Localization and delocalization of light in photonic moiré lattices

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.

Experimental Demonstration of High-Efficiency Harmonic Generation in Photonic Moiré Superlattice Microcavities

Integrated photonic microcavities have demonstrated powerful enhancement of nonlinear effects, but they face a challenge in achieving critical coupling for sufficient use of incident pump power. In this work, we first experimentally demonstrate that highly efficient third-harmonic generation (THG) and detectable second-harmonic generation (SHG) can be produced from high-Q photonic moiré superlattice microcavities, where a critical coupling condition can be achieved via selecting a magic angle. Furthermore, at the magic angle of 13.17°, critical coupling is satisfied, resulting in a normalized THG conversion efficiency of 136%/W2 at a relatively low peak pump power of 6.8 MW/cm2, which is 3 orders of magnitude higher than the best results reported previously. Our work shows the power of photonic moiré superlattices in enhancing nonlinear optical performances through flexible and feasible engineering resonant modes, which can be applied in integrated frequency conversion and generation of quantum light sources.

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.

Twisted photonic Weyl meta-crystals and aperiodic Fermi arc scattering

As a milestone in the exploration of topological physics, Fermi arcs bridging Weyl points have been extensively studied. Weyl points, as are Fermi arcs, are believed to be only stable when preserving translation symmetry. However, no experimental observation of aperiodic Fermi arcs has been reported so far. Here, we continuously twist a bi-block Weyl meta-crystal and experimentally observe the twisted Fermi arc reconstruction. Although both the Weyl meta-crystals individually preserve translational symmetry, continuous twisting operation leads to the aperiodic hybridization and scattering of Fermi arcs on the interface, which is found to be determined by the singular total reflection around Weyl points. Our work unveils the aperiodic scattering of Fermi arcs and opens the door to continuously manipulating Fermi arcs.

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.

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.

Reconfigurable moiré nanolaser arrays with phase synchronization

Miniaturized lasers play a central role in the infrastructure of modern information society. The breakthrough in laser miniaturization beyond the wavelength scale has opened up new opportunities for a wide range of applications1-4, as well as for investigating light-matter interactions in extreme-optical-field localization and lasing-mode engineering5-19. An ultimate objective of microscale laser research is to develop reconfigurable coherent nanolaser arrays that can simultaneously enhance information capacity and functionality. However, the absence of a suitable physical mechanism for reconfiguring nanolaser cavities hinders the demonstration of nanolasers in either a single cavity or a fixed array. Here we propose and demonstrate moiré nanolaser arrays based on optical flatbands in twisted photonic graphene lattices, in which coherent nanolasing is realized from a single nanocavity to reconfigurable arrays of nanocavities. We observe synchronized nanolaser arrays exhibiting high spatial and spectral coherence, across a range of distinct patterns, including P, K and U shapes and the Chinese characters '' and '' ('China' in Chinese). Moreover, we obtain nanolaser arrays that emit with spatially varying relative phases, allowing us to manipulate emission directions. Our work lays the foundation for the development of reconfigurable active devices that have potential applications in communication, LiDAR (light detection and ranging), optical computing and imaging.

Multiple flatbands and localized states in photonic super-Kagome lattices

We demonstrate multiple flatbands and compact localized states (CLSs) in a photonic super-Kagome lattice (SKL) that exhibits coexistence of singular and nonsingular flatbands within its unique band structure. Specifically, we find that the upper two flatbands of an SKL are singular-characterized by singularities due to band touching with their neighboring dispersive bands at the Brillouin zone center. Conversely, the lower three degenerate flatbands are nonsingular and remain spectrally isolated from other dispersive bands. The existence of such two distinct types of flatbands is experimentally demonstrated by observing stable evolution of the CLSs with various geometrical shapes in a laser-written SKL. We also discuss the classification of the flatbands in momentum space, using band-touching singularities of the Bloch wave functions. Furthermore, we validate this classification in real space based on unit cell occupancy of the CLSs in a single SKL plaquette. These results may provide insights for the study of flatband transport, dynamics, and nontrivial topological phenomena in other relevant systems.

Critical Phase Dualities in 1D Exactly Solvable Quasiperiodic Models

We propose a solvable class of 1D quasiperiodic tight-binding models encompassing extended, localized, and critical phases, separated by nontrivial mobility edges. Limiting cases include the Aubry-André model and the models of Sriram Ganeshan, J. H. Pixley, and S. Das Sarma [Phys. Rev. Lett. 114, 146601 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.146601] and J. Biddle and S. Das Sarma [Phys. Rev. Lett. 104, 070601 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.070601]. The analytical treatment follows from recognizing these models as a novel type of fixed points of the renormalization group procedure recently proposed in Phys. Rev. B 108, L100201 (2023)10.1103/PhysRevB.108.L100201 for characterizing phases of quasiperiodic structures. Beyond known limits, the proposed class of models extends previously encountered localized-delocalized duality transformations to points within multifractal critical phases. Besides an experimental confirmation of multifractal duality, realizing the proposed class of models in optical lattices allows stabilizing multifractal critical phases and nontrivial mobility edges in an undriven system without the need for the unbounded potentials required by previous proposals.

