and quasi-BIC states.

All-pass phase shifting enabled by symmetric topological unidirectional guided resonances

All-pass phase shifting (APS), which involves a wave propagating at a constant, unitary amplitude but with pure phase variation, is extremely desired in many optoelectronic applications. In this work, we propose a method of realizing APS by out-of-plane excitation of a topologically enabled unidirectional guided resonance (UGR), which resides in a photonic crystal slab with P or C_2z symmetries. Briefly, the symmetries and unidirectional features reduce the number of ports to one that simultaneously adds or drops energy. As a result, the phase independently shifts by varying the frequency but the amplitude remains as unitary under plane wave excitation. Theory and simulations confirm our findings. A paradox that the background contribution deviates from Fabry-Perot resonance is clarified from a multi-resonances picture.

Investigation of bound states in the continuum in dual-band perfect absorbers

Enhancing the light-matter interaction of two-dimensional materials in the visible and near-infrared regions is highly required in optical devices. In this paper, the optical bound states in the continuum (BICs) that can enhance the interaction between light and matter are observed in the grating-graphene-Bragg mirror structure. The system can generate a dual-band perfect absorption spectrum contributed by guided-mode resonance (GMR) and Tamm plasmon polarition (TPP) modes. The optical switch can also be obtained by switching the TE-TM wave. The dual-band absorption response is analyzed by numerical simulation and coupled-mode theory (CMT), with the dates of each approach displaying consistency. Research shows that the GMR mode can be turned into the Fabry-Pérot BICs through the transverse resonance principle (TRP). The band structures and field distributions of the proposed loss system can further explain the BIC mechanism. Both static (grating pitch P) and dynamic parameters (incident angle θ) can be modulated to generate the Fabry-Pérot BICs. Moreover, we explained the reason why the strong coupling between the GMR and TPPs modes does not produce the Friedrich-Wintgen BIC. Taken together, the proposed structure can not only be applied to dual-band perfect absorbers and optical switches but also provides guidance for the realization of Fabry-Pérot BICs in lossy systems.

Analytical theory of finite-size photonic crystal slabs near the band edge

An analytical three-dimensional (3D) coupled-wave theory (CWT) for the finite-size photonic crystal slabs (PhCs) has been presented to depict the discretized modes at band-edges residing inside and outside the continuum. Specifically, we derive the CWT equations of slow-varying envelop function of dominant Bloch waves. By combining the trial solutions that are composed of a basis of bulk states with appropriate boundary conditions (B.C.), we analytically solve the equations and discuss the far-field patterns, asymptotic behavior and flatband effect of the finite-size modes, respectively. The proposed method presents a clear picture in physics for the origins of finite-size modes and provides an efficient and comprehensive tool for designing and optimizing PhC devices such as PCSELs.

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.

High-Q localized surface plasmon resonance based on bound states in the continuum for enhanced refractive index sensing

Nanophotonics based on localized surface plasmon resonance (LSPR) has emerged as a vibrant arena for research into enhanced light-matter interactions with potential applications in imaging, sensing, and computing. However, the low quality (Q) factor of LSPR is a significant barrier to comprehensive device applications. Here, we demonstrate that coupling the LSPR of a gold nanowire array with the optical bound states in the continuum (BIC) of a dielectric double-layer grating can significantly increase the Q factor of LSPR. We realize two hybrid modes with Q factors of up to 111 at 558 nm and 83 at 582 nm, which are about 14 and 10 times larger than those of an uncoupled gold nanowire array. Based on temporal coupled-mode theory, we further show that the resonance frequencies and Q factors of the hybrid modes can be modulated and optimized by varying relevant structural parameters. This coupled system provides a new platform for improving the figures of merit (FoMs) of LSPR-based refractive index sensors, and the concept of LSPR-BIC coupling can be extended to other similar nanosystems.

