Moiré Quasibound States in the Continuum

Beam Shaping by Stacked Nonlinear Moiré Metasurfaces

Moiré phenomena provide a versatile platform for creating tunable lattices with variable symmetries and periodicities, making them a focal topic in recent photonics research. Moiré photonic devices fused with metasurfaces have demonstrated numerous novel functionalities, yet fabricating moiré metasurfaces, particularly in stacked configurations, poses significant challenges. In this paper, we present an innovative nanofabrication approach for stacked nonlinear moiré metasurfaces, using a focused ion beam-assisted nanostructure transfer-welding technique. This approach allows precise control over interlayer twist angles, enabling complex momentum space engineering along with simultaneous frequency conversion and wavefront manipulation. Experimental results reveal intricate far-field second-harmonic radiation patterns, which are effectively tunable by varying the twist angles. This advancement addresses key fabrication challenges in nonlinear photonics, opening new avenues for applications in nonlinear information processing, optical steering, and nonlinear optical switching.

Topological Degeneracy Induced by Twisting

In recent years, twisting has emerged as a new degree of freedom that plays an increasingly important role in Bloch bands of various physical systems. However, there is currently a lack of reports on the nontrivial physics of topological degeneracy in twisted systems. In this Letter, we investigated the intrinsic physical correlation between twisting and topological degeneracy. We found that twisting not only breaks the symmetry of the system but also introduces topological degeneracy that does not exist under the original symmetric system without twisting. Furthermore, the topological degeneracy can be easily tuned through twisting. This new twist-induced topological degeneracy gives rise to a unique polarization-degenerate birefringent medium, wherein the twist angle acts as a novel degree of freedom for dispersion and polarization management of interface states. Exhibiting fascinating properties and experimental feasibilities, our Letter points to new possibilities in the research of various topological physics in twisted photonics.

Control of Chirality and Directionality of Nonlinear Metasurface Light Source via Moiré Engineering

Metasurfaces have revolutionized nonlinear and quantum light manipulation in the past decade, enabling the design of materials that can tune polarization, frequency, and direction of light simultaneously. However, tuning of metasurfaces is traditionally achieved by changing their microscopic structure, which does not allow in situ tuning and dynamic optimization of the metasurfaces. In this Letter, we explore the concept of twisted bilayer and tetralayer nonlinear metasurfaces, which offer rich tunability in its effective nonlinear susceptibilities. Using gold-based metasurfaces, we demonstrate that a number of different singularities of nonlinear susceptibilities can exist in the parameter space of twist angle and interlayer gap between different twisted layers. At the singularities, reflected or transmitted light from the nonlinear process (such as second-harmonic generation) can either become circularly polarized (for C points), or entirely vanish (for V points). By further breaking symmetries of the system, we can independently tune all aspects of the reflected and transmitted nonlinear emission, achieving unidirectional emission with full-Poincaré polarization tunability, a dark state (V-V point), or any other bidirectional output. Our work paves the way for multidimensional control of polarization and directionality in nonlinear light sources, opening new avenues in ultrafast optics, optical communication, sensing, and quantum optics.

Terahertz bound states in the continuum on-and-off-Г point of a moiré photonic superlattice

Moiré metasurfaces exhibit high optical tuneabilities and versatile light manipulation capabilities. Both infinite quality factor (Q factor) and topological vortex configurations in momentum space (k-space) of the bound state in the continuum (BIC) have introduced new dimensions for light modulation. Herein, we propose a moiré metasurface comprising two identical square photonic lattices superimposed with a commensurate angle of 12.68°. By tuning the incidence angle, the symmetric-protected BICs, Friedrich-Wintgen BIC, and accidental BIC can be achieved simultaneously in our moiré metasurfaces. It is found that the quasi-BICs maintain an ultrahigh Q factor beyond 107. The photonic band structures manifest that the three types of BICs are at the center of far-field polarization vortices in k-space, which have their own topological charges. We experimentally show that these BICs exhibit high sensitivity to subtle changes in analyte refractive index for thin-film sensor application. Our discovery predicts an approach to a highly sensitive multi-channel terahertz biosensor.

