Observation of Photonic Topological Valley Hall Edge States

Observation of nonlinear fractal higher order topological insulator

Higher-order topological insulators (HOTIs) are unique materials hosting topologically protected states, whose dimensionality is at least by 2 lower than that of the bulk. Topological states in such insulators may be strongly confined in their corners which leads to considerable enhancement of nonlinear processes involving such states. However, all nonlinear HOTIs demonstrated so far were built on periodic bulk lattice materials. Here, we demonstrate the first nonlinear photonic HOTI with the fractal origin. Despite their fractional effective dimensionality, the HOTIs constructed here on two different types of the Sierpiński gasket waveguide arrays, may support topological corner states for unexpectedly wide range of coupling strengths, even in parameter regions where conventional HOTIs become trivial. We demonstrate thresholdless spatial solitons bifurcating from corner states in nonlinear fractal HOTIs and show that their localization can be efficiently controlled by the input beam power. We observe sharp differences in nonlinear light localization on outer and multiple inner corners and edges representative for these fractal materials. Our findings not only represent a new paradigm for nonlinear topological insulators, but also open new avenues for potential applications of fractal materials to control the light flow.

Broadband and fabrication-tolerant 3-dB couplers with topological valley edge modes

3-dB couplers, which are commonly used in photonic integrated circuits for on-chip information processing, precision measurement, and quantum computing, face challenges in achieving robust performance due to their limited 3-dB bandwidths and sensitivity to fabrication errors. To address this, we introduce topological physics to nanophotonics, developing a framework for topological 3-dB couplers. These couplers exhibit broad working wavelength range and robustness against fabrication dimensional errors. By leveraging valley-Hall topology and mirror symmetry, the photonic-crystal-slab couplers achieve ideal 3-dB splitting characterized by a wavelength-insensitive scattering matrix. Tolerance analysis confirms the superiority on broad bandwidth of 48 nm and robust splitting against dimensional errors of 20 nm. We further propose a topological interferometer for on-chip distance measurement, which also exhibits robustness against dimensional errors. This extension of topological principles to the fields of interferometers, may open up new possibilities for constructing robust wavelength division multiplexing, temperature-drift-insensitive sensing, and optical coherence tomography applications.

Topologically Protected Quantum Logic Gates with Valley-Hall Photonic Crystals

Topological photonics provide a promising way to realize more robust optical devices against some defects and environmental perturbations. Quantum logic gates are fundamental units of quantum computers, which are widely used in future quantum information processing. Thus, constructing robust universal quantum logic gates is an important way forward to practical quantum computing. However, the most important problem to be solved is how to construct the quantum-logic-gate-required 2 × 2 beam splitter with topological protection. Here, the experimental realization of the topologically protected contradirectional coupler is reported, which can be employed to realize the quantum logic gates, including control-NOT and Hadamard gates, on the silicon photonic platform. These quantum gates not only have high experimental fidelities but also exhibit a certain degree of tolerances against certain types of defects. This work paves the way for the development of practical optical quantum computations and signal processing.

Magnetically controllable multimode interference in topological photonic crystals

Topological photonic insulators show promise for applications in compact integrated photonic circuits due to their ability to transport light robustly through sharp bendings. The number of topological edge states relies on the difference between the bulk Chern numbers across the boundary, as dictated by the bulk edge correspondence. The interference among multiple topological edge modes in topological photonics systems may allow for controllable functionalities that are particularly desirable for constructing reconfigurable photonic devices. In this work, we demonstrate magnetically controllable multimode interference based on gyromagnetic topological photonic insulators that support two unidirectional edge modes with different dispersions. We successfully achieve controllable power splitting in experiments by engineering multimode interference with the magnetic field intensity or the frequency of wave. Our work demonstrates that manipulating the interference among multiple chiral edge modes can facilitate the advancement of highly efficient and adaptable microwave devices.

Information-entropy enabled identifying topological photonic phase in real space

The topological photonics plays an important role in the fields of fundamental physics and photonic devices. The traditional method of designing topological system is based on the momentum space, which is not a direct and convenient way to grasp the topological properties, especially for the perturbative structures or coupled systems. Here, we propose an interdisciplinary approach to study the topological systems in real space through combining the information entropy and topological photonics. As a proof of concept, the Kagome model has been analyzed with information entropy. We reveal that the bandgap closing does not correspond to the topological edge state disappearing. This method can be used to identify the topological phase conveniently and directly, even the systems with perturbations or couplings. As a promotional validation, Su-Schrieffer-Heeger model and the valley-Hall photonic crystal have also been studied based on the information entropy method. This work provides a method to study topological photonic phase based on information theory, and brings inspiration to analyze the physical properties by taking advantage of interdisciplinarity.

Topological protection of dual-polarization biphoton states in photonic crystals

Polarization control is a major issue in topological quantum optics that limits reliable generation and transmission of quantum states. This study presents what we believe to be a novel topological photonic crystal design that provides topological protection for biphoton pairs for both TE and TM polarization. By well-designed cell configurations within the lattice, two topological boundaries emerge that can accommodate TM and TE modes at the same time. By adjusting the dispersion curves, we can further design nonlinear four-wave mixing processes within the topological photonic crystals and provide theoretical explanations for the entanglement of the dual-polarization biphoton states. Numerical results confirm the robust transport of entangled photon pairs, even when subjected to sharp bending. Moreover, combining the dual-polarization topological photonic crystal with a polarization beam splitter enables the preparation of polarization-encoded maximally entangled states. Our work exhibits significant potential for applications in robust optical quantum information processing and quantum secure communication.