Understanding and Controlling Mode Hybridization in Multicavity Optical Resonators Using Quantum Theory and the Surface Forces Apparatus

Optical fields in metal-dielectric multilayers display typical features of quantum systems, such as energy level quantization and avoided crossing, underpinned by an isomorphism between the Helmholtz and Schrödinger wave equations. This article builds on the fundamental concepts and methods of quantum theory to facilitate the understanding and design of multicavity resonators. It also introduces the surface forces apparatus (SFA) as a powerful tool for rapid, continuous, and extensive characterization of mode dispersion and hybridization. Instead of fabricating many different resonators, two equal metal-dielectric-metal microcavities were created on glass lenses and displaced relative to each other in a transparent silicone oil using the SFA. The fluid thickness was controlled in real time with nanometer accuracy from more than 50 μm to less than 20 nm, reaching mechanical contact between the outer cavities in a few minutes. The fluid gap acted as a third microcavity providing optical coupling and producing a complex pattern of resonance splitting as a function of the variable thickness. An optical wave in this symmetric three-cavity resonator emulated a quantum particle with nonzero mass in a potential comprising three square wells. Interference between the wells produced a 3-fold splitting of degenerate energy levels due to hybridization. The experimental results could be explained using the standard methods and formalism of quantum mechanics, including symmetry operators and the variational method. Notably, the interaction between square wells produced bonding, antibonding, and nonbonding states that are analogous to hybridized molecular orbitals and are relevant to the design of "epsilon-near-zero" devices with vanishing dielectric permittivity.

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.

Unveiling the Symmetry Protection of Bound States in the Continuum with Terahertz Near-Field Imaging

Bound states in the continuum (BICs) represent a new paradigm in photonics due to the full suppression of radiation losses. However, this suppression has also hampered the direct observation of them. By using a double terahertz (THz) near-field technique that allows the local excitation and detection of the THz amplitude, we are able to map for the first time the electromagnetic field amplitude and phase of BICs over extended areas, unveiling the field-symmetry protection that suppresses the far-field radiation. This investigation, done for metasurfaces of dimer scatterers, reveals the in-plane extension and formation of BICs with antisymmetric phases, in agreement with coupled-dipole calculations. By displacing the scatterers, we show experimentally that a mirror symmetry is not a necessary condition for a BIC formation. Only π-rotation symmetry is required, making BICs exceptionally robust to structural changes. This work makes the local field of BICs experimentally accessible, which is crucial for the engineering of cavities with infinite lifetimes.

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.

Analogue of Electromagnetically Induced Transparency in an All-Dielectric Double-Layer Metasurface Based on Bound States in the Continuum

Bound states in the continuum (BICs) have attracted much attention due to their infinite Q factor. However, the realization of the analogue of electromagnetically induced transparency (EIT) by near-field coupling with a dark BIC in metasurfaces remains challenging. Here, we propose and numerically demonstrate the realization of a high-quality factor EIT by the coupling of a bright electric dipole resonance and a dark toroidal dipole BIC in an all-dielectric double-layer metasurface. Thanks to the designed unique one-dimensional (D)-two-dimensional (2D) combination of the double-layer metasurface, the sensitivity of the EIT to the relative displacement between the two layer-structures is greatly reduced. Moreover, several designs for widely tunable EIT are proposed and discussed. We believe the proposed double-layer metasurface opens a new avenue for implementing BIC-based EIT with potential applications in filtering, sensing and other photonic devices.

Quantum superposition demonstrated higher-order topological bound states in the continuum

Higher-order topological insulators, as newly found non-trivial materials and structures, possess topological phases beyond the conventional bulk-boundary correspondence. In previous studies, in-gap boundary states such as the corner states were regarded as conclusive evidence for the emergence of higher-order topological insulators. Here, we present an experimental observation of a photonic higher-order topological insulator with corner states embedded into the bulk spectrum, denoted as the higher-order topological bound states in the continuum. Especially, we propose and experimentally demonstrate a new way to identify topological corner states by exciting them separately from the bulk states with photonic quantum superposition states. Our results extend the topological bound states in the continuum into higher-order cases, providing an unprecedented mechanism to achieve robust and localized states in a bulk spectrum. More importantly, our experiments exhibit the advantage of using the time evolution of quantum superposition states to identify topological corner modes, which may shed light on future exploration between quantum dynamics and higher-order topological photonics.

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.

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.

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.

Subwavelength structure enabled ultra-long waveguide grating antenna

Because of the high index contrast, current silicon photonics based optical phased arrays cannot achieve small beam divergence and large field-of-view simultaneously without increasing fabrication complexity. To resolve the dilemma, we propose an ultra-long waveguide grating antenna formed by placing subwavelength segments within the evanescent field of a conventional strip waveguide. Bound state in the continuum effect is leveraged to suppress the sidewall emission. As a proof of concept, we theoretically demonstrated a millimeter-long through-etched waveguide grating antenna with a divergence angle of 0.081° and a feature size compatible with current silicon photonics foundries.

