Topological hybrid silicon microlasers

Interface states and optical coupling functionalities in the super-SSH lattices

We theoretically address the coupling between trimer lattices and reveal the existence of stable multiple edge and interface states. It is shown the superlattice can provides a tunable number of topologically protected edge and interface states depending on the coupling strength and topological phase of the connecting lattices. Dynamics and transport properties of interface states are also investigated, Due to the interference of linear modes with different propagation constants, stable oscillations resulted from the coupling of interface states in finite trimerized waveguide arrays are observed and can give rise to optical coupling functionalities, including directional coupling, beam splitting and beam oscillator.

Bulk-Boundary Correspondence in Point-Gap Topological Phases

A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, and the other is intrinsic to non-Hermitian systems, which are called line-gap topology and point-gap topology, respectively. Whereas the bulk-boundary correspondence is a fundamental principle in the former topology, its role in the latter has not been clear yet. This Letter establishes the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems. After revealing the requirement for point-gap topology in the open boundary conditions, we clarify that the bulk point-gap topology in open boundary conditions can be different from that in periodic boundary conditions. On the basis of real space topological invariants and the K theory, we give a complete classification of the open boundary point-gap topology with symmetry and show that the nontrivial open boundary topology results in robust and exotic surface states.

Single-Mode Laser in the Telecom Range by Deterministic Amplification of the Topological Interface Mode

Photonic integrated circuits are paving the way for novel on-chip functionalities with diverse applications in communication, computing, and beyond. The integration of on-chip light sources, especially single-mode lasers, is crucial for advancing those photonic chips to their full potential. Recently, novel concepts involving topological designs introduced a variety of options for tuning device properties, such as the desired single-mode emission. Here, we introduce a novel cavity design that allows amplification of the topological interface mode by deterministic placement of gain material within a topological lattice. The proposed design is experimentally implemented by a selective epitaxy process to achieve closely spaced Si and InGaAs nanorods embedded within the same layer. This results in the first demonstration of a single-mode laser in the telecom band using the concept of amplified topological modes without introducing artificial losses.

Occupation-Dependent Particle Separation in One-Dimensional Non-Hermitian Lattices

We unveil an exotic phenomenon arising from the intricate interplay between non-Hermiticity and many-body physics, namely, an occupation-dependent particle separation for hardcore bosons in a one-dimensional lattice driven by unidirectional non-Hermitian pumping. Taking hardcore bosons as an example, we find that a pair of particles occupying the same unit cell exhibit an opposite non-Hermitian pumping direction to that of unpaired ones occupying different unit cells. By turning on an intracell interaction, many-body eigenstates split in their real energies, forming separable clusters in the complex energy plane with either left-, right-, or bipolar-types of non-Hermitian skin effect (NHSE). The dependency of skin accumulating directions on particle occupation is further justified with local sublattice correlation and entanglement entropy of many-body eigenstates. Dynamically, this occupation-dependent NHSE manifests as uni- or bidirectional pumping for many-body initial states, allowing for spatially separating paired and unpaired particles. Our results unveil the possibility of designing and exploring novel non-Hermitian phases originated from particle nonconservation in subsystems (e.g., orbitals, sublattices, or spin species) and their spatial configurations.

Perfect Excitation of Topological States by Supersymmetric Waveguides

Topological photonic states provide intriguing strategies for robust light manipulations, however, it remains challenging to perfectly excite these topological eigenstates due to their complicated mode profiles. In this work, we propose to realize the exact eigenmode of the topological edge states by supersymmetric (SUSY) structures. By adiabatically transforming the SUSY partner to its main topological structure, the edge modes can be perfectly excited with simple single-site input. We experimentally verify our strategy in integrated silicon waveguides in telecommunication wavelength, showing a broad working bandwidth. Moreover, a shortcut-to-adiabaticity strategy is further applied to speed up the adiabatic pump process by inverse-design approaches, thus enabling fast mode evolutions and leading to reduced device size. Our method is universal and beneficial to the topology-based or complex eigenmodes systems, ranging from photonics and microwaves to cold atoms and acoustics.

Phase of Topological Lattice with Leaky Guided Mode Resonance

Topological nature in different areas of physics and electronics has often been characterized and controlled through topological invariants depending on the global properties of the material. The validity of bulk-edge correspondence and symmetry-related topological invariants has been extended to non-Hermitian systems. Correspondingly, the value of geometric phases, such as the Pancharatnam-Berry or Zak phases, under the adiabatic quantum deformation process in the presence of non-Hermitian conditions, are now of significant interest. Here, we explicitly calculate the Zak phases of one-dimensional topological nanobeams that sustain guided-mode resonances, which lead to energy leakage to a continuum state. The retrieved Zak phases show as zero for trivial and as π for nontrivial photonic crystals, respectively, which ensures bulk-edge correspondence is still valid for certain non-Hermitian conditions.