Impact of Transforming Interface Geometry on Edge States in Valley Photonic Crystals

We investigate how altering the interface geometry from a zigzag to a glide plane interface between two topologically distinct valley Hall emulating photonic crystals (VPC), profoundly affects edge states. We experimentally observe a transition from gapless to gapped edge states, accompanied by the occurrence of slow light within the Brillouin zone, rather than at its edge. We numerically simulate the propagation and measure the transmittance of the modified edge states through a specially designed valley-conserving defect. The robustness to backscattering gradually decreases, suggesting a disruption of valley-dependent transport. We demonstrate the significance of interface geometry to gapless edge states in a VPC.

Edge State, Band Topology, and Time Boundary Effect in the Fine-Grained Categorization of Chern Insulators

We predict novel topological phases with broken time-reversal symmetry supporting the coexistence of opposite chiral edge states, which are fundamentally different from the photonic spin-Hall, valley-Hall, and higher-order topological phases. We find a fine-grained categorization of Chern insulators, their band topologies characterized by identical Chern numbers are completely different. Furthermore, we prove that different topologies cause zeros in their Bloch wave function overlaps, which imprint the band gap closing and appear at the degenerate points of topological phase transition. The Bloch wave function overlaps predict the reflection and refraction at a topological time boundary, and the overlap zeros ensure the existence of vanishing revival amplitude at critical times even though different topologies before and after the time boundary have identical Chern numbers. Our findings create new opportunities for topological metamaterials, uncover the topological feature hidden in the time boundary effect as a probe of topology, and open a venue for the exploration of the rich physics originating from the long-range couplings.

Hyperbolic photonic topological insulators

Topological photonics provides a new degree of freedom to robustly control electromagnetic fields. To date, most of established topological states in photonics have been employed in Euclidean space. Motivated by unique properties of hyperbolic lattices, which are regular tessellations in non-Euclidean space with a constant negative curvature, the boundary-dominated hyperbolic topological states have been proposed. However, limited by highly crowded boundary resonators and complicated site couplings, the hyperbolic topological insulator has only been experimentally constructed in electric circuits. How to achieve hyperbolic photonic topological insulators is still an open question. Here, we report the experimental realization of hyperbolic photonic topological insulators using coupled ring resonators on silicon chips. Boundary-dominated one-way edge states with pseudospin-dependent propagation directions have been observed. Furthermore, the robustness of edge states in hyperbolic photonic topological insulators is also verified. Our findings have potential applications in the field of designing high-efficient topological photonic devices with enhanced boundary responses.

Observation of Period-Doubling Bloch Oscillations

Bloch oscillations refer to the periodic oscillation of a wave packet in a lattice under a constant force. Typically, the oscillation has a fundamental period that corresponds to the wave packet traversing the first Brillouin zone once. Here, we demonstrate, both theoretically and experimentally, the optical Bloch oscillations where the wave packet must traverse the first Brillouin zone twice to complete a full cycle, resulting in a period of oscillation that is 2 times longer than that of usual Bloch oscillations. The unusual Bloch oscillations arise due to the band crossing of valley-Hall topological edge states at the Brillouin boundary for zigzag domain walls between two staggered honeycomb lattices with inverted on-site energy detuning, which are protected by the glide-reflection symmetry of the underlying structures. Our work sheds light on the direct detection of band crossings resulting from intrinsic symmetries that extend beyond the fundamental translational symmetry in topological systems.

Switching via wave interaction in topological photonic lattices

A honeycomb Floquet lattice with helically rotating waveguides and an interface separating two counter-propagating subdomains is analyzed. Two topologically protected localized waves propagate unidirectionally along the interface. Switching can occur when these interface modes reach the edge of the lattice and the light splits into waves traveling in two opposite directions. The incoming mode, traveling along the interface, can be adjusted and routed entirely or partially along either lattice edge with the switching direction based on a suitable mixing of the interface modes.

Large transmittance contrast via 90-degree sharp bends in square lattice glide-symmetric photonic crystal waveguides

We demonstrate an intriguing transmittance contrast in a glide-symmetric square-lattice photonic crystal waveguide with a 90-degree sharp bend. The glide-symmetry gives rise to a degeneracy point in the band structure and separates a high-frequency and a low-frequency band. Previously, a similar large transmittance contrast between these two bands has been observed in glide-symmetric triangular- or honeycomb-lattice photonic crystals without inversion symmetry, and this phenomenon has been attributed to the valley-photonic effect. In this study, we demonstrate the first example of this phenomenon in square-lattice photonic crystals, which do not possess the valley effect. Our result sheds new light onto unexplored properties of glide-symmetric waveguides. We show that this phenomenon is related to the spatial distribution of circular polarization singularities in glide-symmetric waveguides. This work expands the possible designs of low-loss photonic circuits and provides a new understanding of light transmission via sharp bends in photonic crystal waveguides.