Flatness and boundness of photonic drumhead surface state in a metallic lattice

Nodal chain (NC) semi-metals have the degeneracy of interlacing rings in their band structure in momentum space. With the projection of degenerate rings towards crystal boundaries, there is a special type of surface dispersion appearing at surface Brillouin zone and termed drumhead surface state (DSS). Previously, experimental investigations on photonic NC and DSS have been done on metallic photonic crystals at microwave frequencies. However, far-field detection of DSS and its coupling to radiative modes in free space have not been studied. In the work, we analyze the photonic DSS in a metallic lattice by angle-resolved far-field reflection measurement and numerical simulation at terahertz (THz) frequencies, and reveal its flatness and boundness in band structure, even in the radiation continuum. Particularly, the DSS band can be tuned being from negatively dispersive via flat to positively dispersive by a single surface parameter, and the DSS at Γ point in surface Brillouin zone is in fact a symmetry-protected bound state in the continuum. Our results might have some potential applications towards THz photonics.

Toroidal dipole Fano resonances supported by lattice-perturbed dielectric nanohole arrays in the near-infrared region

The toroidal dipole (TD) plays an important role in light-matter interactions. In this paper, a lattice-perturbed dielectric nanohole array structure has been put forward to excite dominant TD Fano resonances in the near-infrared region. Herein, the numerical investigations and experimental demonstrations have been performed to characterize the TD Fano resonances with a series of lattice perturbations. The scattering power of TD and quality (Q)-factor of the resonance can be tailored by tuning perturbation. By using the lattice perturbation of 53 nm, the highest experimental Q-factor of 584 is obtained.

Highly efficient polarization-entangled photon-pair generation in lithium niobate waveguides based on bound states in continuum

Integrated optics provides a platform for the experimental implementation of highly complex and compact circuits for practical applications as well as for advances in the fundamental science of quantum optics. The lithium niobate (LN) waveguide is an important candidate for the construction of integrated optical circuits. Based on the bound state in the continuum (BIC) in a LN waveguide, we propose an efficient way to produce polarization-entangled photon pairs. The implementation of this method is simple and does not require the polarization process needed for periodically poled LN. The generation rate of the entangled photon pairs increases linearly with the length of the waveguide. For visible light, the generation efficiency can be improved by more than five orders of magnitude with waveguides having the length of only a few millimeters, compared with the corresponding case without BICs. The phenomena can appear in a very wide spectrum range from the visible to THz regions. This study is of great significance for the development of active integrated quantum chips in various wavelength ranges.

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.

Ultra-high quality graphene perfect absorbers for high performance switching manipulation

Wavelength-selective light absorption and the related switching operations are highly desired in optical devices. Herein, we report the approach for ultra-high quality (Q) graphene perfect optical absorption, which possesses impressive performance in switching manipulation. A record-breaking Q-factor (up to 10⁵) is observed, suggesting one or two orders of magnitude larger than that of the conventional graphene absorbers. The ultra-low external leakage loss rate of quasi-bound states in the continuum (BIC) resonator and the ultra-low intrinsic absorption loss rate in the resonant mode volume are the main contributions for the ultra-high Q perfect absorption. By introducing a Kerr nonlinear medium, spectral relative intensity can be changed from 0 to 100% when an ultra-low pump light with the intensity of only 5 kW cm^-2 is used. After a rather slight tuning of the refractive index (Δn = 5×10^-4) for the resonators, the absorption contrast ratio reaches 31 dB. The switching related spectral wavelength shift sensitivity is up to 915 nm/RIU and the figure of merit (FOM) is 50 833. These features confirm the ultra-high tunability and switching manipulation. It is believed that the ultra-high Q-factor absorption offered by all-dielectric configuration provides plentiful potential applications for graphene-based devices in the all-optical switch, modulator, notch filter, etc.