Robust Zero Modes in Non-Hermitian Systems without Global Symmetries

We present an approach to achieve zero modes in lattice models that do not rely on any symmetry or topology of the bulk, which are robust against disorder in the bulk of any type and strength. Such symmetry-free zero modes (SFZMs) are formed by attaching a single site or small cluster with zero mode(s) to the bulk, which serves as the "nucleus" that expands to the entire lattice. We identify the requirements on the couplings between this boundary and the bulk, which reveals that this approach is intrinsically non-Hermitian. We then provide several examples with either an arbitrary or structured bulk, forming spectrally embedded zero modes in the bulk continuum, midgap zero modes, and even restoring the "zeroness" of coupling or disorder-shifted topological corner states. Focusing on viable realizations using photonic lattices, we show that the resulting SFZM can be observed as the single lasing mode when optical gain is applied to the boundary.

Room-temperature continuous-wave topological Dirac-vortex microcavity lasers on silicon

Robust laser sources are a fundamental building block for contemporary information technologies. Originating from condensed-matter physics, the concept of topology has recently entered the realm of optics, offering fundamentally new design principles for lasers with enhanced robustness. In analogy to the well-known Majorana fermions in topological superconductors, Dirac-vortex states have recently been investigated in passive photonic systems and are now considered as a promising candidate for robust lasers. Here, we experimentally realize the topological Dirac-vortex microcavity lasers in InAs/InGaAs quantum-dot materials monolithically grown on a silicon substrate. We observe room-temperature continuous-wave linearly polarized vertical laser emission at a telecom wavelength. We confirm that the wavelength of the Dirac-vortex laser is topologically robust against variations in the cavity size, and its free spectral range defies the universal inverse scaling law with the cavity size. These lasers will play an important role in CMOS-compatible photonic and optoelectronic systems on a chip.

Topological photonic crystal nanowire array laser with edge states

A topological photonic crystal InGaAsP/InP core-shell nanowire array laser operating in the 1550 nm wavelength band is proposed and simulated. The structure is composed of an inner topological nontrivial photonic crystal and outer topological trivial photonic crystal. For a nanowire with height of 8 µm, high quality factor of 4.7 × 104 and side-mode suppression ratio of 11 dB are obtained, approximately 32.9 and 5.5 times that of the uniform photonic crystal nanowire array, respectively. Under optical pumping, the topological nanowire array laser exhibits a threshold 27.3% lower than that of the uniform nanowire array laser, due to the smaller nanowire slit width and stronger optical confinement. Moreover, the topological NW laser exhibits high tolerence to manufacturing errors. This work may pave the way for the development of low-threshold single-mode high-robustness nanolasers.

Observation of a Topological Edge State Stabilized by Dissipation

Robust states emerging at the boundary of a system constitute a hallmark for topological band structures. Other than in closed systems, topologically protected states can occur even in systems with a trivial band structure, if exposed to suitably modulated losses. Here, we study the dissipation-induced emergence of a topological band structure in a non-Hermitian one-dimensional lattice system, realized by arrays of plasmonic waveguides with tailored loss. We obtain direct evidence for a topological edge state that resides in the center of the band gap. By tuning dissipation and hopping, the formation and breakdown of an interface state between topologically distinct regions is demonstrated.

Topological Microlaser with a Non-Hermitian Topological Bulk

Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While bulk-edge correspondence has been extensively studied in Hermitian systems, a non-Hermitian bulk could drastically modify the Hermitian topological band theory due to the interplay between non-Hermiticity and topology, and its effect on bulk-edge correspondence is still an ongoing pursuit. Importantly, including non-Hermicity can significantly expand the horizon of topological states of matter and lead to a plethora of unique properties and device applications, an example of which is a topological laser. However, the bulk topology, and thereby the bulk-edge correspondence, in existing topological edge-mode lasers is not well defined. Here, we propose and experimentally probe topological edge-mode lasing with a well-defined non-Hermitian bulk topology in a one-dimensional (1D) array of coupled ring resonators. By modeling the Hamiltonian with an additional degree of freedom (referred to as synthetic dimension), our 1D structure is equivalent to a 2D non-Hermitian Chern insulator with precise mapping. Our Letter may open a new pathway for probing non-Hermitian topological effects and exploring non-Hermitian topological device applications.