Observation of π solitons in oscillating waveguide arrays

Floquet systems with periodically varying in time parameters enable realization of unconventional topological phases that do not exist in static systems with constant parameters and that are frequently accompanied by appearance of novel types of the topological states. Among such Floquet systems are the Su-Schrieffer-Heeger lattices with periodically-modulated couplings that can support at their edges anomalous π modes of topological origin despite the fact that the lattice spends only half of the evolution period in topologically nontrivial phase, while during other half-period it is topologically trivial. Here, using Su-Schrieffer-Heeger arrays composed from periodically oscillating waveguides inscribed in transparent nonlinear optical medium, we report experimental observation of photonic anomalous π modes residing at the edge or in the corner of the one- or two-dimensional arrays, respectively, and demonstrate a new class of topological π solitons bifurcating from such modes in the topological gap of the Floquet spectrum at high powers. π solitons reported here are strongly oscillating nonlinear Floquet states exactly reproducing their profiles after each longitudinal period of the structure. They can be dynamically stable in both one- and two-dimensional oscillating waveguide arrays, the latter ones representing the first realization of the Floquet photonic higher-order topological insulator, while localization properties of such π solitons are determined by their power.

Topological transport in heterostructure of valley photonic crystals

We propose a heterogeneous structure, which are composed of two valley photonic crystals (VPCs) with opposite valley Chern numbers and air channel. With the increasing width of the air channel, valley-locked waveguide modes are found in topological bandgap by analyzing energy bands. Finite element method (FEM) simulation results show that the fundamental and high order modes are valley-locked, propagating unidirectionally under the excitation of chiral source, and possess higher flux compared to the valley-locked topological edge state in the domain wall. Besides, the immunity to backscattering in bend and couplers, and the robustness to random disorders are discussed in detail. We also investigate the one-way multimode interference (MMI) effect based on valley-locked waveguide modes, and design topological beam splitters. Our study provides a novel idea for topological transport with high flux, and more freedom to design valley-locked waveguide devices, including bends, couplers and splitters.

Coexistence of large-area topological pseudospin and valley states in a tri-band heterostructure system

The rapid development of topological photonics has significantly revolutionized our comprehension of electromagnetic wave manipulation in recent decades. Recent research exploiting large-area topological states inserts an additional gapless PC structure between topologically trivial and nontrivial PCs, effectively introducing the mode width degree of freedom. Nevertheless, these heterostructures mainly support only single-type waveguide states operating within a single frequency band. To address these limitations, we propose a novel, to the best of our knowledge, tri-band three-layer heterostructure system, supporting both large-area pseudospin- and valley-locked states. The system showcases tunable mode widths with different operational bandwidths. Moreover, the heterostructures exhibit inherent topological characteristics and reflection-free interfacing, which are verified in the well-designed Z-shaped channels. The proposed heterostructure system can be used to design multi-band multi-functional high-flexibility topological devices, providing great advantages for enlarging the on-chip integrated communication systems.

Observation of nonlinear disclination states

Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at disclinations. Appearance of these topological states is consistent with the bulk-disclination correspondence principle, and is due to the filling anomaly that results in fractional charges to the boundary unit cells. So far, topological disclination states were observed only in the linear regime, while the interplay between nonlinearity and topology in the systems with disclinations has been never studied experimentally. We report here on the experimental observation of the nonlinear photonic disclination states in waveguide arrays with pentagonal or heptagonal disclination cores inscribed in transparent optical medium using the fs-laser writing technique. The transition between nontopological and topological phases in such structures is controlled by the Kekulé distortion coefficient r with topological phase hosting simultaneously disclination states at the inner disclination core and spatially separated from them corner-I, corner-II, and extended edge states at the outer edge of the structure. We show that the robust nonlinear disclination states bifurcate from their linear counterparts and that location of their propagation constants in the gap and, hence, their spatial localization can be controlled by their power. Nonlinear disclination states can be efficiently excited by Gaussian input beams, but only if they are focused into the waveguides belonging to the disclination core, where such topological states reside. Our results open new prospects for investigation of nonlinear effects in topological systems with disclinations and are relevant for different areas of science, including Bose-Einstein and polariton condensates, where potentials with the disclinations can be created.

Hybrid topological photonic crystals

Topologically protected photonic edge states offer unprecedented robust propagation of photons that are promising for waveguiding, lasing, and quantum information processing. Here, we report on the discovery of a class of hybrid topological photonic crystals that host simultaneously quantum anomalous Hall and valley Hall phases in different photonic band gaps. The underlying hybrid topology manifests itself in the edge channels as the coexistence of the dual-band chiral edge states and unbalanced valley Hall edge states. We experimentally realize the hybrid topological photonic crystal, unveil its unique topological transitions, and verify its unconventional dual-band gap topological edge states using pump-probe techniques. Furthermore, we demonstrate that the dual-band photonic topological edge channels can serve as frequency-multiplexing devices that function as both beam splitters and combiners. Our study unveils hybrid topological insulators as an exotic topological state of photons as well as a promising route toward future applications in topological photonics.

Photonic Realization of a Generic Type of Graphene Edge States Exhibiting Topological Flat Band

Cutting a honeycomb lattice (HCL) ends up with three types of edges (zigzag, bearded, and armchair), as is well known in the study of graphene edge states. Here, we propose and demonstrate a distinctive twig-shaped edge, thereby observing new edge states using a photonic platform. Our main findings are (i) the twig edge is a generic type of HCL edge complementary to the armchair edge, formed by choosing the right primitive cell rather than simple lattice cutting or Klein edge modification; (ii) the twig edge states form a complete flat band across the Brillouin zone with zero-energy degeneracy, characterized by nontrivial topological winding of the lattice Hamiltonian; (iii) the twig edge states can be elongated or compactly localized at the boundary, manifesting both flat band and topological features. Although realized here in a photonic graphene, such twig edge states should exist in other synthetic HCL structures. Moreover, our results may broaden the understanding of graphene edge states, as well as new avenues for realization of robust edge localization and nontrivial topological phases based on Dirac-like materials.