High-Q resonance in GeSn-based bound states in the continuum microcavity

In recent years, the investigations of lasers based on group IV material have been limited by the low quality (Q) factor of the resonant modes. With the improvement of the optical bound states in the continuum (BICs) in various dielectric systems, we propose a novel design that takes advantages of both the direct bandgap dielectric material GeSn and the BIC phenomenon. In addition to the demonstration of the unprecedented high-Q factors (i.e., ∼10¹⁰) that improve the emission process, the vertical symmetry broken structure can emit light at the wavelength of 1870 nm with higher luminous intensity (i.e., ∼24). The modulation effect of the material and geometric parameters on the Q value and the luminous intensity of the structure are also demonstrated. Our investigations provide useful guidelines for potential applications such as on-chip light sources in group IV photonics and optical communications.

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.

Observation of phonon trapping in the continuum with topological charges

Phonon trapping has an immense impact in many areas of science and technology, from the antennas of interferometric gravitational wave detectors to chip-scale quantum micro- and nano-mechanical oscillators. It usually relies on the mechanical suspension-an approach, while isolating selected vibrational modes, leads to serious drawbacks for interrogation of the trapped phonons, including limited heat capacity and excess noises via measurements. To circumvent these constraints, we realize a paradigm of phonon trapping using mechanical bound states in the continuum (BICs) with topological features and conducted an in-depth characterization of the mechanical losses both at room and cryogenic temperatures. Our findings of mechanical BICs combining the microwave frequency and macroscopic size unveil a unique platform for realizing mechanical oscillators in both classical and quantum regimes. The paradigm of mechanical BICs might lead to unprecedented sensing modalities for applications such as rare-event searches and the exploration of the foundations of quantum mechanics in unreached parameter spaces.

Metasurface Enhanced Sensitized Photon Upconversion: Toward Highly Efficient Low Power Upconversion Applications and Nanoscale E-Field Sensors

Large-scale nanoimprinted metasurfaces based on silicon photonic crystal slabs were produced and coated with a NaYF₄:Yb³⁺/Er³⁺ upconversion nanoparticle (UCNP) layer. UCNPs on these metasurfaces yield a more than 500-fold enhanced upconversion emission compared to UCNPs on planar surfaces. It is also demonstrated how the optical response of the UCNPs can be used to estimate the local field energy in the coating layer. Optical simulations using the finite element method validate the experimental results and the calculated spatial three-dimensional field energy distribution helps us to understand the emission enhancement mechanism of the UCNPs closely attached to the metasurface. In addition, we analyzed the spectral shifts of the resonances for uncoated and coated metasurfaces and metasurfaces submerged in water to enable a prediction of the optimum layer thicknesses for different excitation wavelengths, paving the way to applications such as electromagnetic field sensors or bioassays.

Tailoring the lineshapes of coupled plasmonic systems based on a theory derived from first principles

Coupled photonic systems exhibit intriguing optical responses attracting intensive attention, but available theoretical tools either cannot reveal the underlying physics or are empirical in nature. Here, we derive a rigorous theoretical framework from first principles (i.e., Maxwell's equations), with all parameters directly computable via wave function integrations, to study coupled photonic systems containing multiple resonators. Benchmark calculations against Mie theory reveal the physical meanings of the parameters defined in our theory and their mutual relations. After testing our theory numerically and experimentally on a realistic plasmonic system, we show how to utilize it to freely tailor the lineshape of a coupled system, involving two plasmonic resonators exhibiting arbitrary radiative losses, particularly how to create a completely "dark" mode with vanishing radiative loss (e.g., a bound state in continuum). All theoretical predictions are quantitatively verified by our experiments at near-infrared frequencies. Our results not only help understand the profound physics in such coupled photonic systems, but also offer a powerful tool for fast designing functional devices to meet diversified application requests.

Spontaneous symmetry breaking of nonlinear states in optical cavities with radiative losses

The dynamics of one-dimensional periodically modulated optical cavities are studied in the framework of coupled counterpropagating wave approximation. It is shown that in these systems, a spontaneous symmetry breaking bifurcation can occur, resulting in the formation of the dynamically stable asymmetric states with nonzero energy flux. Bright cavity solitons nestling on the spatially uniform backgrounds with broken symmetry are found and investigated in detail. One of the distinguishing features of the solitons on the asymmetric background is that they can exist at the pump powers much less than those needed for the formation of the solitons on the symmetric backgrounds.