Strong Coupling between Moiré-Type Plasmons and Phonons in Suspended Monolayer Metallic Twisted Superlattices

We demonstrate both experimentally and analytically a strong coupling phenomenon between moiré-type plasmons and phonons within moiré superlattices. We study the dependence of moiré wave vector and the twist angle and numerically simulate and experimentally fabricate metallic moiré superlattices on a suspended thin film SiO2 substrate at different twist angles. The results suggest that the coupling strength initially increases and then decreases with increasing twist angles. When the twist angle is at 16.26°, we achieve a moiré-type plasmon-phonon strong coupling with a Rabi splitting strength approaching 45 meV. We further analyze the coupling system by utilizing the coupled-harmonic-oscillators theory and quantum mechanical theory. The calculations and numerical simulations further agree with the experimental results. The proposed strong coupling system has the potential to contribute substantially to electromagnetic field controlling and coupling.

Optical moiré bound states in the continuum

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.

Nonlinear physics of moiré superlattices

Nonlinear physics is one of the most important research fields in modern physics and materials science. It offers an unprecedented paradigm for exploring many fascinating physical phenomena and realizing diverse cutting-edge applications inconceivable in the framework of linear processes. Here we review the recent theoretical and experimental progress concerning the nonlinear physics of synthetic quantum moiré superlattices. We focus on the emerging nonlinear electronic, optical and optoelectronic properties of moiré superlattices, including but not limited to the nonlinear anomalous Hall effect, dynamically twistable harmonic generation, nonlinear optical chirality, ultralow-power-threshold optical solitons and spontaneous photogalvanic effect. We also present our perspectives on the future opportunities and challenges in this rapidly progressing field, and highlight the implications for advances in both fundamental physics and technological innovations.

Engineered moiré photonic and phononic superlattices

Recent discoveries of Mott insulating and unconventional superconducting states in twisted bilayer graphene with moiré superlattices have not only reshaped the landscape of 'twistronics' but also sparked the rapidly growing fields of moiré photonic and phononic structures. These innovative moiré structures have opened new routes of exploration for classical wave physics, leading to intriguing phenomena and robust control of electromagnetic and mechanical waves. Drawing inspiration from the success of twisted bilayer graphene, this Perspective describes an overarching framework of the emerging moiré photonic and phononic structures that promise novel classical wave devices. We begin with the fundamentals of moiré superlattices, before highlighting recent studies that exploit twist angle and interlayer coupling as new ingredients with which to engineer and tailor the band structures and effective material properties of photonic and phononic structures. Finally, we discuss the future directions and prospects of this emerging area in materials science and wave physics.

Construction of Topological Bound States in the Continuum Via Subsymmetry

Topological bound states in the continuum (BICs) are localized topological boundary modes coexisting with a continuous spectrum of extended modes. They have been realized in systems with symmetry-protected topological phases, where their immunity to defects and perturbations depends on the presence of symmetries. Here we propose a method that transforms an in-gap topological boundary state into a BIC by using the concept of subsymmetry. We design the coupling between a system possessing in-gap topological modes and a system possessing a continuum of states that results in topological BICs. We define the criteria for the coupling that yields the desired results. To implement this scheme, we construct representative topological BICs based on one-dimensional Su-Schrieffer-Heeger models and implement them in photonic lattices. Our results not only reveal novel physical phenomena but may also provide methods for designing a new generation of topological devices.

Topological Network Modes in a Twisted Moiré Phononic Crystal

Twisted moiré materials, a new class of layered structures with different twist angles for neighboring layers, are attracting great attention because of the rich intriguing physical phenomena associated with them. Of particular interest are the topological network modes, first proposed in the small angle twisted bilayer graphene under interlayer bias. Here we report the observations of such topological network modes in twisted moiré phononic crystals without requiring the external bias fields. Acoustic topological network modes that can be constructed in a wide range of twist angles are both observed in the domain walls with and without reconstructions, which serve as the analogy of the lattice relaxations in electronic moiré materials. Topological robustness of the topological network modes is observed by introducing valley-preserved defects to the network channel. Furthermore, the network can be reconfigured into two-dimensional patterns with any desired connectivity, offering a unique prototype platform for acoustic applications.