Single-mode quasi PT-symmetric laser with high power emission

Large-area lasers are practical for generating high output powers. However, this often comes at the expense of lower beam quality due to the introduction of higher-order modes. Here, we experimentally demonstrate a new type of electrically pumped, large-area edge-emitting lasers that exhibit a high power emission (∼0.4 W) and a high-quality beam (M²∼1.25). These favorable operational characteristics are enabled by establishing a quasi PT-symmetry between the second-order mode of a large area two-mode laser cavity and that of a single-mode auxiliary partner cavity, i.e., by implementing a partial isospectrality between the two coupled cavities. This in turn enlarges the effective volume of the higher-order modes. As a result, a selective pump applied via current injection into the main laser cavity can provide a stronger modal gain to the fundamental mode, and thus lead to lasing in the single mode regime after filtering out higher order transverse modes. The reported experimental results confirm this intuitive picture and are in good agreement with both theoretical and numerical analysis. Above all, the employed material platform and fabrication process are compatible with the industrial standards of semiconductor lasers. This work provides the first clear demonstration, beyond previous proof-of-concept studies, of the utility of PT-symmetry in building laser geometries with enhanced performance and, at the same time, useful output power levels and emission characteristics.

Electrically-pumped compact topological bulk lasers driven by band-inverted bound states in the continuum

One of the most exciting breakthroughs in physics is the concept of topology that was recently introduced to photonics, achieving robust functionalities, as manifested in the recently demonstrated topological lasers. However, so far almost all attention was focused on lasing from topological edge states. Bulk bands that reflect the topological bulk-edge correspondence have been largely missed. Here, we demonstrate an electrically pumped topological bulk quantum cascade laser (QCL) operating in the terahertz (THz) frequency range. In addition to the band-inversion induced in-plane reflection due to topological nontrivial cavity surrounded by a trivial domain, we further illustrate the band edges of such topological bulk lasers are recognized as the bound states in the continuum (BICs) due to their nonradiative characteristics and robust topological polarization charges in the momentum space. Therefore, the lasing modes show both in-plane and out-of-plane tight confinements in a compact laser cavity (lateral size ~3λlaser). Experimentally, we realize a miniaturized THz QCL that shows single-mode lasing with a side-mode suppression ratio (SMSR) around 20 dB. We also observe a cylindrical vector beam for the far-field emission, which is evidence for topological bulk BIC lasers. Our demonstration on miniaturization of single-mode beam-engineered THz lasers is promising for many applications including imaging, sensing, and communications.

Edge states in coupled non-Hermitian resonators

Small perturbations may dramatically influence the physical properties of a single non-Hermitian cavity. However, how these small perturbations interplay with bulk-edge properties is still to be demonstrated by experimentation. Here, we experimentally demonstrate edge states in coupled non-Hermitian resonators, based on a chain of all-dielectric coupled resonators where each resonator consists of two target particles. The evanescent coupling between the cavity and the target particles leads to tunable asymmetric backscattering, which plays a key role in the appearance of edge states in the bulk bandgap. We also demonstrate that these observed edge states are robust against weak disorders introduced to the system. Our study may inspire further explorations of the non-Hermitian bulk-edge properties.

A second wave of topological phenomena in photonics and acoustics

Light and sound are the most ubiquitous forms of waves, associated with a variety of phenomena and physical effects such as rainbows and echoes. Light and sound, both categorized as classical waves, have lately been brought into unexpected connections with exotic topological phases of matter. We are currently witnessing the onset of a second wave of active research into this topic. The past decade has been marked by fundamental advances comprising two-dimensional quantum Hall insulators and quantum spin and valley Hall insulators, whose topological properties are characterized using linear band topology. Here, going beyond these conventional topological systems, we focus on the latest frontiers, including non-Hermitian, nonlinear and non-Abelian topology as well as topological defects, for which the characterization of the topological features goes beyond the standard band-topology language. In addition to an overview of the current state of the art, we also survey future research directions for valuable applications.

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.

Higher-order topological polariton corner state lasing

Unlike conventional laser, the topological laser is able to emit coherent light robustly against disorders and defects because of its nontrivial band topology. As a promising platform for low-power consumption, exciton polariton topological lasers require no population inversion, a unique property that can be attributed to the part-light-part-matter bosonic nature and strong nonlinearity of exciton polaritons. Recently, the discovery of higher-order topology has shifted the paradigm of topological physics to topological states at boundaries of boundaries, such as corners. However, such topological corner states have never been realized in the exciton polariton system yet. Here, on the basis of an extended two-dimensional Su-Schrieffer-Heeger lattice model, we experimentally demonstrate the topological corner states of perovskite polaritons and achieved polariton corner state lasing with a low threshold (approximately microjoule per square centimeter) at room temperature. The realization of such polariton corner states also provides a mechanism of polariton localization under topological protection, paving the way toward on-chip active polaritonics using higher-order topology.