Fabrications of twisted moiré photonic crystal and random moiré photonic crystal and their potential applications in light extraction

Twisted moiré photonic crystal is an optical analog of twisted graphene or twisted transition metal dichalcogenide bilayers. In this paper, we report the fabrication of twisted moiré photonic crystals and randomized moiré photonic crystals and their use in enhanced extraction of light in light-emitting diodes (LEDs). Fractional diffraction orders from randomized moiré photonic crystals are more uniform than those from moiré photonic crystals. Extraction efficiencies of 76.5%, 77.8% and 79.5% into glass substrate are predicted in simulations of LED patterned with twisted moiré photonic crystals, defect-containing photonic crystals and random moiré photonic crystals, respectively, at 584 nm. Extraction efficiencies of optically pumped LEDs with 2D perovskite (BA)2(MA)n-1PbnI3n+1ofn= 3 and (5-(2'-pyridyl)-tetrazolato)(3-CF3-5-(2'-pyridyl)pyrazolato) platinum(II) (PtD) have been measured.

Surface gap solitons in the Schrödinger equation with quintic nonlinearity and a lattice potential

We demonstrate the existence of surface gap solitons, a special type of asymmetric solitons, in the one-dimensional nonlinear Schrödinger equation with quintic nonlinearity and a periodic linear potential. The nonlinearity is suddenly switched in a step-like fashion in the middle of the transverse spatial region, while the periodic linear potential is chosen in the form of a simple sin 2 lattice. The asymmetric nonlinearities in this work can be realized by the Feshbach resonance in Bose-Einstein condensates or by the photorefractive effect in optics. The major peaks in the gap soliton families are asymmetric and they are located at the position of the jump in nonlinearity (at x = 0). In addition, the major peaks of the two-peak and multi-peak solitons at the position x = 0 are higher than those after that position, at x > 0. And such phenomena are more obvious when the value of chemical potential is large, or when the difference of nonlinearity values across the jump is big. Along the way, linear stability analysis of the surface gap solitons is performed and the stability domains are identified. It is found that in this model, the solitons in the first band gap are mostly stable (excepting narrow domains of instability at the edges of the gap), while those in the second band gap are mostly unstable (excepting extremely narrow domains of stability for fundamental solitons). These findings are also corroborated by direct numerical simulations.

Overcrowding induces fast colloidal solitons in a slowly rotating potential landscape

Collective particle transport across periodic energy landscapes is ubiquitously present in many condensed matter systems spanning from vortices in high-temperature superconductors, frictional atomic sliding, driven skyrmions to biological and active matter. Here we report the emergence of fast solitons propagating against a rotating optical landscape. These experimentally observed solitons are stable cluster waves that originate from a coordinated particle exchange process which occurs when the number of trapped microparticles exceeds the number of potential wells. The size and speed of individual solitons rapidly increase with the particle diameter as predicted by theory and confirmed by numerical simulations. We show that when several solitons coexist, an effective repulsive interaction can stabilize their propagation along the periodic potential. Our experiments demonstrate a generic mechanism for cluster-mediated transport with potential applications to condensed matter systems on different length scales.

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.

Vortex solitons in moiré optical lattices

We show that optical moiré lattices enable the existence of vortex solitons of different types in self-focusing Kerr media. We address the properties of such states both in lattices having commensurate and incommensurate geometries (i.e., constructed with Pythagorean and non-Pythagorean twist angles, respectively), in the different regimes that occur below and above the localization-delocalization transition. We find that the threshold power required for the formation of vortex solitons strongly depends on the twist angle and, also, that the families of solitons exhibit intervals where their power is a nearly linear function of the propagation constant and they exhibit a strong stability. Also, in the incommensurate phase above the localization-delocalization transition, we found stable embedded vortex solitons whose propagation constants belong to the linear spectral domain of the system.

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.

Loss Difference Induced Localization in a Non-Hermitian Honeycomb Photonic Lattice

Non-Hermitian systems with complex-valued energy spectra provide an extraordinary platform for manipulating unconventional dynamics of light. Here, we demonstrate the localization of light in an instantaneously reconfigurable non-Hermitian honeycomb photonic lattice that is established in a coherently prepared atomic system. One set of the sublattices is optically modulated to introduce the absorptive difference between neighboring lattice sites, where the Dirac points in reciprocal space are extended into dispersionless local flat bands, with two shared eigenstates: low-loss (high-loss) one with fields confined at sublattice B (A). When these local flat bands are broad enough due to larger loss difference, the incident beam with its tangential wave vector being at the K point in reciprocal space is effectively localized at sublattice B with weaker absorption, namely, the commonly seen power exchange between adjacent channels in photonic lattices is effectively prohibited. The current work unlocks a new capability from non-Hermitian two-dimensional photonic lattices and provides an alternative route for engineering tunable local flat bands in photonic structures.

