Antichiral surface states in time-reversal-invariant photonic semimetals

Besides chiral edge states, the hallmark of quantum Hall insulators, antichiral edge states can exhibit unidirectional transport behavior but in topological semimetals. Although such edge states provide more flexibility for molding the flow of light, their realization usually suffers from time-reversal breaking. In this study, we propose the realization of antichiral surface states in a time-reversal-invariant manner and demonstrate our idea with a three-dimensional (3D) photonic metacrystal. Our system is a photonic semimetal possessing two asymmetrically dispersed Dirac nodal lines. Via dimension reduction, the nodal lines are rendered a pair of offset Dirac points. By introducing synthetic gauge flux, each two-dimensional (2D) subsystem with nonzero k_z is analogous to a modified Haldane model, yielding a k_z-dependent antichiral surface transport. Through microwave experiments, the bulk dispersion with asymmetric nodal lines and associated twisted ribbon surface states are demonstrated in our 3D time-reversal-invariant system. Although our idea is demonstrated in a photonic system, we propose a general approach to realize antichiral edge states in time-reversal-invariant systems. This approach can be easily extended to systems beyond photonics and may pave the way for further applications of antichiral transport.

A chiral microchip laser using anisotropic grating mirrors for single mode emission

A pair of nanostructured mirrors made of a diffraction grating inscribed in the top layer of a Bragg mirror are designed such that a phase shift near π and different reflected amplitudes exist between transverse electric (TE) and magnetic (TM) reflected polarization states at normal incidence. When a standing wave laser resonator is formed with two such mirrors and the two mirrors' principal axes are twisted one with respect to the other, this phase shift condition suppresses multiple longitudinal mode emission arising from axial spatial hole burning. In addition, the different amplitudes of TE and TM reflected polarizations create polarization eigenstates with different round-trip losses, suppressing one polarization eigenstate. Laser experiments made with a Yb3+-doped Y3Al5O12 active material reveal enhanced purity of the emission spectrum compared to similar lasers using conventional laser mirrors. The proposed design enables a miniature single mode laser, replacing more complex designs usually needed to achieve that goal.

Perovskite Microlaser Integration with Metasurface Supporting Topological Waveguiding

Halide perovskite nano- and microlasers have become a very convenient tool for many applications from sensing to reconfigurable optical chips. Indeed, they exhibit outstanding emission robustness to crystalline defects due to so-called "defect tolerance" allowing for their simple chemical synthesis and further integration with various photonic designs. Here we demonstrate that such robust microlasers can be combined with another class of resilient photonic components, namely, with topological metasurfaces supporting topological guided boundary modes. We show that this approach allows to outcouple and deliver the generated coherent light over tens of microns despite the presence of defects of different nature in the structure: sharp corners in the waveguide, random location of the microlaser, and defects in the microlaser caused by mechanical pressure applied during its transfer to the metasurface. As a result, the developed platform provides a strategy to attain robust integrated lasing-waveguiding designs resilient to a broad range of structural imperfections, both for electrons in a laser and for pseudo-spin-polarized photons in a waveguide.

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.

Light transport through a magneto-optical medium: simple theory revealing fruitful phenomena

Electromagnetic wave transmission in a magneto-optical (MO) medium is a basic and old topic but has raised new interest in recent years, because MO medium plays a vital role in optical isolator, topological optics, electromagnetic field regulation, microwave engineering, and many other technological applications. Here, we describe several fascinating physical images and classical physical variables in MO medium by using a simple and rigorous electromagnetic field solution approach. We can easily obtain explicit formulations for all relevant physical quantities, such as the electromagnetic field distribution, energy flux, reflection/transmission phase, reflection/transmission coefficients, and Goos-Hänchen (GH) shift in MO medium. This theory can help to deepen and broaden our physical understanding of basic electromagnetics, optics, and electrodynamics in application to gyromagnetic and MO homogeneous medium and microstructures, and might help to disclose and develop new ways and routes to high technologies in optics and microwave.

Non-Hermitian kagome photonic crystal with a totally topological spatial mode selection

Recently, the study of non-Hermitian topological edge and corner states in sonic crystals (SCs) and photonic crystals (PCs) has drawn much attention. In this paper, we propose a Wannier-type higher-order topological insulator (HOTI) model based on the kagome PC containing dimer units and study its non-Hermitian topological corner states. When balanced gain and loss are introduced into the dimer units with a proper parity-time symmetric setting, the system will show asymmetric Wannier bands and can support two Hermitian corner states and two pairs of complex-conjugate or pseudo complex-conjugate non-Hermitian corner states. These topological corner states are solely confined at three corners of the triangular supercell constructed by the trivial and non-trivial kagome PCs, corresponding to a topological spatial mode selection effect. As compared to the non-Hermitian quadrupole-type HOTIs, the non-Hermitian Wannier-type HOTIs can realize totally topological spatial mode selection by using much lower coefficients of gain and loss. Our results pave the way for the development of novel non-Hermitian photonic topological devices based on Wannier-type HOTIs.