On-chip integrated exceptional surface microlaser

The on-chip integrated visible microlaser is a core unit of high-speed visible-light communication with huge bandwidth resources, which needs robustness against fabrication errors, compressible linewidth, reducible threshold, and in-plane emission. However, until now, it has been a great challenge to meet these requirements simultaneously. Here, we report a scalable strategy to realize a robust on-chip integrated visible microlaser with further improved lasing performances enabled by the increased orders (n) of exceptional surfaces, and experimentally verify the strategy by demonstrating the performances of a second-order exceptional surface-tailored microlaser. We further prove the potential application of the strategy by discussing an exceptional surface-tailored topological microlaser with unique performances. This work lays a foundation for further development of on-chip integrated high-speed visible-light communication and processing systems, provides a platform for the fundamental study of non-Hermitian photonics, and proposes a feasible method of joint research for non-Hermitian photonics with nonlinear optics and topological photonics.

Exceptional Non-Abelian Topology in Multiband Non-Hermitian Systems

Defective spectral degeneracy, known as exceptional point (EP), lies at the heart of various intriguing phenomena in optics, acoustics, and other nonconservative systems. Despite extensive studies in the past two decades, the collective behaviors (e.g., annihilation, coalescence, braiding, etc.) involving multiple exceptional points or lines and their interplay have been rarely understood. Here we put forward a universal non-Abelian conservation rule governing these collective behaviors in generic multiband non-Hermitian systems and uncover several counterintuitive phenomena. We demonstrate that two EPs with opposite charges (even the pairwise created) do not necessarily annihilate, depending on how they approach each other. Furthermore, we unveil that the conservation rule imposes strict constraints on the permissible exceptional-line configurations. It excludes structures like Hopf link yet permits novel staggered rings composed of noncommutative exceptional lines. These intriguing phenomena are illustrated by concrete models which could be readily implemented in platforms like coupled acoustic cavities, optical waveguides, and ring resonators. Our findings lay the cornerstone for a comprehensive understanding of the exceptional non-Abelian topology and shed light on the versatile manipulations and applications based on exceptional degeneracies in nonconservative systems.

Dissipative Pairing Interactions: Quantum Instabilities, Topological Light, and Volume-Law Entanglement

We analyze an unusual class of bosonic dynamical instabilities that arise from dissipative (or non-Hermitian) pairing interactions. We show that, surprisingly, a completely stable dissipative pairing interaction can be combined with simple hopping or beam-splitter interactions (also stable) to generate instabilities. Further, we find that the dissipative steady state in such a situation remains completely pure up until the instability threshold (in clear distinction from standard parametric instabilities). These pairing-induced instabilities also exhibit an extremely pronounced sensitivity to wave function localization. This provides a simple yet powerful method for selectively populating and entangling edge modes of photonic (or more general bosonic) lattices having a topological band structure. The underlying dissipative pairing interaction is experimentally resource friendly, requiring the addition of a single additional localized interaction to an existing lattice, and is compatible with a number of existing platforms, including superconducting circuits.

Non-Abelian effects in dissipative photonic topological lattices

Topology is central to phenomena that arise in a variety of fields, ranging from quantum field theory to quantum information science to condensed matter physics. Recently, the study of topology has been extended to open systems, leading to a plethora of intriguing effects such as topological lasing, exceptional surfaces, as well as non-Hermitian bulk-boundary correspondence. Here, we show that Bloch eigenstates associated with lattices with dissipatively coupled elements exhibit geometric properties that cannot be described via scalar Berry phases, in sharp contrast to conservative Hamiltonians with non-degenerate energy levels. This unusual behavior can be attributed to the significant population exchanges among the corresponding dissipation bands of such lattices. Using a one-dimensional example, we show both theoretically and experimentally that such population exchanges can manifest themselves via matrix-valued operators in the corresponding Bloch dynamics. In two-dimensional lattices, such matrix-valued operators can form non-commuting pairs and lead to non-Abelian dynamics, as confirmed by our numerical simulations. Our results point to new ways in which the combined effect of topology and engineered dissipation can lead to non-Abelian topological phenomena.