Dynamic Acoustic Beamshaping with Coupling-Immune Moiré Metasurfaces

Moiré effects arising from mutually twisted metasurfaces have showcased remarkable wave manipulation capabilities, unveiling tantalizing emerging phenomena such as acoustic moiré flat bands and topological phase transitions. However, the pursuit of strong near-field coupling in layers has necessitated acoustic moiré metasurfaces to be tightly stacked at narrow distances in the subwavelength range. Here, moiré effects beyond near-field interlayer coupling in acoustics are reported and the concept of coupling-immune moiré metasurfaces is proposed. Remote acoustic moiré effects decoupled from the interlayer distance are theoretically, numerically, and experimentally demonstrated. Tunable out-of-plane acoustic beam scanning is successfully achieved by dynamically controlling twist angles. The engineered coupling-immune properties are further extended to multilayered acoustic moiré metasurfaces and manipulation of acoustic vortices. Good robustness against external disturbances is also observed for the fabricated coupling-immune acoustic moiré metasurfaces. The presented work unlocks the potential of twisted moiré devices for out-of-plane acoustic beam shaping, enabling practical applications in remote dynamic detection, and multiplexed underwater acoustic communication.

Ultra-narrowband and rainbow-free mid-infrared thermal emitters enabled by a flat band design in distorted photonic lattices

Most reported thermal emitters to date employing photonic nanostructures to achieve narrow bandwidth feature the rainbow effect due to the steep dispersion of the involved high-Q resonances. In this work, we propose to realize thermal emissions with high temporal coherence but free from rainbow effect, by harnessing a novel flat band design within a large range of wavevectors. This feature is achieved by introducing geometric perturbations into a square lattice of high-index disks to double the period along one direction. As a result of the first Brillouin zone halving, the guided modes will be folded to the Γ point and interact with originally existing guided-mode resonances to form a flat band of dispersion with overall high Q. Despite the use of evaporated amorphous materials, we experimentally demonstrate a thermal emission with the linewidth of 23 nm at 5.144 μm within a wide range of output angles (from -17.5° to 17.5°).

High-Q optical resonances with robustness based on the quasi-guided modes in waveguide moiré gratings

High-Q resonances, especially those with high spectral tunability and large robustness of the Q factors, are always sought in photonic research for enhanced light-matter interactions. In this work, by rotating the 1D ridge grating on a slab waveguide in both the clockwise and counterclockwise directions by a certain angle θ, we show that the original subwavelength lattice can be converted into waveguide moiré gratings (WMGs), with the period increased to a larger value determined by the value of θ. These period-increasing perturbations will cause the First Brillouin Zone (FBZ) of the 1D grating to shrink, and thus convert the non-radiating guided modes with the dispersion band below the light line into quasi-guided modes (QGMs) above the light line, which can be accessed by free space radiations. We present the numerically calculated dispersion band and the Q-values for the QGMs supported by the WMGs with θ = 60°, and demonstrate that high-Q resonances can be achieved in a wide region of the energy-momentum space with the Q-values exhibiting large robustness over wavevectors. As an example of application, we show that the QGMs in the WMGs can be exploited to produce quite high optical gradient forces at different wavenumbers or wavelengths. Our results show that the QGMs supported by the WMGs work as a new type of high-Q resonances and may find prospective applications in various photonic systems.

Non-Abelian Topological Bound States in the Continuum

Bound states in the continuum (BICs), which are spatially localized states with energies lying in the continuum of extended modes, have been widely investigated in both quantum and classical systems. Recently, the combination of topological band theory with BICs has led to the creation of topological BICs that exhibit extraordinary robustness against disorder. However, the previously proposed topological BICs are only limited in systems with Abelian gauge fields. Whether non-Abelian gauge fields can induce topological BICs and how to experimentally explore these phenomena remains unresolved. Here, we report the theoretical and experimental realization of non-Abelian topological BICs, which are generated by the interplay between two inseparable pseudospins and can coexist in each pseudospin subspace. This unique characteristic necessitates non-Abelian couplings that lack any Abelian counterparts. Furthermore, the non-Abelian couplings can also offer a new avenue for constructing topological subspace-induced BICs at bulk dislocations. Those exotic phenomena are observed by non-Abelian topolectrical circuits. Our results establish the connection between topological BICs and non-Abelian gauge fields, and serve as the catalyst for future investigations on non-Abelian topological BICs across different platforms.

Photonic Flatband Resonances in Multiple Light Scattering

We introduce the concept of photonic flatband resonances and demonstrate it for an array of high-index dielectric particles. We employ the multiple Mie scattering theory and demonstrate that both short- and long-range interactions between the resonators are crucial for the emerging collective resonances and their associated photonic flatbands. By examining both near- and far-field characteristics, we uncover how the flatbands emerge due to a fine tuning of resonators' radiation fields, and predict that hybridization of a flatband resonance with an electric hot spot can lead to giant values of the Purcell factor for the electric dipolar emitters.