Photonic Majorana quantum cascade laser with polarization-winding emission

Topological cavities, whose modes are protected against perturbations, are promising candidates for novel semiconductor laser devices. To date, there have been several demonstrations of topological lasers (TLs) exhibiting robust lasing modes. The possibility of achieving nontrivial beam profiles in TLs has recently been explored in the form of vortex wavefront emissions enabled by a structured optical pump or strong magnetic field, which are inconvenient for device applications. Electrically pumped TLs, by contrast, have attracted attention for their compact footprint and easy on-chip integration with photonic circuits. Here, we experimentally demonstrate an electrically pumped TL based on photonic analogue of a Majorana zero mode (MZM), implemented monolithically on a quantum cascade chip. We show that the MZM emits a cylindrical vector (CV) beam, with a topologically nontrivial polarization profile from a terahertz (THz) semiconductor laser.

Single-Photon Source in a Topological Cavity

The introduction of topological physics into the field of photonics has led to the development of photonic devices endowed with robustness against structural disorder. While a range of platforms have been successfully implemented demonstrating topological protection of light in the classical domain, the implementation of quantum light sources in photonic devices harnessing topologically nontrivial resonances is largely unexplored. Here, we demonstrate a single photon source based on a single semiconductor quantum dot coupled to a topologically nontrivial Su-Schrieffer-Heeger (SSH) cavity mode. We provide an in-depth study of Purcell enhancement for this topological quantum light source and demonstrate its emission of nonclassical light on demand. Our approach is a promising step toward the application of topological cavities in quantum photonics.

Topological laser with higher-order corner states in the 2-dimensional Su-Schrieffer-Heeger model

A nonlinear non-Hermitian topological laser system based on the higher-order corner states of the 2-dimensional (2D) Su-Schrieffer-Heeger (SSH) model is investigated. The topological property of this nonlinear non-Hermitian system described by the quench dynamics is in accordance with that of a normal 2D SSH model. In the topological phase, all sites belonging to the topological corner states begin to emit stable laser light when a pulse is given to any one site of the lattice, while no laser light is emitted when the lattice is in the trivial phase. Furthermore, the next-nearest-neighbor (NNN) couplings are introduced into the strong-coupling unit cells of the 2D SSH model, which open a band gap in the continuous band structure. In the topological phase, similar to the case of 2D SSH model without NNN couplings, the corner sites can emit stable laser light due to the robustness of the higher-order corner states when the NNN couplings are regarded as the perturbation. However, amplitude of the stimulated site does not decay to zero in the trivial phase, because the existence of the NNN couplings in the strong-coupling unit cells make the lattice like one in the tetramer limit, and a weaker laser light is emitted by each corner.

Topological super-modes engineering with acoustic graphene plasmons

Acoustic graphene plasmons (AGPs) in a graphene-dielectric-metal structure possess extreme field localization and low loss, which have promising applications in strong photon-matter interaction and integrated photonic devices. Here, we propose two kinds of one-dimensional crystals supporting propagating AGPs with different topological properties, which is confirmed by the Zak phase calculations and the electric field symmetry analysis. Moreover, by combining these two plasmonic crystals to form a superlattice system, the super-modes exist because of the coupling between isolated topological interface states. A flat-like dispersion of super-modes is observed by designing the superlattice. These results should find applications in optical sensing and integrating photonic devices with plasmonic crystals.

Topological phase transition and robust pseudospin interface states induced by angular perturbation in 2D topological photonic crystals

In recent years the research about topological photonic structures has been a very attractive topic in nanoscience from both a basic science and a technological point of view. In this work we propose a two-dimensional topological photonic structure, composed of a trivial and a topological photonic crystals, made of dumbbell-shaped dielectric rods. The topological behavior is induced by introducing an angular perturbation in the dumbbell-shaped dielectric rods. We show that this composed structure supports pseudospin interface states at the interface between the trivial and topological crystals. Our numerical results show that a bandgap is opened in the band structure by introducing the angular perturbation in the system, lifting the double degeneracy of the double Dirac cone at the [Formula: see text] point of the Brillouin zone, despite keeping the [Formula: see text] symmetry group. A pseudospin topological behavior was observed and analyzed with emphasis on the photonic bands at the [Formula: see text] point. We have also investigated the robustness of these pseudospin interface states and, according with our numerical results, we conclude that they are robust against defects, disorder and reflection. Finally, we have shown that the two edge modes present energy flux propagating in opposite directions, which is the photonic analogue of the quantum spin Hall effect.

Planar Optical Cavities Hybridized with Low-Dimensional Light-Emitting Materials

Low-dimensional light-emitting materials have been actively investigated due to their unprecedented optical and optoelectronic properties that are not observed in their bulk forms. However, the emission from low-dimensional light-emitting materials is generally weak and difficult to use in nanophotonic devices without being amplified and engineered by optical cavities. Along with studies on various planar optical cavities over the last decade, the physics of cavity-emitter interactions as well as various integration methods are investigated deeply. These integrations not only enhance the light-matter interaction of the emitters, but also provide opportunities for realizing nanophotonic devices based on the new physics allowed by low-dimensional emitters. In this review, the fundamentals, strengths and weaknesses of various planar optical resonators are first provided. Then, commonly used low-dimensional light-emitting materials such as 0D emitters (quantum dots and upconversion nanoparticles) and 2D emitters (transition-metal dichalcogenide and hexagonal boron nitride) are discussed. The integration of these emitters and cavities and the expect interplay between them are explained in the following chapters. Finally, a comprehensive discussion and outlook of nanoscale cavity-emitter integrated systems is provided.