Perovskite quantum dot one-dimensional topological laser

Various topological laser concepts have recently enabled the demonstration of robust light-emitting devices that are immune to structural deformations and tolerant to fabrication imperfections. Current realizations of photonic cavities with topological boundaries are often limited by outcoupling issues or poor directionality and require complex design and fabrication that hinder operation at small wavelengths. Here we propose a topological cavity design based on interface states between two one-dimensional photonic crystals with distinct Zak phases. Using a few monolayers of solution-processed all-inorganic cesium lead halide perovskite quantum dots as the ultrathin gain medium, we demonstrate a lithography-free, vertical-emitting, low-threshold, and single-mode laser emitting in the green. We show that the topological laser, akin to vertical-cavity surface-emitting lasers (VCSELs), is robust against local perturbations of the multilayer structure. We argue that the design simplicity and reduction of the gain medium thickness enabled by the topological cavity make this architecture suitable for low-cost and efficient quantum dot vertical emitting lasers operating across the visible spectral region.

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.

Continuum of Bound States in a Non-Hermitian Model

In a Hermitian system, bound states must have quantized energies, whereas free states can form a continuum. We demonstrate how this principle fails for non-Hermitian systems, by analyzing non-Hermitian continuous Hamiltonians with an imaginary momentum and Landau-type vector potential. The eigenstates, which we call "continuum Landau modes" (CLMs), have Gaussian spatial envelopes and form a continuum filling the complex energy plane. We present experimentally realizable 1D and 2D lattice models that host CLMs; the lattice eigenstates are localized and have other features matching the continuous model. One of these lattices can serve as a rainbow trap, whereby the response to an excitation is concentrated at a position proportional to the frequency. Another lattice can act a wave funnel, concentrating an input excitation onto a boundary over a wide frequency bandwidth. Unlike recent funneling schemes based on the non-Hermitian skin effect, this requires a simple lattice design with reciprocal couplings.

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.

Observation of Weyl Interface States in Non-Hermitian Synthetic Photonic Systems

Weyl medium has triggered remarkable interest owing to its nontrivial topological edge states in 3D photonic band structures that were mainly revealed as surface modes yet. It is undoubted that the connection of two different Weyl media will give rise to more fruitful physics at their interface, while they face extreme difficulty in high-dimensional lattice matching. Here, we successfully demonstrate the non-Hermitian Weyl interface physics in complex synthetic parameter space, which is implemented in a loss-controlled silicon waveguide array. By establishing non-Hermitian Hamiltonian in the parameter space, new Weyl interfaces with distinct topological origins are predicted and experimentally observed in silicon waveguides. Significantly, our Letter exploits the non-Hermitian parameter to create the synthetic dimension by manipulating the non-Hermitian order, which successfully circumvents the difficulty in lattice matching for high-dimensional interfaces. The revealed rich topological Weyl interface states and their phase transitions in silicon waveguide platform further imply potentials in chip-scale photonics integrations.

Imaginary Gauge Transformation in Momentum Space and Dirac Exceptional Point

An imaginary gauge transformation is at the core of the non-Hermitian skin effect. Here, we show that such a transformation can be performed in momentum space as well, which reveals that certain gain- and loss-modulated systems in their parity-time (PT) symmetric phases are equivalent to Hermitian systems with real potentials. Our analysis in momentum space also distinguishes two types of exceptional points (EPs) in the same system. Besides the conventional type that leads to a PT transition upon the continuous increase of gain and loss, we find real-valued energy bands connected at a Dirac EP in hybrid dimensions, consisting of a spatial dimension and a synthetic dimension for the gain and loss strength.

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.

First-principles investigation of polytypic defects in InP

In this paper we study polytypic defects in Indium Phosphide (InP) using the complementary first-principles methods of density functional theory and non-equilibrium Greens functions. Specifically we study interfaces between the ground state Zincblende crystal structure and the meta-stable Wurtzite phase, with an emphasis on the rotational twin plane defect, which forms due to the polytypic nature of InP. We found that the transition of the band structure across the interface is anisotropic and lasts 7 nm (3.5 nm). Due to this, a crystal-phase quantum well would require a minimal width of 10 nm, which eliminates rotational twin planes as possible quantum wells. We also found that for conducting current, the interfaces increase conductivity along the defect-plane ([11$$\bar{2}$$ 2 ¯ ]), whereas due to real growth limitations, despite the interfaces reducing conductivity across the defect-plane ([111]), we found that a high degree of polytypic defects are still desirable. This was argued to be the case, due to a higher fraction of Wurtzite segments in a highly phase-intermixed system.