Manipulating the Generation of Photonic Moiré Lattices Using Plasmonic Metasurfaces

The generation of moiré lattices by superimposing two identical sublattices at a specific twist angle has garnered significant attention owing to its potential applications, ranging from two-dimensional materials to manipulating light propagation. While macroscale moiré lattices have been widely studied, further developments in manipulating moiré lattices at the subwavelength scale would be crucial for miniaturizing and integrating platforms. Here, we propose a plasmonic metasurface design consisting of rotated nanoslits arranged within N + N' round apertures for generating focused moiré lattices. By introducing a spin-dependent geometric phase through the rotated nanoslits, an overall lens and spiral phase can be achieved, allowing each individual set of round apertures to generate a periodic lattice in the focal plane. Superimposing two sets of N and N' apertures at specific twist angles and varying phase differences allows for the superposition of two sublattices with different periods, leading to the formation of diverse moiré patterns. Our simulations and theoretical results demonstrate the feasibility of our proposed metasurface design. Due to their compactness and tunability, the utilization of metasurfaces in creating nanoscale photonic moiré lattices is anticipated to find extensive applications in integrated and on-chip optical systems.

Giant enhancement of second harmonic generation from monolayer 2D materials placed on photonic moiré superlattice

We numerically investigate second harmonic generation (SHG) from a monolayer of 2D-material placed on photonic moiré superlattice fabricated by dielectric materials. The greatly enhanced local field at the resonance modes of moiré superlattice can dramatically boost the SHG response in 2D materials. Considering a typical 2D-material MoS2 monolayer placed on a photonic moiré superlattice of a twist angle 9.43°, the maximum SHG conversion efficiency reaches up to 10-1 at a relatively low intensity of fundamental light 1 kW/cm2, which is around 14 orders of magnitude larger than that from the monolayer placed on a flat dielectric slab without moiré superlattices. The SHG conversion efficiency from the monolayer can be further enhanced with the decrease of the twist angles of moiré superlattice due to the even more confinement of local field. The flat bands in the moiré superlattices formed by the small twist angles can particularly ensure the efficiency even under wide-angle illuminations. The results indicate that photonic moiré superlattice which can tightly confine light is a promising platform for efficient nonlinear optics.

Twisted moiré photonic crystal enabled optical vortex generation through bound states in the continuum

The twisted stacking of two layered crystals has led to the emerging moiré physics as well as intriguing chiral phenomena such as chiral phonon and photon generation. In this work, we identified and theoretically formulated a non-trivial twist-enabled coupling mechanism in twisted bilayer photonic crystal (TBPC), which connects the bound state in the continuum (BIC) mode to the free space through the twist-enabled channel. Moreover, the radiation from TBPC hosts an optical vortex in the far field with both odd and even topological orders. We quantitatively analyzed the twist-enabled coupling between the BIC mode and other non-local modes in the photonic crystals, giving rise to radiation carrying orbital angular momentum. The optical vortex generation is robust against geometric disturbance, making TBPC a promising platform for well-defined vortex generation. As a result, TBPCs not only provide a new approach to manipulating the angular momentum of photons, but may also enable novel applications in integrated optical information processing and optical tweezers. Our work broadens the field of moiré photonics and paves the way toward the novel application of moiré physics.

Passive nonreciprocal transmission and optical bistability based on polarization-independent bound states in the continuum

Free-space nonreciprocal transmission is a crucial aspect of modern optics devices. The implementation of nonreciprocal optical devices through optical nonlinearity has been demonstrated. However, due to the weak nonlinearity of traditional materials, most self-biased nonreciprocal devices are heavily dependent on the high Q strong resonances. In general, these resonances are frequently polarization sensitive. In this work, we propose ultrathin optical metasurface embedding Kerr nonlinearities to achieve nonreciprocal transmission and optical bistability for free-space propagation based on symmetry-protected bound states in the continuum (BICs). Since the structure of the metasurface retains C4ν symmetry, the symmetry-protected BIC is polarization-independent. It is also shown that the nonreciprocal intensity range could be largely tuned by the structure parameters. The demonstrated devices merge the field of nonreciprocity with ultrathin metasurface technologies making this design an exciting prospect for an optical switch, routing, and isolator with optimal performance.