Topological supermodes in photonic crystal fiber

Topological states enable robust transport within disorder-rich media through integer invariants inextricably tied to the transmission of light, sound, or electrons. However, the challenge remains to exploit topological protection in a length-scalable platform such as optical fiber. We demonstrate, through both modeling and experiment, optical fiber that hosts topological supermodes across multiple light-guiding cores. We directly measure the photonic winding number invariant characterizing the bulk and observe topological guidance of visible light over meter length scales. Furthermore, the mechanical flexibility of fiber allows us to reversibly reconfigure the topological state. As the fiber is bent, we find that the edge states first lose their localization and then become relocalized because of disorder. We envision fiber as a scalable platform to explore and exploit topological effects in photonic networks.

Anomalous π modes by Floquet engineering in optical lattices with long-range coupling

Photonic Floquet topological insulators provide a powerful tool to manipulate the optical fields, which have been extensively studied with only nearest-neighbor coupling. Here, we demonstrate that nontrivial Floquet topological phase and photonic π modes are brought from long-range coupling in a one-dimensional periodically driven optical lattice. Interestingly, the long-range coupling is found to give rise to new Floquet π modes that do not exist in the traditional Floquet lattices. We interpret the underlying physics by analyzing the replica bands, which shows quasienergies band crossing and reopening of new nontrivial π gaps due to the long-range coupling. Our results provide a new route in manipulating optical topological modes by Floquet engineering with long-range coupling.

An operator-based approach to topological photonics

Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, nonreciprocal chiral edge states and cavity-like confined states that have applications in both linear and nonlinear devices. However, current band theoretic approaches to understanding topology in photonic systems yield fundamental limitations on the classes of structures that can be studied. Here, we develop a theoretical framework for assessing a photonic structure's topology directly from its effective Hamiltonian and position operators, as expressed in real space, and without the need to calculate the system's Bloch eigenstates or band structure. Using this framework, we show that nontrivial topology, and associated boundary-localized chiral resonances, can manifest in photonic crystals with broken time-reversal symmetry that lack a complete band gap, a result that may have implications for new topological laser designs. Finally, we use our operator-based framework to develop a novel class of invariants for topology stemming from a system's crystalline symmetries, which allows for the prediction of robust localized states for creating waveguides and cavities.

Experimental Identification of the Second-Order Non-Hermitian Skin Effect with Physics-Graph-Informed Machine Learning

Topological phases of matter are conventionally characterized by the bulk-boundary correspondence in Hermitian systems. The topological invariant of the bulk in d dimensions corresponds to the number of (d - 1)-dimensional boundary states. By extension, higher-order topological insulators reveal a bulk-edge-corner correspondence, such that nth order topological phases feature (d - n)-dimensional boundary states. The advent of non-Hermitian topological systems sheds new light on the emergence of the non-Hermitian skin effect (NHSE) with an extensive number of boundary modes under open boundary conditions. Still, the higher-order NHSE remains largely unexplored, particularly in the experiment. An unsupervised approach-physics-graph-informed machine learning (PGIML)-to enhance the data mining ability of machine learning with limited domain knowledge is introduced. Through PGIML, the second-order NHSE in a 2D non-Hermitian topoelectrical circuit is experimentally demonstrated. The admittance spectra of the circuit exhibit an extensive number of corner skin modes and extreme sensitivity of the spectral flow to the boundary conditions. The violation of the conventional bulk-boundary correspondence in the second-order NHSE implies that modification of the topological band theory is inevitable in higher dimensional non-Hermitian systems.

Polarization-independent and ultra-sensitive biosensor with a one-dimensional topological photonic crystal

Optical biosensor, which perceptively captures the variety of refractive index (RI) of the surrounding environment, has great potential applications in detecting property changes and types of analytes. However, the disequilibrium of light-matter interaction in different polarizations lead to the polarization-dependence and low sensitivity. Here, we propose a polarization-independent and ultrasensitive biosensor by introducing a one-dimensional topological photonic crystal (1D TPhC), where two N-period 1D photonic crystals (PhC1 and PhC2) with different topological invariants are designed for compressing the interaction region of the optical fields, and enhancing the interaction between the light and analyte. Since the strong light-matter interaction caused by the band-inversion is polarization-independent, the biosensor can obtain superior sensing performance both for TE and TM polarization modes. The sensitivity and Figure of Merit (FOM) of the designed biosensor are 1.5677×10⁶ RIU^-1 (1.3497 × 10⁶ RIU^-1) and 7.8387×10¹⁰ RIU^-1deg^-1 (4.4990×10¹⁰ RIU^-1deg^-1) for TM (TE) polarization mode, which performs two orders of magnitude enhancement compared with the reported biosensors. With the protection of the topological edge state, this biosensor has high tolerance to the thickness deviations and refractive index (RI) variations of the component materials, which can reduce the requirements on fabrication and working environment. It is anticipated that the proposed biosensor possesses excellent sensing performances, may have great potentials in environmental monitoring, medical detection, etc.