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 the topological phase transition from the spatial correlation of a biphoton in a one-dimensional topological photonic waveguide array

We propose a simple method, using the first singular value (FSV) of the spatial correlation of biphotons, to characterize topological phase transitions (TPTs) in one-dimensional (1D) topological photonic waveguide arrays (PWAs). After analyzing the spatial correlation of biphotons using the singular value decomposition, we found that the FSV of the spatial correlation of biphotons in real space can characterize TPTs and distinguish between the topological trivial and nontrivial phases in PWAs based on the Su-Schrieffer-Heeger model. The analytical simulation results were demonstrated by applying the coupled-mode theory to biphotons and were found to be in good agreement with those of the numerical simulation. Moreover, the numerical simulation of the FSV (of the spatial correlation of biphotons) successfully characterized the TPT in a PWA based on the Aubry-André-Harper and Rice-Mele models, demonstrating the universality of this method for 1D topological PWAs. Our method provides biphotons with the possibility of acquiring information regarding TPTs directly from the spatial correlation in real space, and their potential applications in quantum topological photonics and topological quantum computing as quantum simulators and information carriers.

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.

3D-Printed Möbius Microring Lasers: Topology Engineering in Photonic Microstructures

Manipulating photons in artificially structured materials is highly desired in modern photonic technology. Nontrivial topological structures are rapidly emerging as a state-of-art platform for achieving unprecedented fascinating phenomena of photon manipulation. However, the current studies mainly focus on planar structures, and the fabrication of photonic microstructures with specific topological geometric features still remains a great challenge. Extending the topological photonics to 3D microarchitectures is expected to enrich the photon manipulation capabilities and further advance the topological photonic devices. Here, a femtosecond laser direct writing technique is employed to fabricate 3D topological Möbius microring resonators from dye-doped polymer. The high-quality-factor Möbius microring resonator supports a unique spin-orbit coupled lasing at very low threshold. Due to the spin-orbit coupling induced geometric/Berry phase, the Möbius microrings, in striking contrast with ordinary microrings, output laser signals with all polarization states. The manipulation of miniaturized coherent light sources in the fabricated Möbius microrings represents a significant step forward toward 3D topological photonics that offers a novel design philosophy for functional photonic and optoelectronic devices.

Effective Hamiltonian for Photonic Topological Insulator with Non-Hermitian Domain Walls

The gain and loss in photonic lattices provide possibilities for many functional phenomena. In this Letter, we consider photonic topological insulators with different types of gain-loss domain walls, which will break the translational symmetry of the lattices. A method is proposed to construct effective Hamiltonians, which accurately describe states and the corresponding energies at the domain walls for different types of photonic topological insulators and domain walls with arbitrary shapes. We also consider domain-induced higher-order topological states in two-dimensional non-Hermitian Aubry-André-Harper lattices and use our method to explain such phenomena successfully. Our results reveal the physics in photonic topological insulators with gain-loss domain walls, which provides advanced pathways for manipulation of non-Hermitian topological states in photonic systems.

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.

High-efficiency topological pumping with discrete supersymmetry transformations

Making use of the isospectrality of Supersymmetry transformations, we propose a general and high-fidelity method to prepare gapped topological modes in discrete systems from a single-site excitation. The method consists of adiabatically connecting two superpartner structures, deforming the input state into the desired mode. We demonstrate the method by pumping topological states of the Su-Schrieffer-Heeger model in an optical waveguide array, where the adiabatic deformation is performed along the propagation direction. We obtain fidelities above F = 0.99 for a wide range of coupling strengths when pumping edge and interface states.

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.

Non-Hermitian laser arrays with tunable phase locking

Inspired by the idea of non-Hermitian spectral engineering and non-Hermitian skin effect, a novel, to the best of our knowledge, design for stable emission of coupled laser arrays with tunable phase locking and strong supermode competition suppression is suggested. We consider a linear array of coupled resonators with asymmetric mode coupling displaying the non-Hermitian skin effect and show that, under suitable tailoring of complex frequencies of the two edge resonators, the laser array can stably emit in a single extended supermode with tunable phase locking and with strong suppression of all other skin supermodes. The proposed laser array design offers strong robustness against both structural imperfections of the system and dynamical instabilities typical of semiconductor laser arrays.