Vector valley Hall edge solitons in distorted type-II Dirac photonic lattices

Topological edge states have recently garnered a lot of attention across various fields of physics. The topological edge soliton is a hybrid edge state that is both topologically protected and immune to defects or disorders, and a localized bound state that is diffraction-free, owing to the self-balance of diffraction by nonlinearity. Topological edge solitons hold great potential for on-chip optical functional device fabrication. In this report, we present the discovery of vector valley Hall edge (VHE) solitons in type-II Dirac photonic lattices, formed by breaking lattice inversion symmetry with distortion operations. The distorted lattice features a two-layer domain wall that supports both in-phase and out-of-phase VHE states, appearing in two different band gaps. Superposing soliton envelopes onto VHE states generates bright-bright and bright-dipole vector VHE solitons. The propagation dynamics of such vector solitons reveal a periodic change in their profiles, accompanied by the energy periodically transferring between the layers of the domain wall. The reported vector VHE solitons are found to be metastable.

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.

Topological edge and corner states in honeycomb-kagome photonic crystals

We systematically study the first- and second-order band topologies, which are tied to the pseudospin and valley degree of freedoms (DOFs), in honeycomb-kagome photonic crystals (HKPCs). We first demonstrate the quantum spin Hall phase as the first-order pseudospin-induced topology in HKPCs by observing the partial pseudospin-momentum locked edge states. By employing the topological crystalline index, we also discover the multiple corner states emerging in the hexagon-shaped supercell as the manifestation of the second-order pseudospin-induced topology in HKPCs. Next, by gapping the Dirac points, a lower band gap associated with the valley DOF emerges, in which the valley-momentum locked edge states are observed as the first-order valley-induced topology. Such HKPCs without inversion symmetry are proved to be Wannier-type second-order topological insulators, which manifested with valley-selective corner states. Additionally, we also discuss the symmetry breaking effect on pseudospin-momentum locked edge states. Our work realizes both pseudospin-induced and valley-induced topologies in a higher-order manner and thus provides more flexibility in manipulating electromagnetic waves, which may find potential applications in topological routings.

All-optical control of topological valley transport in graphene metasurfaces

We demonstrate that the influence of Kerr effect on valley-Hall topological transport in graphene metasurfaces can be used to implement an all-optical switch. In particular, by taking advantage of the large Kerr coefficient of graphene, the index of refraction of a topologically-protected graphene metasurface can be tuned via a pump beam, which results in an optically controllable frequency shift of the photonic bands of the metasurface. This spectral variation can in turn be readily employed to control and switch the propagation of an optical signal in certain waveguide modes of the graphene metasurface. Importantly, our theoretical and computational analysis reveals that the threshold pump power needed to optically switch ON/OFF the signal is strongly dependent on the group velocity of the pump mode, especially when the device is operated in the slow-light regime. This study could open up new routes towards active photonic nanodevices whose underlying functionality stems from their topological characteristics.

Elastic Valley Spin Controlled Chiral Coupling in Topological Valley Phononic Crystals

Distinct from the phononic valley pseudospin, the real physical spin of elastic waves adds a novel tool kit capable of envisaging the valley-spin physics of topological valley phononic crystals from a local viewpoint. Here, we report the observation of local elastic valley spin as well as the hidden elastic spin-valley locking mechanism overlooked before. We demonstrate that the selective one-way routing of valley phonon states along the topological interface can be reversed by imposing the elastic spin metasource at different interface locations with opposite valley-spin correspondence. We unveil the physical mechanism of selective directionality as the elastic spin controlled chiral coupling of valley phonon states, through both analytical theory and experimental measurement of the opposite local elastic spin density at different interface locations for different transport directions. The elastic spin of valley topological edge phonons can be extended to other topological states and offers new tool to explore topological metamaterials.

A topological nonlinear parametric amplifier

Topological boundary states are well localized eigenstates at the boundary between two different bulk topologies. As long as bulk topology is preserved, the topological boundary mode will endure. Here, we report topological nonlinear parametric amplification of light in a dimerized coupled waveguide system based on the Su-Schrieffer-Heeger model with a domain wall. The good linear transmission properties of the topological waveguide arising from the strong localization of light to the topological boundary is demonstrated through successful high-speed transmission of 30 Gb/s non-return-to-zero and 56 Gb/s pulse amplitude 4-level data. The strong localization of a co-propagating pump and probe to the boundary waveguide is harnessed for efficient, low power optical parametric amplification and wavelength conversion. A nonlinear tuning mechanism is shown to induce chiral symmetry breaking in the topological waveguide, demonstrating a pathway in which Kerr nonlinearities may be applied to tune the topological boundary mode and control the transition to bulk states.