Topological polarization singular lasing with highly efficient radiation channel

Bound states in the continuum (BICs) in photonic crystals describe the originally leaky Bloch modes that can become bounded when their radiation fields carry topological polarization singularities. However, topological polarization singularities do not carry energy to far field, which limits radiation efficiencies of BICs for light emitting applications. Here, we demonstrate a topological polarization singular laser which has a topological polarization singular channel in the second Brillouin zone and a paired linearly polarized radiation channel in the first Brillouin zone. The presence of the singular channel enables the lasing mode with a higher quality factor than other modes for single mode lasing. In the meanwhile, the presence of the radiation channel secures the lasing mode with high radiation efficiency. The demonstrated topological polarization singular laser operates at room temperature with an external quantum efficiency exceeding 24%. Our work presents a new paradigm in eigenmode engineering for mode selection, exotic field manipulation and lasing.

Interaction-Induced Non-Hermitian Topological Phases from a Dynamical Gauge Field

We present a minimal non-Hermitian model where a topologically nontrivial complex energy spectrum is induced by interparticle interactions. Our model consists of a one-dimensional chain with a dynamical non-Hermitian gauge field with density dependence. The model is topologically trivial for a single-particle system, but exhibits nontrivial non-Hermitian topology with a point gap when two or more particles are present in the system. We construct an effective doublon model to describe the nontrivial topology in the presence of two particles, which quantitatively agrees with the full interacting model. Our model can be realized by modulating hoppings of the Hatano-Nelson model; we provide a concrete Floquet protocol to realize the model in atomic and optical settings.

Different phases in non-Hermitian topological semiconductor stripe laser arrays

As a novel branch of topology, non-Hermitian topological systems have been extensively studied in theory and experiments recently. Topological parity-time (PT)-symmetric semiconductor stripe laser arrays based on the Su-Schreiffer-Heeger model are proposed. The degree of non-Hermicity can be tuned by altering the length of the cavities, and PT symmetry can be realized by patterned electrode. Three laser arrays working in different non-Hermitian phases are analyzed and fabricated. With the increasing degree of non-Hermicity, the peaks of output intensities move from the edge to the bulk. The proposed semiconductor stripe laser array can function as an active, flexible, and feasible platform to investigate and explore non-Hermitian topology for further developments in this field.

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.

Photonic topological insulator induced by a dislocation in three dimensions

The hallmark of topological insulators (TIs) is the scatter-free propagation of waves in topologically protected edge channels¹. This transport is strictly chiral on the outer edge of the medium and therefore capable of bypassing sharp corners and imperfections, even in the presence of substantial disorder. In photonics, two-dimensional (2D) topological edge states have been demonstrated on several different platforms^2-4 and are emerging as a promising tool for robust lasers⁵, quantum devices^6-8 and other applications. More recently, 3D TIs were demonstrated in microwaves⁹ and  acoustic waves^10-13, where the topological protection in the latter  is induced by dislocations. However, at optical frequencies, 3D photonic TIs have so far remained out of experimental reach. Here we demonstrate a photonic TI with protected topological surface states in three dimensions. The topological protection is enabled by a screw dislocation. For this purpose, we use the concept of synthetic dimensions^14-17 in a 2D photonic waveguide array¹⁸ by introducing a further modal dimension to transform the system into a 3D topological system. The lattice dislocation endows the system with edge states propagating along 3D trajectories, with topological protection akin to strong photonic TIs^19,20. Our work paves the way for utilizing 3D topology in photonic science and technology.

Intrinsic mode coupling in mirror-symmetric whispering gallery resonators

Rotationally symmetric micro-cavities with disk, ring or toroidal shape displaying whispering gallery modes (WGMs) play an essential role in modern-day photonics. Due to the reduced symmetry of such resonators compared to spheres, an exact analytical model yielding WGMs as solutions does not exist. The established WGM classification scheme based on approximated analytical solutions is generally useful but neglects a possible interaction between the different modes. In this paper, we assess the limitation of the validity of this established classification based on extensive finite element method (FEM) simulations. We investigate respective mode couplings as well as underlying selection rules based on avoided crossings of the modes' resonance wavelengths. We propose conserved mode properties solely based on true symmetries of the underlying refractive-index distribution and deduce a novel WGM classification scheme.

Non-Hermitian morphing of topological modes

Topological modes (TMs) are usually localized at defects or boundaries of a much larger topological lattice^1,2. Recent studies of non-Hermitian band theories unveiled the non-Hermitian skin effect (NHSE), by which the bulk states collapse to the boundary as skin modes^3-6. Here we explore the NHSE to reshape the wavefunctions of TMs by delocalizing them from the boundary. At a critical non-Hermitian parameter, the in-gap TMs even become completely extended in the entire bulk lattice, forming an 'extended mode outside of a continuum'. These extended modes are still protected by bulk-band topology, making them robust against local disorders. The morphing of TM wavefunction is experimentally realized in active mechanical lattices in both one-dimensional and two-dimensional topological lattices, as well as in a higher-order topological lattice. Furthermore, by the judicious engineering of the non-Hermiticity distribution, the TMs can deform into a diversity of shapes. Our findings not only broaden and deepen the current understanding of the TMs and the NHSE but also open new grounds for topological applications.

Mutual coupling of corner-localized quasi-BICs in high-order topological PhCs and sensing applications

Recently, high-order topological photonic crystals (PhCs) have attracted huge research attention due to their novel physics mechanism and the application potential in integrated photonics. Based on the two-dimensional Su-Schrieffer-Heeger model, we construct and study the mutual coupling between the high-order corner states in 2D dielectric PhCs. Simulation results show that the Q-factor of such corner-localized quasi-bound states in the continuum (BICs) could be enhanced following mutual coupling in finite size. Furthermore, we study the side-coupled structure based on defect-hybrid waveguides and the edge state microring, the quasi-BIC microcavity. The refractive index sensing application based on corner-localized quasi-BICs shows outstanding simulated sensitivity (312.8 nm/RIU) and figure of merit (∼10³ 1/RIU). The robustness against fabrication errors due to its topologically protected nature makes it competitive compared with other quasi-BICs sensors.