Twisted lattice nanocavity with theoretical quality factor exceeding 200 billion

Simultaneous localization of light to extreme spatial and spectral scales is of high importance for testing fundamental physics and various applications. However, there is a longstanding trade-off between localizing a light field in space and in frequency. Here we discover a new class of twisted lattice nanocavities based on mode locking in momentum space. The twisted lattice nanocavity hosts a strongly localized light field in a 0.048 λ3 mode volume with a quality factor exceeding 2.9 × 1011 (∼250 μs photon lifetime), which presents a record high figure of merit of light localization among all reported optical cavities. Based on the discovery, we have demonstrated silicon-based twisted lattice nanocavities with quality factor over 1 million. Our result provides a powerful platform to study light-matter interaction in extreme conditions for tests of fundamental physics and applications in nanolasing, ultrasensing, nonlinear optics, optomechanics and quantum-optical devices.

Ab Initio Spin Hamiltonian and Topological Noncentrosymmetric Magnetism in Twisted Bilayer CrI3

Twist engineering of van der Waals magnets has emerged as an outstanding platform for manipulating exotic magnetic states. However, the complicated form of spin interactions in the large moiré superlattice obstructs a concrete understanding of such spin systems. To tackle this problem, for the first time, we developed a generic ab initio spin Hamiltonian for twisted bilayer magnets. Our atomistic model reveals that strong AB sublattice symmetry breaking due to the twist introduces a promising route to realize the novel noncentrosymmetric magnetism. Several unprecedented features and phases are uncovered including the peculiar domain structure and skyrmion phase induced by noncentrosymmetricity. The diagram of those distinctive magnetic phases has been constructed, and the detailed nature of their transitions analyzed. Further, we established the topological band theory of moiré magnons relevant to each of these phases. By respecting the full lattice structure, our theory provides the characteristic features that can be detected in experiments.

Holographic Fabrication of 3D Moiré Photonic Crystals Using Circularly Polarized Laser Beams and a Spatial Light Modulator

A moiré photonic crystal is an optical analog of twisted graphene. A 3D moiré photonic crystal is a new nano-/microstructure that is distinguished from bilayer twisted photonic crystals. Holographic fabrication of a 3D moiré photonic crystal is very difficult due to the coexistence of the bright and dark regions, where the exposure threshold is suitable for one region but not for the other. In this paper, we study the holographic fabrication of 3D moiré photonic crystals using an integrated system of a single reflective optical element (ROE) and a spatial light modulator (SLM) where nine beams (four inner beams + four outer beams + central beam) are overlapped. By modifying the phase and amplitude of the interfering beams, the interference patterns of 3D moiré photonic crystals are systemically simulated and compared with the holographic structures to gain a comprehensive understanding of SLM-based holographic fabrication. We report the holographic fabrication of phase and beam intensity ratio-dependent 3D moiré photonic crystals and their structural characterization. Superlattices modulated in the z-direction of 3D moiré photonic crystals have been discovered. This comprehensive study provides guidance for future pixel-by-pixel phase engineering in SLM for complex holographic structures.

Observation of bulk quadrupole in topological heat transport

The quantized bulk quadrupole moment has so far revealed a non-trivial boundary state with lower-dimensional topological edge states and in-gap zero-dimensional corner modes. In contrast to photonic implementations, state-of-the-art strategies for topological thermal metamaterials struggle to achieve such higher-order hierarchical features. This is due to the absence of quantized bulk quadrupole moments in thermal diffusion fundamentally prohibiting possible band topology expansions. Here, we report a recipe for generating quantized bulk quadrupole moments in fluid heat transport and observe the quadrupole topological phases in non-Hermitian thermal systems. Our experiments show that both the real- and imaginary-valued bands exhibit the hierarchical features of bulk, gapped edge and in-gap corner states-in stark contrast to the higher-order states observed only on real-valued bands in classical wave fields. Our findings open up unique possibilities for diffusive metamaterial engineering and establish a playground for multipolar topological physics.

Far-field coupling between moiré photonic lattices

Superposing two or more periodic structures to form moiré patterns is emerging as a promising platform to confine and manipulate light. However, moiré-facilitated interactions and phenomena have been constrained to the vicinity of moiré lattices. Here we report on the observation of ultralong-range coupling between photonic lattices in bilayer and multilayer moiré architectures mediated by dark surface lattice resonances in the vertical direction. We show that two-dimensional plasmonic nanoparticle lattices enable twist-angle-controlled directional lasing emission, even when the lattices are spatially separated by distances exceeding three orders of magnitude of lattice periodicity. Our discovery of far-field interlattice coupling opens the possibility of using the out-of-plane dimension for optical manipulation on the nanoscale and microscale.