Edge State, Localization Length, and Critical Exponent from Survival Probability in Topological Waveguides

Edge states in topological phase transitions have been observed in various platforms. To date, verification of the edge states and the associated topological invariant are mostly studied, and yet a quantitative measurement of topological phase transitions is still lacking. Here, we show the direct measurement of edge states and their localization lengths from survival probability. We employ photonic waveguide arrays to demonstrate the topological phase transitions based on the Su-Schrieffer-Heeger model. By measuring the survival probability at the lattice boundary, we show that in the long-time limit, the survival probability is P=(1-e^{-2/ξ_{loc}})^{2}, where ξ_{loc} is the localization length. This length derived from the survival probability is compared with the distance from the transition point, yielding a critical exponent of ν=0.94±0.04 at the phase boundary. Our experiment provides an alternative route to characterizing topological phase transitions and extracting their key physical quantities.

Observation of boundary induced chiral anomaly bulk states and their transport properties

The most useful property of topological materials is perhaps the robust transport of topological edge modes, whose existence depends on bulk topological invariants. This means that we need to make volumetric changes to many atoms in the bulk to control the transport properties of the edges in a sample. We suggest here that we can do the reverse in some cases: the properties of the edge can be used to induce chiral transport phenomena in some bulk modes. Specifically, we show that a topologically trivial 2D hexagonal phononic crystal slab (waveguide) bounded by hard-wall boundaries guarantees the existence of bulk modes with chiral anomaly inside a pseudogap due to finite size effect. We experimentally observed robust valley-selected transport, complete valley state conversion, and valley focusing of the chiral anomaly bulk states (CABSs) in such phononic crystal waveguides. The same concept also applies to electromagnetics.

Helical Polariton Lasing from Topological Valleys in an Organic Crystalline Microcavity

Topological photonics provides an important platform for the development of photonic devices with robust disorder-immune light transport and controllable helicity. Mixing photons with excitons (or polaritons) gives rise to nontrivial polaritonic bands with chiral modes, allowing the manipulation of helical lasers in strongly coupled light-matter systems. In this work, helical polariton lasing from topological valleys of an organic anisotropic microcrystalline cavity based on tailored local nontrivial band geometry is demonstrated. This polariton laser emits light of different helicity along different angular directions. The significantly enhanced chiral characteristics are achieved by the nonlinear relaxation process. Helical topological polariton lasers may provide a perfect platform for the exploration of novel topological phenomena that involve light-matter interaction and the development of polariton-based spintronic devices.

Inverse Design of Valley-Like Edge States of Sound Degenerated Away from the High-Symmetry Points in a Square Lattice

Robust edge states of periodic crystals with Dirac points fixed at the corners or centers of the Brillouin zones have drawn extensive attention. Recently, researchers have observed a special edge state associated with Dirac cones degenerated at the high symmetric boundaries of the first irreducible Brillouin zone. These nodal points, characterized by vortex structures in the momentum space, are attributed to the unavailable band crossing protected by mirror symmetry. By breaking the time reversal symmetry with intuitive rotations, valley-like states can be observed in a pair of inequivalent insulators. In this paper, an improved direct inverse design method is first applied to realize the valley-like states. Compared with the conventional strategy, the preparation of transition structures with degeneracy points is skipped. By introducing the quantitative gauge of mode inversion error, insulator pairs are directly obtained without manually tuning the structure with Dirac cone features.

Phototunable chip-scale topological photonics: 160 Gbps waveguide and demultiplexer for THz 6G communication

The revolutionary 5G cellular systems represent a breakthrough in the communication network design to provide a single platform for enabling enhanced broadband communications, virtual reality, autonomous driving, and the internet of everything. However, the ongoing massive deployment of 5G networks has unveiled inherent limitations that have stimulated the demand for innovative technologies with a vision toward 6G communications. Terahertz (0.1-10 THz) technology has been identified as a critical enabler for 6G communications with the prospect of massive capacity and connectivity. Nonetheless, existing terahertz on-chip communication devices suffer from crosstalk, scattering losses, limited data speed, and insufficient tunability. Here, we demonstrate a new class of phototunable, on-chip topological terahertz devices consisting of a broadband single-channel 160 Gbit/s communication link and a silicon Valley Photonic Crystal based demultiplexer. The optically controllable demultiplexing of two different carriers modulated signals without crosstalk is enabled by the topological protection and a critically coupled high-quality (Q) cavity. As a proof of concept, we demultiplexed high spectral efficiency 40 Gbit/s signals and demonstrated real-time streaming of uncompressed high-definition (HD) video (1.5 Gbit/s) using the topological photonic chip. Phototunable silicon topological photonics will augment complementary metal oxide semiconductor (CMOS) compatible terahertz technologies, vital for accelerating the development of futuristic 6G and 7G communication era driving the real-time terabits per second wireless connectivity for network sensing, holographic communication, and cognitive internet of everything.

Unidirectional edge modes in time-modulated metamaterials

We prove the possibility of achieving unidirectional edge modes in time-modulated supercell structures. Such finite structures consist of two trimers repeated periodically. Because of their symmetry, they admit degenerate edge eigenspaces. When the trimers are time-modulated with two opposite orientations, the degenerate eigenspace splits into two one-dimensional eigenspaces described by an analytical formula, each corresponding to a mode which is localized at one edge of the structure. Our results on the localization and stability of these edge modes with respect to fluctuations in the time-modulation amplitude are illustrated by several numerical simulations.