Edge states in plasmonic meta-arrays

Photonic edge states provide a novel platform to control and enhance light-matter interactions. Recently, it becomes increasing popular to generate such localized states using the bulk-edge correspondence of topological photonic crystals. While the topological approach is elegant, the design and fabrication of these complex photonic topological crystals is tedious. Here, we report a simple and effective strategy to construct and steer photonic edge state in a plasmonic meta-array, which just requires a small number of plasmonic nanoparticles to form a simple lattice. To demonstrate the idea, different lattice configurations, including square, triangular, and honeycomb lattices of meta-arrays, are fabricated and measured by using an ultrahigh spatial resolution photoemission electron microscopy. The properties of edge states depend on the geometric details such as the row and column number of the lattice, as well as the gap distance between the particles. Moreover, numerical simulations show that the excited edge states can be used for the generation of the quantum entanglement. This work not only provides a new platform for the study of nanoscale photonic devices, but also open a new way for the fundamental study of nanophotonics based on edge states.

Observation of Topological Edge States in Thermal Diffusion

Topological band theory predicts that bulk materials with nontrivial topological phases support topological edge states. This phenomenon is universal for various wave systems and is widely observed for electromagnetic and acoustic waves. Here, the notion of band topology is extended from wave to diffusion dynamics. Unlike wave systems that are usually Hermitian, diffusion systems are anti-Hermitian with purely imaginary eigenvalues corresponding to decay rates. By direct probe of the temperature diffusion, the Hamiltonian of a thermal lattice is experimentally retrieved, and the emergence of topological edge decays is observed within the gap of bulk decays. The results of this work show that such edge states exhibit robust decay rates, which are topologically protected against disorder. This work constitutes a thermal analogue of topological insulators and paves the way to exploring defect-immune heat dissipation.

Straight Photonic Nodal Lines with Quadrupole Berry Curvature Distribution and Superimaging "Fermi Arcs"

In periodic systems, nodal lines are loops in the three-dimensional momentum space with each point on them representing a band degeneracy. Nodal lines exhibit rich topological features, as they can take various configurations such as rings, links, chains, and knots. These line nodes are generally protected by mirror or PT symmetry and frequently accompanied by drumhead surface states. Here, we propose and demonstrate a novel type of photonic straight nodal lines in a D_{2D} metacrystal, which are protected by an unusual rotoinversion time (roto-PT) symmetry. These nodal lines are located at the central axis and hinges of the Brillouin zone. They appear as quadrupole sources of Berry curvature flux in contrast to the Weyl points, which are monopoles. Interestingly, topological surface states exist at all three cutting surfaces, as guaranteed by π-quantized Zak phases along all three directions. As frequency changes, the surface state equifrequency contours evolve from closed to open and become straight lines at a critical transition frequency, at which diffractionless surface wave propagations are experimentally demonstrated, paving the way toward development of superimaging topological devices.

Anomalous Single-Mode Lasing Induced by Nonlinearity and the Non-Hermitian Skin Effect

Single-mode operation is a desirable but elusive property for lasers operating at high pump powers. Typically, single-mode lasing is attainable close to threshold, but increasing the pump power gives rise to multiple lasing peaks due to inter-modal gain competition. We propose a laser with the opposite behavior: multimode lasing occurs at low output powers, but pumping beyond a certain value produces a single lasing mode, with all other candidate modes experiencing negative effective gain. This phenomenon arises in a lattice of coupled optical resonators with non-fine-tuned asymmetric couplings, and is caused by an interaction between nonlinear gain saturation and the non-Hermitian skin effect. The single-mode lasing is observed in both frequency domain and time domain simulations. It is robust against on-site disorder, and scales up to large lattice sizes. This finding might be useful for implementing high-power laser arrays.

Experimental Observation of Non-Abelian Earring Nodal Links in Phononic Crystals

Nodal lines are symmetry-protected one-dimensional band degeneracies in momentum space, which can appear in numerous topological configurations such as nodal rings, chains, links, and knots. Very recently, non-Abelian topological physics have been proposed in space-time inversion (PT) symmetric systems. One of the most special configurations in such systems is the earring nodal link, composing of a nodal chain linking with an isolated nodal line. Such earring nodal links have not been observed in real systems. We designed phononic crystals with earring nodal links, and experimentally observed two different kinds of earring nodal links by measuring the band structures. We found that the order of the nodal chain and line can be switched after band inversion but their link cannot be severed. Our Letter provides experimental evidence for phenomena unique to non-Abelian band topology and our acoustic system provides a convenient platform for studying the new materials carrying non-Abelian charges.