Moiré Lattice in One-Dimensional Synthetic Frequency Dimension

The moiré lattice has recently attracted broad interest in both solid-state physics and photonics where exotic phenomena in manipulating the quantum states are explored. In this work, we study the one-dimensional (1D) analogs of "moiré" lattices in a synthetic frequency dimension constructed by coupling two resonantly modulated ring resonators with different lengths. Unique features associated with the flatband manipulation as well as the flexible control of localization position inside each unit cell in the frequency dimension have been found, which can be controlled via the choice of flatband. Our work therefore provides insight into simulating moiré physics in 1D synthetic frequency space, which holds important promise for potential applications toward optical information processing.

Triangular bright solitons in nonlinear optics and Bose-Einstein condensates

We demonstrate what we believe to be novel triangular bright solitons that can be supported by the nonlinear Schrödinger equation with inhomogeneous Kerr-like nonlinearity and external harmonic potential, which can be realized in nonlinear optics and Bose-Einstein condensates. The profiles of these solitons are quite different from the common Gaussian or sech envelope beams, as their tops and bottoms are similar to the triangle and inverted triangle functions, respectively. The self-defocusing nonlinearity gives rise to the triangle-up solitons, while the self-focusing nonlinearity supports the triangle-down solitons. Here, we restrict our attention only to the lowest-order fundamental triangular solitons. All such solitons are stable, which is demonstrated by the linear stability analysis and also clarified by direct numerical simulations. In addition, the modulated propagation of both types of triangular solitons, with the modulated parameter being the strength of nonlinearity, is also presented. We find that such propagation is strongly affected by the form of the modulation of the nonlinearity. For example, the sudden change of the modulated parameter causes instabilities in the solitons, whereas the gradual variation generates stable solitons. Also, a periodic variation of the parameter causes the regular oscillation of solitons, with the same period. Interestingly, the triangle-up and triangle-down solitons can change into each other, when the parameter changes the sign.

Atomic Bose-Einstein condensate in twisted-bilayer optical lattices

Observation of strong correlations and superconductivity in twisted-bilayer graphene^1-4 has stimulated tremendous interest in fundamental and applied physics^5-8. In this system, the superposition of two twisted honeycomb lattices, generating a moiré pattern, is the key to the observed flat electronic bands, slow electron velocity and large density of states^9-12. Extension of the twisted-bilayer system to new configurations is highly desired, which can provide exciting prospects to investigate twistronics beyond bilayer graphene. Here we demonstrate a quantum simulation of superfluid to Mott insulator transition in twisted-bilayer square lattices based on atomic Bose-Einstein condensates loaded into spin-dependent optical lattices. The lattices are made of two sets of laser beams that independently address atoms in different spin states, which form the synthetic dimension accommodating the two layers. The interlayer coupling is highly controllable by a microwave field, which enables the occurrence of a lowest flat band and new correlated phases in the strong coupling limit. We directly observe the spatial moiré pattern and the momentum diffraction, which confirm the presence of two forms of superfluid and a modified superfluid to insulator transition in twisted-bilayer lattices. Our scheme is generic and can be applied to different lattice geometries and for both boson and fermion systems. This opens up a new direction for exploring moiré physics in ultracold atoms with highly controllable optical lattices.

Observation of Linear and Nonlinear Light Localization at the Edges of Moiré Arrays

We observe linear and nonlinear light localization at the edges and in the corners of truncated moiré arrays created by the superposition of periodic mutually twisted at Pythagorean angles square sublattices. Experimentally exciting corner linear modes in the femtosecond-laser written moiré arrays we find drastic differences in their localization properties in comparison with the bulk excitations. We also address the impact of nonlinearity on the corner and bulk modes and experimentally observe the crossover from linear quasilocalized states to the surface solitons emerging at the higher input powers. Our results constitute the first experimental demonstration of localization phenomena induced by truncation of periodic moiré structures in photonic systems.

Terahertz Spin-Conjugate Symmetry Breaking for Nonreciprocal Chirality and One-Way Transmission Based on Magneto-Optical Moiré Metasurface

In this work, the gyrotropic semiconductor InSb into the twisted bilayer metasurface to form a magneto-optical moiré metasurface is introduced. Through the theoretical analysis, the "moiré angle" is developed in which case the nonreciprocity and chirality with the spin-conjugate asymmetric transmission are obtained due to the simultaneous breaking of both time-reversal symmetry and spatial mirror symmetry. The experiments confirm that the chirality can be actively manipulated by rotating the twisted angle and the external magnetic field, realizing spin-conjugate asymmetric transmission. Meanwhile, the two spin states also realize the nonreciprocal one-way transmission, and their isolation spectra are also spin-conjugate asymmetric: one is enhanced up to 48 dB, and the other's bandwidth is widened to over 730 GHz. This spin-conjugate symmetry-breaking effect in the MOMM brings a combination of time-space asymmetric transmission, and it also provides a new scheme for the implementation of high-performance THz chirality controllers and isolators.