Experimental probe of twist angle-dependent band structure of on-chip optical bilayer photonic crystal

Recently, twisted bilayer photonic materials have been extensively used for creating and studying photonic tunability through interlayer couplings. While twisted bilayer photonic materials have been experimentally demonstrated in microwave regimes, a robust platform for experimentally measuring optical frequencies has been elusive. Here, we demonstrate the first on-chip optical twisted bilayer photonic crystal with twist angle-tunable dispersion and great simulation-experiment agreement. Our results reveal a highly tunable band structure of twisted bilayer photonic crystals due to moiré scattering. This work opens the door to realizing unconventional twisted bilayer properties and novel applications in optical frequency regimes.

Universal Mirror-Stacking Approach for Constructing Topological Bound States in the Continuum

Bound states in the continuum (BICs) are counterintuitive localized states with eigenvalues embedded in the continuum of extended states. Recently, nontrivial band topology is exploited to enrich the BIC physics, resulting in topological BICs (TBICs) with extraordinary robustness against perturbations or disorders. Here, we propose a simple but universal mirror-stacking approach to turn nontrivial bound states of any topological monolayer model into TBICs. Physically, the mirror-stacked bilayer Hamiltonian can be decoupled into two independent subspaces of opposite mirror parities, each of which directly inherits the energy spectrum information and band topology of the original monolayer. By tuning the interlayer couplings, the topological bound state of one subspace can move into and out of the continuum of the other subspace continuously without hybridization. As representative examples, we construct one-dimensional first-order and two-dimensional higher-order TBICs, and demonstrate them unambiguously by acoustic experiments. Our findings will expand the research implications of both topological materials and BICs.

Arbitrarily polarized bound states in the continuum with twisted photonic crystal slabs

Arbitrary polarized vortex beam induced by polarization singularity offers a new platform for both classical optics and quantum entanglement applications. Bound states in the continuum (BICs) have been demonstrated to be associated with topological charge and vortex polarization singularities in momentum space. For conventional symmetric photonic crystal slabs (PhCSs), BIC is enclosed by linearly polarized far fields with winding angle of 2π, which is unfavorable for high-capacity and multi-functionality integration-optics applications. Here, we show that by breaking σ_z-symmetry of the PhCS, asymmetry in upward and downward directions and arbitrarily polarized BIC can be realized with a bilayer-twisted PhCS. It exhibits elliptical polarization states with constant ellipticity angle at every point in momentum space within the vicinity of BIC. The topological nature of BIC reflects on the orientation angle of polarization state, with a topological charge of 1 for any value of ellipticity angle. Full coverage of Poincaré sphere (i.e., [Formula: see text] and [Formula: see text]) and higher-order Poincaré sphere can be realized by tailoring the twist angles. Our findings may open up new avenues for applications in structured light, quantum optics, and twistronics for photons.

Ultralow-level all-optical self-switching in a nanostructured moiré superlattice

We report an all-optical self-switching performed at an ultralow-level of intensity in a nanostructured moiré superlattice on a silicon platform. The moiré superlattice was formed by twisting two sets of triangular lattices in a silicon membrane in the same layer with a twist angle of 9.43°. The near flatband was formed, and the electric field was well confined in the center of the superlattice, which enabled all-optical switching under an ultralow intensity when the Kerr nonlinearity of silicon was considered. The intensity, which was reduced to 300 W/m² and even 20 W/m², can cause the transmittance of the nanostructure to change from 0 to 80% under x- and y-polarized pump light, respectively, and could be further decreased by optimizing the nanostructure or nonlinear materials. The results indicate that moiré superlattices fabricated from nonlinear materials are promising for integrated all-optical devices.

Magnetic moiré effects and two types of topological transition in a twisted-bilayer hyperbolic metasurface with double-split ring arrays

Moiré configurations have recently attracted much attention due to their ability to enhance photonic responses and manipulate surface waves in the subwavelength ranges. However, previous studies have usually been focused on natural hyperbolic materials with limitations on patterning procedures, controlling rotation angles, and merely manipulating electric surface plasmons. Here, we theoretically and numerically investigate a novel magnetic moiré hyperbolic metasurface in the terahertz region, which enables two types of topological transition and a plethora of unusual magnetic moiré effects (magnetic surface wave manipulation, dispersion engineering, magic angles, spacer-dependent topological transition, and local field enhancement). This work extends twistronics and moiré physics to the terahertz region and magnetic polaritons, with potential applications in quantum physics, energy transfer, and planarized magnetic plasmonic devices.