Gain-Loss-Induced Hybrid Skin-Topological Effect

Non-Hermitian topological effects are of crucial importance both in fundamental physics and applications. Here we discover the gain-loss-induced hybrid second-order skin-topological effect and the PT phase transition in skin-topological modes. By studying a non-Hermitian Haldane model, we find that the topological edge modes are localized on a special type of corner, while the bulk modes remain extended. Such an effect originates from the interplay between gain, loss, and the chiral edge currents induced by the nonlocal flux, which can be characterized by considering the properties of the edge sites as a one-dimensional chain. We establish a relation between the skin-topological effect and the PT symmetries belonging to different edges. Moreover, we discover the PT phase transition with the emergence of exceptional points between pairs of skin-topological modes. Our results pave the way for the investigation of non-Hermitian topological physics and PT phase transition in higher-dimensional systems.

Strongly correlated electron-photon systems

An important goal of modern condensed-matter physics involves the search for states of matter with emergent properties and desirable functionalities. Although the tools for material design remain relatively limited, notable advances have been recently achieved by controlling interactions at heterointerfaces, precise alignment of low-dimensional materials and the use of extreme pressures. Here we highlight a paradigm based on controlling light-matter interactions, which provides a way to manipulate and synthesize strongly correlated quantum matter. We consider the case in which both electron-electron and electron-photon interactions are strong and give rise to a variety of phenomena. Photon-mediated superconductivity, cavity fractional quantum Hall physics and optically driven topological phenomena in low dimensions are among the frontiers discussed in this Perspective, which highlights a field that we term here 'strongly correlated electron-photon science'.

Observation of novel topological states in hyperbolic lattices

The discovery of novel topological states has served as a major branch in physics and material sciences. To date, most of the established topological states have been employed in Euclidean systems. Recently, the experimental realization of the hyperbolic lattice, which is the regular tessellation in non-Euclidean space with a constant negative curvature, has attracted much attention. Here, we demonstrate both in theory and experiment that exotic topological states can exist in engineered hyperbolic lattices with unique properties compared to their Euclidean counterparts. Based on the extended Haldane model, the boundary-dominated first-order Chern edge state with a nontrivial real-space Chern number is achieved. Furthermore, we show that the fractal-like midgap higher-order zero modes appear in deformed hyperbolic lattices, and the number of zero modes increases exponentially with the lattice size. These novel topological states are observed in designed hyperbolic circuit networks by measuring site-resolved impedance responses and dynamics of voltage packets. Our findings suggest a useful platform to study topological phases beyond Euclidean space, and may have potential applications in the field of high-efficient topological devices, such as topological lasers, with enhanced edge responses.

Advances and Prospects in Topological Nanoparticle Photonics

Topological nanophotonics is a new avenue for exploring nanoscale systems from visible to THz frequencies, with unprecedented control. By embracing their complexity and fully utilizing the properties that make them distinct from electronic systems, we aim to study new topological phenomena. In this Perspective, we summarize the current state of the field and highlight the use of nanoparticle systems for exploring topological phases beyond electronic analogues. We provide an overview of the tools needed to capture the radiative, retardative, and long-range properties of these systems. We discuss the application of dielectric and metallic nanoparticles in nonlinear systems and also provide an overview of the newly developed topic of topological insulator nanoparticles. We hope that a comprehensive understanding of topological nanoparticle photonic systems will allow us to exploit them to their full potential and explore new topological phenomena at very reduced dimensions.

Fractal photonic topological insulators

Topological insulators constitute a novel state of matter with scatter-free edge states surrounding an insulating bulk. Conventional wisdom regards the insulating bulk as essential, since the invariants describing the topological properties of the system are defined therein. Here, we study fractal topological insulators based on exact fractals comprised exclusively of edge sites. We present experimental proof that, despite the lack of bulk bands, photonic lattices of helical waveguides support topologically protected chiral edge states. We show that light transport in our topological fractal system features increased velocities compared to the corresponding honeycomb lattice. By going beyond the confines of the bulk-boundary correspondence, our findings pave the way toward an expanded perception of topological insulators and open a new chapter of topological fractals.

On-chip nanophotonic topological rainbow

The era of Big Data requires nanophotonic chips to have large information processing capacity. Multiple frequency on-chip nanophotonic devices are highly desirable for density integration, but such devices are more susceptible to structural imperfection because of their nano-scale. Topological photonics provides a robust platform for next-generation nanophotonic chips. Here we give an experimental report of an on-chip nanophotonic topological rainbow realized by employing a translational deformation freedom as a synthetic dimension. The topological rainbow can separate, slow, and trap topological photonic states of different frequencies into different positions. A homemade scattering scanning near-field optical microscope with high resolution is introduced to directly measure the topological rainbow effect of the silicon-based photonic chip. The topological rainbow based on synthetic dimension have no restrictions for optical lattice types, symmetries, materials, wavelength band, and is easy for on-chip integration. This work builds a bridge between silicon chip technologies and topological photonics.

Here the authors provide the experimental observation of a topological rainbow in a silicon-based nanophotonic chip. The system is robust against disorders allows to separate and trap topological photonic states of different wavelength into different positions.

Observation of Degenerate Zero-Energy Topological States at Disclinations in an Acoustic Lattice

Building upon the bulk-boundary correspondence in topological phases of matter, disclinations have recently been harnessed to trap fractionally quantized density of states (DOS) in classical wave systems. While these fractional DOS have associated states localized to the disclination's core, such states are not protected from deconfinement due to the breaking of chiral symmetry, generally leading to resonances which, even in principle, have finite lifetimes and suboptimal confinement. Here, we devise and experimentally validate in acoustic lattices a paradigm by which topological states bind to disclinations without a fractional DOS but which preserve chiral symmetry. The preservation of chiral symmetry pins the states at the midgap, resulting in their protected maximal confinement. The integer DOS at the defect results in twofold degenerate states that, due to symmetry constraints, do not gap out. Our study provides a fresh perspective about the interplay between symmetry protection in topological phases and topological defects, with possible applications in classical and quantum systems alike.