Photonic flatband resonances for free-electron radiation

Flatbands have become a cornerstone of contemporary condensed-matter physics and photonics. In electronics, flatbands entail comparable energy bandwidth and Coulomb interaction, leading to correlated phenomena such as the fractional quantum Hall effect and recently those in magic-angle systems. In photonics, they enable properties including slow light1 and lasing2. Notably, flatbands support supercollimation-diffractionless wavepacket propagation-in both systems3,4. Despite these intense parallel efforts, flatbands have never been shown to affect the core interaction between free electrons and photons. Their interaction, pivotal for free-electron lasers5, microscopy and spectroscopy6,7, and particle accelerators8,9, is, in fact, limited by a dimensionality mismatch between localized electrons and extended photons. Here we reveal theoretically that photonic flatbands can overcome this mismatch and thus remarkably boost their interaction. We design flatband resonances in a silicon-on-insulator photonic crystal slab to control and enhance the associated free-electron radiation by tuning their trajectory and velocity. We observe signatures of flatband enhancement, recording a two-order increase from the conventional diffraction-enabled Smith-Purcell radiation. The enhancement enables polarization shaping of free-electron radiation and characterization of photonic bands through electron-beam measurements. Our results support the use of flatbands as test beds for strong light-electron interaction, particularly relevant for efficient and compact free-electron light sources and accelerators.

Bio-Inspired Nanomembranes as Building Blocks for Nanophotonics, Plasmonics and Metamaterials

Nanomembranes are the most widespread building block of life, as they encompass cell and organelle walls. Their synthetic counterparts can be described as freestanding or free-floating structures thinner than 100 nm, down to monatomic/monomolecular thickness and with giant lateral aspect ratios. The structural confinement to quasi-2D sheets causes a multitude of unexpected and often counterintuitive properties. This has resulted in synthetic nanomembranes transiting from a mere scientific curiosity to a position where novel applications are emerging at an ever-accelerating pace. Among wide fields where their use has proven itself most fruitful are nano-optics and nanophotonics. However, the authors are unaware of a review covering the nanomembrane use in these important fields. Here, we present an attempt to survey the state of the art of nanomembranes in nanophotonics, including photonic crystals, plasmonics, metasurfaces, and nanoantennas, with an accent on some advancements that appeared within the last few years. Unlimited by the Nature toolbox, we can utilize a practically infinite number of available materials and methods and reach numerous properties not met in biological membranes. Thus, nanomembranes in nano-optics can be described as real metastructures, exceeding the known materials and opening pathways to a wide variety of novel functionalities.

Light localization in defective periodic photonic moiré-like lattices

Photonic moiré-like lattices, a readily accessible platform for realizing the spatial localization of light, attract intensive attention due to their unique flatband characteristics. In this paper, a periodic moiré-like lattice with embedded defects is proposed theoretically, and the linear propagation of the probe beam in such a system is investigated intensively. The results show that the positions of defects in periodic moiré-like lattices depend on the sublattice rotation angle. Further studies show that the localization of light could be improved by adjusting the apodization function of defects. In addition, the experimental observation of the moiré-like lattice with apodized defects also confirms the theoretical analysis. Our study enriches the physical connotation of photonic moiré lattices and guides the design of novel photonic crystal fibers.

Atomic-Scale Confinement and Negative Refraction of Plasmons by Twisted Bilayer Graphene

Moiré superlattices provide in-plane quantum restriction for light-matter interactions in twisted bilayer graphene (tBLG), leading to the exotic photon-Moiré physics and potential applications for light manipulation. Recently, our experiment identified a highly confined slow surface plasmons polaritons (SPPs) mode in tBLG. Here, we demonstrate that the propagation of the slow SPPs mode in tBLG is spatially tailored and steered at deep subwavelengths. Analysis by the perturbation theory indicates that the coupling between the slow SPPs mode and the Moiré system is greatly strengthened, which regulates the wavefront at the atomic scale and makes tBLG serve as a universal optical metamaterial. Consequently, the negative refraction is achieved at the interface of monolayer graphene and tBLG, by which a metalens with a controllable focal length and an extremely high resolution up to 1/150 of wavelength is devised. Our work paves the way for constructing optical metamaterial at the atomic scale and develops future photon-Moiré interaction systems.

Two-dimensional Thouless pumping of light in photonic moiré lattices

Continuous and quantized transports are profoundly different. The latter is determined by the global rather than local properties of a system, it exhibits unique topological features, and its ubiquitous nature causes its occurrence in many areas of science. Here we report the first observation of fully-two-dimensional Thouless pumping of light by bulk modes in a purpose-designed tilted moiré lattices imprinted in a photorefractive crystal. Pumping in such unconfined system occurs due to the longitudinal adiabatic and periodic modulation of the refractive index. The topological nature of this phenomenon manifests itself in the magnitude and direction of shift of the beam center-of-mass averaged over one pumping cycle. Our experimental results are supported by systematic numerical simulations in the frames of the continuous Schrödinger equation governing propagation of probe light beam in optically-induced photorefractive moiré lattice. Our system affords a powerful platform for the exploration of topological pumping in tunable commensurate and incommensurate geometries.