Domain-Wall Topology Induced by Spontaneous Symmetry Breaking in Polariton Graphene

We present a numerical study of exciton-polariton (polariton) condensation in a staggered polariton graphene showing a gapped s band. The condensation occurs at the kinetically favorable negative mass extrema (K and K^{'} valleys) of the valence band. Considering attractive polariton-polariton interaction allows us to generate a spatially extended condensate. The symmetry breaking occurring during the condensate buildup leads to the formation of valley-polarized domains. This process can either be spontaneous, following the Kibble-Zurek scenario, or triggered, leading to a controlled spatial distribution of valley-polarized domains. The selection of a single valley breaks time-reversal symmetry, and the walls separating domains exhibit a reconfigurable topologically protected chiral current. This current emerges as a result of the interplay between the nontrivial valley topology and the condensation-induced symmetry breaking.

Optically reconfigurable higher-order valley photonic crystals based on enhanced Kerr effect

The reconfigurable higher-order topological states are realized in valley photonic crystals with enhanced optical Kerr nonlinearity. The inversion symmetry of the designed valley photonic crystal is broken due to the difference in optical responses between adjacent elements rather than their geometry structures. Therefore, by constructing photonic crystals with distinct topological phases, valley-dependent topological states can be realized, and their reconfigurability is demonstrated based on the Kerr effect. The investigated higher-order topological photonic crystals exhibit great robustness against the structural defects and inferior quality of pump introduced around the corner. Our work provides a new, to the best of our knowledge, platform for studying optical field manipulation and optical devices fabrication in the context of nonlinear higher-order topology.

Bound valley edge states in the continuum

Topological valley photonics provides a unique way to manipulate the flow of light. In general, valley edge states that exhibit unidirectional propagation and are immune to defects and disorders could be realized at the interface between two valley photonic crystals with opposite valley Chern numbers. Herein, by merging the physics of valley edge states and bound states in the continuum, we propose and numerically demonstrate a novel, to the best of our knowledge, concept of edge states termed bound valley edge states in the continuum, which enjoys the topological features of valley edge states, such as, unidirectional propagation and immunity to disorders, but are formed at the interface between air and a single valley photonic crystal. Our results not only provide an effective way to reduce the size of valley photonic structures but also facilitate new applications where the proposed concept of bound valley edge states in the continuum could be exploited for optical sensing and unidirectional waveguiding.

Tracking Valley Topology with Synthetic Weyl Paths

Inspired by the newly emergent valleytronics, great interest has been attracted to the topological valley transport in classical metacrystals. The presence of nontrivial domain-wall states is interpreted with a concept of valley Chern number, which is well defined only in the limit of small band gap. Here, we propose a new visual angle to track the intricate valley topology in classical systems. Benefiting from the controllability of our acoustic metacrystals, we construct Weyl points in synthetic three-dimensional momentum space through introducing an extra structural parameter (rotation angle here). As such, the two-dimensional valley-projected band topology can be tracked with the strictly quantized topological charge in three-dimensional Weyl crystal, which features open surface arcs connecting the synthetic Weyl points and gapless chiral surface states along specific Weyl paths. All theoretical predictions are conclusively identified by our acoustic experiments. Our findings may promote the development of topological valley physics, which is less well defined yet under hot debate in multiple physical disciplines.

Extended topological valley-locked surface acoustic waves

Stable and efficient guided waves are essential for information transmission and processing. Recently, topological valley-contrasting materials in condensed matter systems have been revealed as promising infrastructures for guiding classical waves, for they can provide broadband, non-dispersive and reflection-free electromagnetic/mechanical wave transport with a high degree of freedom. In this work, by designing and manufacturing miniaturized phononic crystals on a semi-infinite substrate, we experimentally realized a valley-locked edge transport for surface acoustic waves (SAWs). Critically, original one-dimensional edge transports could be extended to quasi-two-dimensional ones by doping SAW Dirac “semimetal” layers at the boundaries. We demonstrate that SAWs in the extended topological valley-locked edges are robust against bending and wavelength-scaled defects. Also, this mechanism is configurable and robust depending on the doping, offering various on-chip acoustic manipulation, e.g., SAW routing, focusing, splitting, and converging, all flexible and high-flow. This work may promote future hybrid phononic circuits for acoustic information processing, sensing, and manipulation.

Topological cavity laser with valley edge states

Topological edge states (ES) arise at the boundary between spatial domains with diverse topological properties in photonic crystals, which can transmit unidirectionally to suppress the backscattering and robustly to be immune to defects and disorders. In addition, optical devices with arbitrary geometries of cavities, such as lasers, are expected to be designed on the basis of ES. Herein, we first propose a topological cavity laser based on a honeycomb lattice of ring holes with the bearded interface in two-dimensional (2D) all-dielectric valley photonic crystals (VPhCs) at telecommunication wavelengths. Specifically, we construct a topological cavity using topological valley edge states (VES) and further study the lasing action of the optically pumped cavity with high-quality factors. Our findings could provide opportunities for practical applications of VES-based lasers as ultra-small light sources with the topological protection.

Valley Hall edge solitons in a photonic graphene

We predict the existence and study properties of the valley Hall edge solitons in a composite photonic graphene with a domain wall between two honeycomb lattices with broken inversion symmetry. Inversion symmetry in our system is broken due to detuning introduced into constituent sublattices of the honeycomb structure. We show that nonlinear valley Hall edge states with sufficiently high amplitude bifurcating from the linear valley Hall edge state supported by the domain wall, can split into sets of bright spots due to development of the modulational instability, and that such an instability is a precursor for the formation of topological bright valley Hall edge solitons localized due to nonlinear self-action and travelling along the domain wall over large distances. Topological protection of the valley Hall edge solitons is demonstrated by modeling their passage through sharp corners of the Ω-shaped domain wall.