A large-scale single-mode array laser based on a topological edge mode

Topological lasers have been intensively investigated as a strong candidate for robust single-mode lasers. A typical topological laser employs a single-mode topological edge state, which appears deterministically in a designed topological bandgap and exhibits robustness to disorder. These properties seem to be highly attractive in pursuit of high-power lasers capable of single mode operation. In this paper, we theoretically analyze a large-scale single-mode laser based on a topological edge state. We consider a sizable array laser consisting of a few hundreds of site resonators, which support a single topological edge mode broadly distributed among the resonators. We build a basic model describing the laser using the tight binding approximation and evaluate the stability of single mode lasing based on the threshold gain difference Δα between the first-lasing edge mode and the second-lasing competing bulk mode. Our calculations demonstrate that stronger couplings between the cavities and lower losses are advantageous for achieving stable operation of the device. When assuming an average coupling of 100 cm-1 between site resonators and other realistic parameters, the threshold gain difference Δα can reach about 2 cm-1, which would be sufficient for stable single mode lasing using a conventional semiconductor laser architecture. We also consider the effects of possible disorders and long-range interactions to assess the robustness of the laser under non-ideal situations. These results lay the groundwork for developing single-mode high-power topological lasers.

Collective topological corner modes in all-dielectric photonic crystal supercell arrays

In this Letter, we propose collective topological corner modes in all-dielectric photonic crystal (PhC) supercell arrays, where each supercell is a second-order topological insulator. We show that coupled multipole corner modes are embedded in surrounding bulk modes at the Γ point even without the band gap, and individual or superposed dipole corner modes are selectively excited with collective behaviors by incident plane waves. These collective modes possess high-quality factors with an optimized thickness of the slab, and multipole decomposition reveals they are dominated by toroidal dipole and magnetic quadrupoles. Finally, we shrink the nontrivial region in each supercell to one unit-cell limit, where we show that collective corner modes still exist. Potential large-area topological applications are also discussed.

Meta-coupler arrays linking propagating waves and photonic topological modes on a chip

Photonic topological modes (PTMs) have attracted increasing attention due to their robust optical performance, which provides a defect-tolerant strategy for chip-integrated photonic systems. The current coupling schemes rely on bulky structures that severely limit their potential applications in high-density optical integration. Here, plasmonic metasurfaces loaded on topological waveguide arrays are explored to generate PTMs. The normally incident circularly polarized beam can be coupled into the topological interface or edge modes after carefully optimizing the metasurfaces. The result provides a compact and flexible method for PTMs generation on a chip, suggesting a promising avenue toward the application of topological photonic devices.

Topological optical parametric oscillation

Topological insulators possess protected boundary states which are robust against disorders and have immense implications in both fermionic and bosonic systems. Harnessing these topological effects in nonequilibrium scenarios is highly desirable and has led to the development of topological lasers. The topologically protected boundary states usually lie within the bulk bandgap, and selectively exciting them without inducing instability in the bulk modes of bosonic systems is challenging. Here, we consider topological parametrically driven nonlinear resonator arrays that possess complex eigenvalues only in the edge modes in spite of the uniform pumping. We show parametric oscillation occurs in the topological boundary modes of one and two dimensional systems as well as in the corner modes of a higher order topological insulator system. Furthermore, we demonstrate squeezing dynamics below the oscillation threshold, where the quantum properties of the topological edge modes are robust against certain disorders. Our work sheds light on the dynamics of weakly nonlinear topological systems driven out-of-equilibrium and reveals their intriguing behavior in the quantum regime.

Long-Range-Ordered Assembly of Micro-/Nanostructures at Superwetting Interfaces

On-chip integration of solution-processable materials imposes stringent and simultaneous requirements of controlled nucleation and growth, tunable geometry and dimensions, and long-range-ordered assembly, which is challenging in solution process far from thermodynamic equilibrium. Superwetting interfaces, underpinned by programmable surface chemistry and topography, are promising for steering transport, dewetting, and microfluid dynamics of liquids, thus opening a new paradigm for micro-/nanostructure assembly in solution process. Herein, assembly methods on the basis of superwetting interfaces are reviewed for constructing long-range-ordered micro-/nanostructures. Confined capillary liquids, including capillary bridges and capillary corner menisci realized by controlling local wettability and surface topography, are highlighted for simultaneously attained deterministic patterning and long-range order. The versatility and robustness of confined capillary liquids are discussed with assembly of single-crystalline micro-/nanostructures of organic semiconductors, metal-halide perovskites, and colloidal-nanoparticle superlattices, which lead to enhanced device performances and exotic functionalities. Finally, a perspective for promising directions in this realm is provided.