Extending the control over topological system will open the doors to both fundamental studies and applications. Here the authors demonstrate thouless topological transport of light in a bulk tunable moiré lattice.

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.

Strong interlayer coupling and stable topological flat bands in twisted bilayer photonic Moiré superlattices

The moiré superlattice of misaligned atomic bilayers paves the way for designing a new class of materials with wide tunability. In this work, we propose a photonic analog of the moiré superlattice based on dielectric resonator quasi-atoms. In sharp contrast to van der Waals materials with weak interlayer coupling, we realize the strong coupling regime in a moiré superlattice, characterized by cascades of robust flat bands at large twist-angles. Surprisingly, we find that these flat bands are characterized by a non-trivial band topology, the origin of which is the moiré pattern of the resonator arrangement. The physical manifestation of the flat band topology is a robust one-dimensional conducting channel on edge, protected by the reflection symmetry of the moiré superlattice. By explicitly breaking the underlying reflection symmetry on the boundary terminations, we show that the first-order topological edge modes naturally deform into higher-order topological corner modes. Our work pioneers the physics of topological phases in the designable platform of photonic moiré superlattices beyond the weakly coupled regime.

Dual-path inscription of plasmonic nano-Ag moiré fringes

Construction of moiré surface patterns has attracted considerable attention due to the fascinating function of photoelectric manipulation. Holographic inscription offers superposition of two or more sinusoidal gratings to form moiré structures. However, the current material platforms primarily depend on a single process of photoinduced physical property change to build up multicomponent gratings. Herein, we demonstrate a strategy of bidirectional photochemical reaction on mesoporous TiO₂ matrices to form plasmonic nano-Ag moiré fringes. This consists of a photoreduction grating from in situ growth of Ag nanoparticles (NPs) and a photooxidation grating utilizing the Schottky interface of Ag/TiO₂. The pattern obtained under the superposition of double spatial frequencies exhibits non-equidistant moiré fringes. This Letter provides a pathway for implementing complex surface structures.

Scalable and CMOS compatible silicon photonic physical unclonable functions for supply chain assurance

We demonstrate the uniqueness, unclonability and secure authentication of N = 56 physical unclonable functions (PUFs) realized from silicon photonic moiré quasicrystal interferometers. Compared to prior photonic-PUF demonstrations typically limited in scale to only a handful of unique devices and on the order of 10 false authentication attempts, this work examines > 10³ inter-device comparisons and false authentication attempts. Device fabrication is divided across two separate fabrication facilities, allowing for cross-fab analysis and emulation of a malicious foundry with exact knowledge of the PUF photonic circuit design and process. Our analysis also compares cross-correlation based authentication to the traditional Hamming distance method and experimentally demonstrates an authentication error rate AER = 0%, false authentication rate FAR = 0%, and an estimated probability of cloning below 10⁻³⁰. This work validates the potential scalability of integrated photonic-PUFs which can attractively leverage mature wafer-scale manufacturing and automated contact-free optical probing. Such structures show promise for authenticating hardware in the untrusted supply chain or augmenting conventional electronic-PUFs to enhance system security.

Light bullets in moiré lattices

We predict that photonic moiré lattices produced by two mutually twisted periodic sublattices in a medium with Kerr nonlinearity can support stable three-dimensional (3D) light bullets localized in both space and time. The stability of light bullets and their properties are closely connected with the properties of linear spatial eigenmodes of moiré lattices that undergo localization-delocalization transition (LDT) upon the increase of the depth of one of the sublattices forming the moiré lattice, but only for twist angles corresponding to incommensurate, aperiodic moiré structures. Above the LDT threshold, such incommensurate moiré lattices support stable light bullets without an energy threshold. In contrast, commensurate-or periodic-moiré lattices arising at Pythagorean twist angles, whose eigenmodes are delocalized Bloch waves, can support stable light bullets only above a certain energy threshold. Moiré lattices below the LDT threshold cannot support stable light bullets for our parameters. Our results illustrate that the periodicity/aperiodicity of the underlying lattice is a crucial factor in determining the stability properties of the nonlinear 3D states.

Periodic evolution of the out-of-phase dipole and the single-charged vortex solitons in periodic photonic moiré lattice with saturable self-focusing nonlinearity media

We survey the propagation properties of the out-of-phase (OOP) dipole solitons and the single-charged vortex (SCV) soliton in a periodic photonic moiré lattice with θ=arctan⁡(3/4) under self-focusing nonlinearity media. Since the rotation angle, periodic photonic moiré lattices have peculiar energy band structures, with highly flat bands and the bandgaps being much more extensive, which is very favorable for the realization and stability of the solitons. When exciting a single point on-site with the OOP dipole beam, its evolution shows a periodic rollover around the lattice axis. Whereas, when exciting a single point on-site with the SCV beam, it transmits counterclockwise rotating periodically. Both the OOP dipole solitons and the SVC soliton maintain the local state, but their phase exhibits different variations. The phase of the OOP dipole solitons is flipped, while that of the SCV is rotated counterclockwise. Our work further complements the exploration of solitons in photonic moiré lattice with nonlinearity.