Optimization and robustness of the topological corner state in second-order topological photonic crystals

The second-order topological photonic crystal with the 0D corner state provides a new way to investigate cavity quantum electrodynamics and develop topological nanophotonic devices with diverse functionalities. Here, we report on the optimization and robustness of the topological corner state in the second-order topological photonic crystal both in theory and in experiment. The topological nanocavity is formed based on the 2D generalized Su-Schrieffer-Heeger model. The quality factor of the corner state is optimized theoretically and experimentally by changing the gap between two photonic crystals or just modulating the position or size of the airholes surrounding the corner. The fabricated quality factors are further optimized by the surface passivation treatment which reduces surface absorption. A maximum quality factor of the fabricated devices is about 6000, which is the highest value ever reported for the active topological corner state. Furthermore, we demonstrate the robustness of the corner state against strong disorders including the bulk defect, edge defect, and even corner defect. Our results lay a solid foundation for further investigations and applications of the topological corner state, such as the investigation of a strong coupling regime and the development of optical devices for topological nanophotonic circuitry.

Transport of light in a moving photonic lattice via atomic coherence

In this Letter, we have investigated experimentally the photonic realization of a moving lattice with an instantaneously tunable transverse velocity in a three-level Λ-type warm ⁸⁵Rb atomic medium. The dynamic photonic lattice moving along the direction of its spatial periodicity was constructed by introducing a frequency difference (determining the velocity) between two coupling beams, whose interference pattern could optically induce a (spatial) periodic refractive index change inside the atomic vapor under electromagnetically induced transparency. When a Gaussian probe field is launched into this optically induced lattice, the output diffraction patterns can shift along the transverse direction, indicating dynamical features of induced photonic structures. The realization of this effectively controllable moving photonic lattice provides a new platform for guiding the transport of light.

Optically Reconfigurable Spin-Valley Hall Effect of Light in Coupled Nonlinear Ring Resonator Lattice

Scattering immune propagation of light in topological photonic systems may revolutionize the design of integrated photonic circuits for information processing and communications. In optics, various photonic topological circuits have been developed, which were based on classical emulation of either quantum spin Hall effect or quantum valley Hall effect. On the other hand, the combination of both the valley and spin degrees of freedom can lead to a new kind of topological transport phenomenon, dubbed spin-valley Hall effect (SVHE), which can further expand the number of topologically protected edge channels and would be useful for information multiplexing. However, it is challenging to realize SVHE in most known material platforms, due to the requirement of breaking both the (pseudo)fermionic time-reversal (T) and parity symmetries (P) individually, but leaving the combined symmetry S≡TP intact. Here, we propose an experimentally feasible platform to realize SVHE for light, based on coupled ring resonators mediated by optical Kerr nonlinearity. Thanks to the inherent flexibility of cross-mode modulation, the coupling between the probe light can be engineered in a controllable way such that spin-dependent staggered sublattice potential emerges in the effective Hamiltonian. With delicate yet experimentally feasible pump conditions, we show the existence of spin-valley Hall-induced topological edge states. We further demonstrate that both degrees of freedom, i.e., spin and valley, can be manipulated simultaneously in a reconfigurable manner to realize spin-valley photonics, doubling the degrees of freedom for enhancing the information capacity in optical communication systems.

Topological kink states in graphene

Due to the unique band structure, graphene exhibits a number of exotic electronic properties that have not been observed in other materials. Among them, it has been demonstrated that there exist the one-dimensional valley-polarized topological kink states localized in the vicinity of the domain wall of graphene systems, where a bulk energy gap opens due to the inversion symmetry breaking. Notably, the valley-momentum locking nature makes the topological kink states attractive to the property manipulation in valleytronics. This paper systematically reviews both the theoretical research and experimental progress on topological kink states in monolayer graphene, bilayer graphene and graphene-like classical wave systems. Besides, various applications of topological kink states, including the valley filter, current partition, current manipulation, Majorana zero modes and etc, are also introduced.

Group Velocity Modulation and Light Field Focusing of the Edge States in Chirped Valley Graphene Plasmonic Metamaterials

The valley degree of freedom, like the spin degree of freedom in spintronics, is regarded as a new information carrier, promoting the emerging valley photonics. Although there exist topologically protected valley edge states which are immune to optical backscattering caused by defects and sharp edges at the inverse valley Hall phase interfaces composed of ordinary optical dielectric materials, the dispersion and the frequency range of the edge states cannot be tuned once the geometrical parameters of the materials are determined. In this paper, we propose a chirped valley graphene plasmonic metamaterial waveguide composed of the valley graphene plasmonic metamaterials (VGPMs) with regularly varying chemical potentials while keeping the geometrical parameters constant. Due to the excellent tunability of graphene, the proposed waveguide supports group velocity modulation and zero group velocity of the edge states, where the light field of different frequencies focuses at different specific locations. The proposed structures may find significant applications in the fields of slow light, micro-nano-optics, topological plasmonics, and on-chip light manipulation.