Topological constant-intensity waves

Topological constant-intensity (TCI) waves are introduced in the context of non-Hermitian photonics. Unlike other known examples of topological defects, the proposed TCI waves exhibit a counterintuitive behavior because a phase difference occurs across space without any accompanying intensity variations. Such solutions exist only on non-Hermitian systems, because the associated nonzero phase difference is directly related to the real and imaginary parts of the potential. The free space diffraction and the existence of such waves in two spatial dimensions are also discussed in detail.

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.

Topological boundary states of two-dimensional restricted isosceles triangular photonic crystals

We propose an all-media photonic crystal (PC) composed of isosceles triangle dielectric cylinders that realizes the topological phase transition by simply rotating the isosceles triangular dielectric cylinders. Additionally, the topological phase transition is closely linked with the size parameters and rotation angle of the isosceles triangle. The topological boundary states with lossless transmission are constructed on the interface of two different topological structures, and the optical quantum spin Hall effect is simulated. Further, we verified that the boundary state is unidirectional and immune to disorder, cavity, and sharp bend defects. By rotating the angle of the triangle to control the transmission path of the pseudo-spin state, we realize diverse transport pathways of light, such as the "straight line" shape, "Z" shape, "U" shape, and "Y" shape. This topological system shows a higher degree of freedom, which can promote the research on topological boundary states and the development of topological insulators in practical applications.

Non-Hermitian metasurface with non-trivial topology

The synergy between topology and non-Hermiticity in photonics holds immense potential for next-generation optical devices that are robust against defects. However, most demonstrations of non-Hermitian and topological photonics have been limited to super-wavelength scales due to increased radiative losses at the deep-subwavelength scale. By carefully designing radiative losses at the nanoscale, we demonstrate a non-Hermitian plasmonic-dielectric metasurface in the visible with non-trivial topology. The metasurface is based on a fourth order passive parity-time symmetric system. The designed device exhibits an exceptional concentric ring in its momentum space and is described by a Hamiltonian with a non-HermitianZ 3 topological invariant of V = -1. Fabricated devices are characterized using Fourier-space imaging for single-shot k-space measurements. Our results demonstrate a way to combine topology and non-Hermitian nanophotonics for designing robust devices with novel functionalities.

Topological dislocation modes in three-dimensional acoustic topological insulators

Dislocations are ubiquitous in three-dimensional solid-state materials. The interplay of such real space topology with the emergent band topology defined in reciprocal space gives rise to gapless helical modes bound to the line defects. This is known as bulk-dislocation correspondence, in contrast to the conventional bulk-boundary correspondence featuring topological states at boundaries. However, to date rare compelling experimental evidences have been presented for this intriguing topological observable in solid-state systems, owing to the huge challenges in creating controllable dislocations and conclusively identifying topological signals. Here, using a three-dimensional acoustic weak topological insulator with precisely controllable dislocations, we report an unambiguous experimental evidence for the long-desired bulk-dislocation correspondence, through directly measuring the gapless dispersion of the one-dimensional topological dislocation modes. Remarkably, as revealed in our further experiments, the pseudospin-locked dislocation modes can be unidirectionally guided in an arbitrarily-shaped dislocation path. The peculiar topological dislocation transport, expected in a variety of classical wave systems, can provide unprecedented control over wave propagations.

Light-Driven Fabrication of a Chiral Photonic Lattice of the Helical Nanofilament Liquid Crystal Phase

A photonic lattice is an efficient platform for optically exploring quantum phenomena. However, its fabrication requires high costs and complex procedures when conventional materials, such as silicon or metals, are used. Here, we demonstrate a simple and cost-effective fabrication method for a reconfigurable chiral photonic lattice of the helical nanofilament (HNF) liquid crystal (LC) phase and diffraction grating showing wavelength-dependent diffraction with a rotated polarization state. Furthermore, the UV-exposed areas of the HNF film having chiral characteristics act as optical building blocks that induce resonant intensity modulation in the reflectance and transmittance modes and the optical rotation of the linear polarization. Our photonic lattice of the HNF can be an efficient platform for a chirality-embedded photonic lattice at a low cost.

Direct modulation of electrically pumped coupled microring lasers

We demonstrate how the presence of gain-loss contrast between two coupled identical resonators can be used as a new degree of freedom to enhance the modulation frequency response of laser diodes. An electrically pumped microring laser system with a bending radius of 50 μm is fabricated on an InAlGaAs/InP MQW p-i-n structure. The room temperature continuous wave (CW) laser threshold current of the device is 27 mA. By adjusting the ratio between the injection current levels in the two coupled microrings, our experimental results clearly show a bandwidth improvement by up to 1.63 times the fundamental resonant frequency of the individual device. This matches well with our rate equation simulation model.

Long-Range Dipole-Dipole Interactions in a Plasmonic Lattice

Spontaneous emission of quantum emitters can be enhanced by increasing the local density of optical states, whereas engineering dipole-dipole interactions requires modifying the two-point spectral density function. Here, we experimentally demonstrate long-range dipole-dipole interactions (DDIs) mediated by surface lattice resonances in a plasmonic nanoparticle lattice. Using angle-resolved spectral measurements and fluorescence lifetime studies, we show that unique nanophotonic modes mediate long-range DDI between donor and acceptor molecules. We observe significant and persistent DDI strengths for a range of densities that map to ∼800 nm mean nearest-neighbor separation distance between donor and acceptor dipoles, a factor of ∼100 larger than free space. Our results pave the way to engineer and control long-range DDIs between an ensemble of emitters at room temperature.