Metasurfaces with high-Q resonances governed by topological edge state

Achieving high-quality (Q)-factor resonances in metasurfaces is essential for various applications, including nano-lasers, nonlinear optics, and quantum optics. In this work, we propose a high-Q metasurface using a topological strategy: constructing the metasurface by stacking two conjugated nanopillar arrays with different topological invariants. Our study shows that a topological edge state steadily appears at the interfaces of the nanopillars, and a sharp transmission resonance with a Q-factor of more than 1000 can be obtained. The sensing application of such high-Q topological metasurface is also demonstrated, whose figure of merit reaches approximately 145. The proposed strategy and underlying theory can open up new avenues to realize ultrasharp resonances, which can promote numerous potential applications, such as biosensing, optical modulation, and slow-light devices.

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.

Asymmetric topological pumping in nonparaxial photonics

Topological photonics was initially inspired by the quantum-optical analogy between the Schrödinger equation for an electron wavefunction and the paraxial equation for a light beam. Here, we reveal an unexpected phenomenon in topological pumping observed in arrays of nonparaxial optical waveguides where the quantum-optical analogy becomes invalid. We predict theoretically and demonstrate experimentally an asymmetric topological pumping when the injected field transfers from one side of the waveguide array to the other side whereas the reverse process is unexpectedly forbidden. Our finding could open an avenue for exploring topological photonics that enables nontrivial topological phenomena and designs in photonics driven by nonparaxiality.

The understanding of the topological properties of light is at the base of the future optical devices development. In this work the authors aim to suggesting a different paradigm for topological transport and manipulation of nonparaxial light, paving the way toward the new developments in the field of topological photonics

Observing 0D subwavelength-localized modes at ~100 THz protected by weak topology

Topological photonic crystals (TPhCs) provide robust manipulation of light with built-in immunity to fabrication tolerances and disorder. Recently, it was shown that TPhCs based on weak topology with a dislocation inherit this robustness and further host topologically protected lower-dimensional localized modes. However, TPhCs with weak topology at optical frequencies have not been demonstrated so far. Here, we use scattering-type scanning near-field optical microscopy to verify mid-bandgap zero-dimensional light localization close to 100 THz in a TPhC with nontrivial Zak phase and an edge dislocation. We show that because of the weak topology, differently extended dislocation centers induce similarly strong light localization. The experimental results are supported by full-field simulations. Along with the underlying fundamental physics, our results lay a foundation for the application of TPhCs based on weak topology in active topological nanophotonics, and nonlinear and quantum optic integrated devices because of their strong and robust light localization.

Symmetry-protected solitons and bulk-boundary correspondence in generalized Jackiw-Rebbi models

We investigate the roles of symmetry and bulk-boundary correspondence in characterizing topological edge states in generalized Jackiw-Rebbi (JR) models. We show that time-reversal (T), charge-conjugation (C), parity (P), and discrete internal field rotation ([Formula: see text]) symmetries protect and characterize the various types of edge states such as chiral and nonchiral solitons via bulk-boundary correspondence in the presence of the multiple vacua. As two representative models, we consider the JR model composed of a single fermion field having a complex mass and the generalized JR model with two massless but interacting fermion fields. The JR model shows nonchiral solitons with the [Formula: see text] rotation symmetry, whereas it shows chiral solitons with the broken [Formula: see text] rotation symmetry. In the generalized JR model, only nonchiral solitons can emerge with only [Formula: see text] rotation symmetry, whereas both chiral and nonchiral solitons can exist with enhanced [Formula: see text] rotation symmetry. Moreover, we find that the nonchiral solitons have C, P symmetries while the chiral solitons do not, which can be explained by the symmetry-invariant lines connecting degenerate vacua. Finally, we find the symmetry correspondence between multiply-degenerate global vacua and solitons such that T, C, P symmetries of a soliton inherit from global minima that are connected by the soliton, which provides a novel tool for the characterization of topological solitons.

Dynamically Emerging Topological Phase Transitions in Nonlinear Interacting Soliton Lattices

We demonstrate dynamical topological phase transitions in evolving Su-Schrieffer-Heeger lattices made of interacting soliton arrays, which are entirely driven by nonlinearity and thereby exemplify an emergent nonlinear topological phenomenon. The phase transitions occur from the topologically trivial-to-nontrivial phase in periodic succession with crossovers from the topologically nontrivial-to-trivial regime. The signature of phase transition is the gap-closing and reopening point, where two extended states are pulled from the bands into the gap to become localized topological edge states. Crossovers occur via decoupling of the edge states from the bulk of the lattice.