Bound vortex light in an emulated topological defect in photonic lattices

Topology have prevailed in a variety of branches of physics. And topological defects in cosmology are speculated akin to dislocation or disclination in solids or liquid crystals. With the development of classical and quantum simulation, such speculative topological defects are well-emulated in a variety of condensed matter systems. Especially, the underlying theoretical foundations can be extensively applied to realize novel optical applications. Here, with the aid of transformation optics, we experimentally demonstrated bound vortex light on optical chips by simulating gauge fields of topological linear defects in cosmology through position-dependent coupling coefficients in a deformed photonic graphene. Furthermore, these types of photonic lattices inspired by topological linear defects can simultaneously generate and transport optical vortices, and even can control the orbital angular momentum of photons on integrated optical chips.

Inhibition and Reconstruction of Zener Tunneling in Photonic Honeycomb Lattices

Quantum coherence is the central element of particle states, and it characterizes the overall performance of various quantum materials. Bloch oscillation is a fundamental coherent behavior of particles under a static potential, which can be easily destroyed by Zener tunneling in multiband 2D lattice materials. The control of Zener tunneling therefore plays the key role in quantum engineering for complicated physical systems. Here, the inhibition and reconstruction of Zener tunneling in photonic honeycomb lattices are experimentally demonstrated.  Deformed honeycomb lattices are integrated and an effective static potential is realized on the 2D lattice materials. Zener tunneling disappears in stretch-type lattices and wave packets stay in the dispersionless upper energy band. On the contrary, Zener tunneling is greatly enhanced in compression-type lattices and wave packets exhibit directional oscillations without branches, which manifest the preserved coherence of the wave packets. The results demonstrate the protection of photonic coherence by structurally controlling the Zener tunneling, representing a step toward flexible quantum engineering for large-scale artificial quantum materials.

Photonic Moiré lattice waveguide with a large slow light bandwidth and delay-bandwidth product

We proposed an effective approach to enlarge the slow light bandwidth and normalized-delay-bandwidth product in an optimized moiré lattice-based photonic crystal waveguide that exhibits intrinsic mid-band characteristics. A flatband corresponding to a nearly constant group index of 34 over a wide bandwidth of 82 nm centered at 1550 nm with near-zero group velocity dispersion was achieved. A large normalized-delay-bandwidth product of 0.5712 with a relative dispersion of 0.114%/µm was obtained, which is a significant improvement if compared with previous results. Our results indicate that the photonic moiré lattice waveguide could advance slow light applications.

Moiré Quasibound States in the Continuum

The novel physics of twisted bilayer graphene has motivated extensive studies of magic-angle flat bands hosted by moiré structures in electronic, photonic, and acoustic systems. On the other hand, bound states in the continuum (BICs) have also attracted great attention in recent years because of their potential applications in the field of designing superior optical devices. Here, we combine these two independent concepts to construct a new optical state in a twisted bilayer photonic crystal slab, which is called as moiré quasi-BIC, and numerically demonstrate that such an exotic optical state possesses dual characteristics of moiré flat bands and quasi-BICs. To illustrate the mechanism for the formation of moiré flat bands, we develop an effective model at the center of the Brillouin zone and show that moiré flat bands could be fulfilled by balancing the interlayer coupling strength and the twist angle around the band edge above the light line. Moreover, by decreasing the twist angle of moiré photonic crystal slabs with flat bands, it is shown that the moiré flat-band mode at the Brillouin center gradually approaches a perfect BIC, where the total radiation loss from all diffraction channels is significantly suppressed. To clarify the advantage of moiré quasi-BICs, enhanced second-harmonic generation (SHG) is numerically proven with a wide-angle optical source. The efficiency of SHG assisted by designed moiré quasi-BICs can be greatly improved compared with that based on dispersive quasi-BICs with similar quality factors.

Observation of Anderson localization beyond the spectrum of the disorder

Anderson localization predicts that transport in one-dimensional uncorrelated disordered systems comes to a complete halt, experiencing no transport whatsoever. However, in reality, a disordered physical system is always correlated because it must have a finite spectrum. Common wisdom in the field states that localization is dominant only for wave packets whose spectral extent resides within the region of the wave number span of the disorder. Here, we show experimentally that Anderson localization can occur and even be dominant for wave packets residing entirely outside the spectral extent of the disorder. We study the evolution of wave packets in synthetic photonic lattices containing bandwidth-limited (correlated) disorder and observe strong localization for wave packets centered at twice the mean wave number of the disorder spectral extent and at low wave numbers, both far beyond the spectrum of the disorder. Our results shed light on fundamental aspects of disordered systems and offer avenues for using spectrally shaped disorder for controlling transport.