Topologically Protected Valley-Dependent Quantum Photonic Circuits

Topological photonics has been introduced as a powerful platform for integrated optics, since it can deal with robust light transport, and be further extended to the quantum world. Strikingly, valley-contrasting physics in topological photonic structures contributes to valley-related edge states, their unidirectional coupling, and even valley-dependent wave division in topological junctions. Here, we design and fabricate nanophotonic topological harpoon-shaped beam splitters (HSBSs) based on 120-deg-bending interfaces and demonstrate the first on-chip valley-dependent quantum information process. Two-photon quantum interference, namely, Hong-Ou-Mandel interference with a high visibility of 0.956±0.006, is realized with our 50/50 HSBS, which is constructed by two topologically distinct domain walls. Cascading this kind of HSBS together, we also demonstrate a simple quantum photonic circuit and generation of a path-entangled state. Our work shows that the photonic valley state can be used in quantum information processing, and it is possible to realize more complex quantum circuits with valley-dependent photonic topological insulators, which provides a novel method for on-chip quantum information processing.

Valley-dependent corner states in honeycomb photonic crystals without inversion symmetry

We study topological states of honeycomb photonic crystals in the absence of inversion symmetry using plane wave expansion and finite element methods. The breaking of inversion symmetry in honeycomb lattice leads to contrasting topological valley indices, i.e., the valley-dependent Chern numbers in momentum space. We find that the topological corner states appear for 60^° degree corners, but absent for other corners, which can be understood as the sign flip of valley Chern number at the corner. Our results provide an experimentally feasible platform for exploring valley-dependent higher-order topology in photonic systems.

Topological rainbow based on graded topological photonic crystals

Topological photonic crystal provides a robust platform for nanophotonic devices. However, few reports have been found to realize multiple frequency routing based on topological photonic states, which have restricted further applications in the field of nanophotonic devices. Here, for the first time, to the best of our knowledge, we propose an efficient method to realize a topological rainbow based on graded dielectric topological photonic crystals, which are constructed by changing the degree of lattice contraction and expansion. The topological edge states of different frequencies are separated and trapped at different positions. The all-dielectric planar nanostructures of graded topological photonic crystals are low-loss, robust, and easy for integration. This Letter plays a key role in the use of robust nanophotonic wavelength routers, optical storage, and optical buffers.

Tailoring topological edge states with photonic crystal nanobeam cavities

The realization of topological edge states (TESs) in photonic systems has provided unprecedented opportunities for manipulating light in novel manners. The Su-Schrieffer-Heeger (SSH) model has recently gained significant attention and has been exploited in a wide range of photonic platforms to create TESs. We develop a photonic topological insulator strategy based on SSH photonic crystal nanobeam cavities. In contrast to the conventional photonic SSH schemes which are based on alternately tuned coupling strength in one-dimensional lattice, our proposal provides higher flexibility and allows tailoring TESs by manipulating mode coupling in a two-dimensional manner. We reveal that the proposed hole-array based nanobeams in a dielectric membrane can selectively tailor single or double TESs in the telecommunication region by controlling the coupling strength of the adjacent SSH nanobeams in both transverse and axial directions. Our finding provides an additional degree of freedom in exploiting the SSH model for integrated topological photonic devices and functionalities based on the well-established photonic crystal nanobeam cavity platforms.

Observation of chiral edge states in gapped nanomechanical graphene

Emerging in diverse areas of physics, edge states have been exploited as an efficient strategy of manipulating electrons, photons, and phonons for next-generation hybrid electro-optomechanical circuits. Among various edge states, gapless chiral edge states harnessing quantum spin/valley Hall effects in graphene or graphene-like materials are especially unique. Here, we report on an experimental demonstration of chiral edge states in gapped "nanomechanical graphene"-a honeycomb lattice of free-standing silicon nitride nanomechanical membranes with broken spatial inversion symmetry. These chiral edge states can emerge from the conventional flat-band edge states by tuning the on-site boundary potentials. We experimentally demonstrated that they are backscattering-immune against sharp bends and exhibit the "valley-momentum locking" effect. We further realized smooth transition between the chiral edge states and the well-known valley kink states. Our results open the door to experimental investigation of exotic graphene-related physics in the very-high-frequency integrated nanomechanical systems.

Topology-Controlled Photonic Cavity Based on the Near-Conservation of the Valley Degree of Freedom

We demonstrate a novel path to localizing topologically nontrivial photonic edge modes along their propagation direction. Our approach is based on the near-conservation of the photonic valley degree of freedom associated with valley-polarized edge states. When the edge state is reflected from a judiciously oriented mirror, its optical energy is localized at the mirror surface because of an extended time delay required for valley index flipping. The degree of energy localization at the resulting topology-controlled photonic cavity is determined by the valley-flipping time, which is in turn controlled by the geometry of the mirror. Intuitive analytic descriptions of the "leaky" and closed topology-controlled photonic cavities are presented, and two specific designs-one for the microwave and the other for the optical spectral ranges-are proposed.

Moiré Fringe Induced Gauge Field in Photonics

We realize moiré fringe induced gauge field in a double-layer photonic honeycomb metacrystal with mismatched lattice constants. Benefitting from the generated strong effective gauge field, we report direct measurement of the band diagrams of both Landau level flat bands and intermagnetic-domain edge states. Importantly, we observe the correlation between the momentum and orbital position of the Landau modes, serving as an evidence of the noncommuteness between orthogonal components of the momentum. Without complicated time driving mechanics and careful site-by-site engineering, moiré superlattices could emerge as a powerful means to generate effective gauge fields for photonics benefiting from its simplicity and reconfigurability, which can be applied to nonlinearity enhancement and lasing applications at optical frequencies.