Non-Hermitian topological whispering gallery

In 1878, Lord Rayleigh observed the highly celebrated phenomenon of sound waves that creep around the curved gallery of St Paul's Cathedral in London^1,2. These whispering-gallery waves scatter efficiently with little diffraction around an enclosure and have since found applications in ultrasonic fatigue and crack testing, and in the optical sensing of nanoparticles or molecules using silica microscale toroids. Recently, intense research efforts have focused on exploring non-Hermitian systems with cleverly matched gain and loss, facilitating unidirectional invisibility and exotic characteristics of exceptional points^3,4. Likewise, the surge in physics using topological insulators comprising non-trivial symmetry-protected phases has laid the groundwork in reshaping highly unconventional avenues for robust and reflection-free guiding and steering of both sound and light^5,6. Here we construct a topological gallery insulator using sonic crystals made of thermoplastic rods that are decorated with carbon nanotube films, which act as a sonic gain medium by virtue of electro-thermoacoustic coupling. By engineering specific non-Hermiticity textures to the activated rods, we are able to break the chiral symmetry of the whispering-gallery modes, which enables the out-coupling of topological 'audio lasing' modes with the desired handedness. We foresee that these findings will stimulate progress in non-destructive testing and acoustic sensing.

Multi-dimensional wave steering with higher-order topological phononic crystal

The recent discovery and realizations of higher-order topological insulators enrich the fundamental studies on topological phases. Here, we report three-dimensional (3D) wave-steering capabilities enabled by topological boundary states at three different orders in a 3D phononic crystal with nontrivial bulk topology originated from the synergy of mirror symmetry of the unit cell and a non-symmorphic glide symmetry of the lattice. The multitude of topological states brings diverse possibilities of wave manipulations. Through judicious engineering of the boundary modes, we experimentally demonstrate two functionalities at different dimensions: 2D negative refraction of sound wave enabled by a first-order topological surface state with negative dispersion, and a 3D acoustic interferometer leveraging on second-order topological hinge states. Our work showcases that topological modes at different orders promise diverse wave steering applications across different dimensions.

Room temperature electrically pumped topological insulator lasers

Topological insulator lasers (TILs) are a recently introduced family of lasing arrays in which phase locking is achieved through synthetic gauge fields. These single frequency light source arrays operate in the spatially extended edge modes of topologically non-trivial optical lattices. Because of the inherent robustness of topological modes against perturbations and defects, such topological insulator lasers tend to demonstrate higher slope efficiencies as compared to their topologically trivial counterparts. So far, magnetic and non-magnetic optically pumped topological laser arrays as well as electrically pumped TILs that are operating at cryogenic temperatures have been demonstrated. Here we present the first room temperature and electrically pumped topological insulator laser. This laser array, using a structure that mimics the quantum spin Hall effect for photons, generates light at telecom wavelengths and exhibits single frequency emission. Our work is expected to lead to further developments in laser science and technology, while opening up new possibilities in topological photonics.

Conjugated topological interface-states in coupled ring resonators

The optical properties of topological photonics have attracted much interest recently because its potential applications for robust unidirectional transmission that are immune to scattering at disorder. However, researches on topological series coupled ring resonators (T-SCRR) have been much less discussed. The existence of topological interface-states (TIS) in the T-SCRR is described for the first time in this article. An approach has been developed to achieve this goal via the band structure of dielectric binary ring resonators and the Zak phase of each bandgap. It is found that an ultra-high-Q with complete transmission is obtained by the conjugated topological series coupled ring resonators due to the excitation of conjugated topological interface-states, which is different from those in conventional TIS. Furthermore, the problem of transmission decreases resulting from high-Q increases in the traditional photonic system is significantly improved by this approach. These findings could pave a novel path for developing advanced high-Q filters, optical sensors, switches, resonators, communications and quantum information processors.

Non-Hermitian semi-Dirac semi-metals

Recently, many novel and exotic phases have been proposed by considering the role of topology in non-Hermitian systems, and their emergent properties are of wide current interest. In this work we propose the non-Hermitian generalization of semi-Dirac semimetals, which feature a linear dispersion along one momentum direction and a quadratic one along the other. We study the topological phase transitions in such two-dimensional semi-Dirac semimetals in the presence of a particle gain-and-loss term. We show that such a non-Hermitian term creates exceptional points (EPs) originating out of each semi-Dirac point. We map out the topological phase diagram of our model, using winding number and vorticity as topological invariants of the system. By means of numerical and analytical calculations, we examine the nature of edge states for different types of semi-Dirac models and establish bulk-boundary correspondence and absence of the non-Hermitian skin effect, in one class. On the other hand, for other classes of semi-Dirac models with asymmetric hopping, we restore the non-Hermitian skin effect, an anomalous feature usually present in non-Hermitian topological systems.