Nonreciprocal Single-Photon Band Structure

We study a single-photon band structure in a one-dimensional coupled-resonator optical waveguide that chirally couples to an array of two-level quantum emitters (QEs). The chiral interaction between the resonator mode and the QE can break the time-reversal symmetry without the magneto-optical effect and an external or synthetic magnetic field. As a result, nonreciprocal single-photon edge states, band gaps, and flat bands appear. By using such a chiral QE coupled-resonator optical waveguide system, including a finite number of unit cells and working in the nonreciprocal band gap, we achieve frequency-multiplexed single-photon circulators with high fidelity and low insertion loss. The chiral QE-light interaction can also protect one-way propagation of single photons against backscattering. Our work opens a new door for studying unconventional photonic band structures without electronic counterparts in condensed matter and exploring its applications in the quantum regime.

Flatband mode in photonic moiré superlattice for boosting second-harmonic generation with monolayer van der Waals crystals

We theoretically investigate boosting second-harmonic generation (SHG) of monolayer van der Waals crystals by employing flatband modes hosted by photonic moiré superlattices. Such a system with high quality factor and a monolayer crystal accommodated on the top of it, provides a unique opportunity to enhance and manipulate SHG emission. We show that employing a doubly resonant diagram on such a moiré superlattice system not only boosts the SHG, but also tunes the directional emission of the second-harmonic wave. Moreover, we demonstrate that a structured beam illumination could further boost SHG, with the phase structure retrieved through a two-beam second-harmonic interference configuration. These results suggest the flatband modes in moiré superlattice as a promising platform for boosting SHG with monolayer van der Waals crystals, offering new possibilities for developing compact nonlinear photonic devices.

Moiré-Driven Topological Transitions and Extreme Anisotropy in Elastic Metasurfaces

The twist angle between a pair of stacked 2D materials has been recently shown to control remarkable phenomena, including the emergence of flat-band superconductivity in twisted graphene bilayers, of higher-order topological phases in twisted moiré superlattices, and of topological polaritons in twisted hyperbolic metasurfaces. These discoveries, at the foundations of the emergent field of twistronics, have so far been mostly limited to explorations in atomically thin condensed matter and photonic systems, with limitations on the degree of control over geometry and twist angle, and inherent challenges in the fabrication of carefully engineered stacked multilayers. Here, this work extends twistronics to widely reconfigurable macroscopic elastic metasurfaces consisting of LEGO pillar resonators. This work demonstrates highly tailored anisotropy over a single-layer metasurface driven by variations in the twist angle between a pair of interleaved spatially modulated pillar lattices. The resulting quasi-periodic moiré patterns support topological transitions in the isofrequency contours, leading to strong tunability of highly directional waves. The findings illustrate how the rich phenomena enabled by twistronics and moiré physics can be translated over a single-layer metasurface platform, introducing a practical route toward the observation of extreme phenomena in a variety of wave systems, potentially applicable to both quantum and classical settings without multilayered fabrication requirements.

Enhanced light-matter interaction in two-dimensional transition metal dichalcogenides

Two-dimensional (2D) transition metal dichalcogenide (TMDC) materials, such as MoS₂, WS₂, MoSe₂, and WSe₂, have received extensive attention in the past decade due to their extraordinary electronic, optical and thermal properties. They evolve from indirect bandgap semiconductors to direct bandgap semiconductors while their layer number is reduced from a few layers to a monolayer limit. Consequently, there is strong photoluminescence in a monolayer (1L) TMDC due to the large quantum yield. Moreover, such monolayer semiconductors have two other exciting properties: large binding energy of excitons and valley polarization. These properties make them become ideal materials for various electronic, photonic and optoelectronic devices. However, their performance is limited by the relatively weak light-matter interactions due to their atomically thin form factor. Resonant nanophotonic structures provide a viable way to address this issue and enhance light-matter interactions in 2D TMDCs. Here, we provide an overview of this research area, showcasing relevant applications, including exotic light emission, absorption and scattering features. We start by overviewing the concept of excitons in 1L-TMDC and the fundamental theory of cavity-enhanced emission, followed by a discussion on the recent progress of enhanced light emission, strong coupling and valleytronics. The atomically thin nature of 1L-TMDC enables a broad range of ways to tune its electric and optical properties. Thus, we continue by reviewing advances in TMDC-based tunable photonic devices. Next, we survey the recent progress in enhanced light absorption over narrow and broad bandwidths using 1L or few-layer TMDCs, and their applications for photovoltaics and photodetectors. We also review recent efforts of engineering light scattering, e.g., inducing Fano resonances, wavefront engineering in 1L or few-layer TMDCs by either integrating resonant structures, such as plasmonic/Mie resonant metasurfaces, or directly patterning monolayer/few layers TMDCs. We then overview the intriguing physical properties of different van der Waals heterostructures, and their applications in optoelectronic and photonic devices. Finally, we draw our opinion on potential opportunities and challenges in this rapidly developing field of research.