Third-Harmonic Generation in Photonic Topological Metasurfaces

Polaritonic states trapped by topological defects

The miniaturization of photonic technologies calls for a deliberate integration of diverse materials to enable novel functionalities in chip-scale devices. Topological photonic systems are a promising platform to couple structured light with solid-state matter excitations and establish robust forms of 1D polaritonic transport. Here, we demonstrate a mechanism to efficiently trap mid-IR structured phonon-polaritons in topological defects of a metasurface integrated with hexagonal boron nitride (hBN). These defects, created by stitching displaced domains of a Kekulé-patterned metasurface, sustain localized polaritonic modes that originate from coupling of electromagnetic fields with hBN lattice vibrations. These 0D higher-order topological modes, comprising phononic and photonic components with chiral polarization, are imaged in real- and Fourier-space. The results reveal a singular radiation leakage profile and selective excitation through spin-polarized edge waves at heterogeneous topological interfaces. This offers impactful opportunities to control light-matter waves in their dimensional hierarchy, paving the way for topological polariton shaping, ultrathin structured light sources, and thermal management at the nanoscale.

Fast topological pumps via quantum metric engineering on photonic chips

Topological pumps have garnered substantial attention in physics. However, the requirement for slow evolution speed to satisfy adiabaticity greatly restricts their application in on-chip devices. Here, we discover a direct link between adiabaticity and quantum metric, the real part of quantum geometry that has been relatively less explored compared to its imaginary counterpart, the Berry curvature. We demonstrate that the evolution speed of topological pumps between nontrivial edge states can be increased by reducing the quantum metric via introduction of long-range coupling to the celebrated Rice-Mele model. This fast topological pump can occur without affecting the bulk state evolution, which challenges the common understanding. We experimentally confirm our findings by using a platform consisting of bilayer integrated silicon waveguides operating at telecommunication wavelengths. Our work provides possibilities for lifting topological pumps from the constraints of slow evolution and paves the way toward compact photonic integration.

Localized thermal emission from topological interfaces

The control of thermal radiation by shaping its spatial and spectral emission characteristics plays a key role in many areas of science and engineering. Conventional approaches to tailoring thermal emission using metamaterials are hampered both by the limited spatial resolution of the required subwavelength material structures and by the materials' strong absorption in the infrared. In this work, we demonstrate an approach based on the concept of topology. By changing a single parameter of a multilayer coating, we were able to control the reflection topology of a surface, with the critical point of zero reflection being topologically protected. The boundaries between subcritical and supercritical spatial domains host topological interface states with near-unity thermal emissivity. These topological concepts enable unconventional manipulation of thermal light for applications in thermal management and thermal camouflage.

Topological protection of dual-polarization biphoton states in photonic crystals

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

Sum and difference frequency generation in a valley-photonic-crystal-like topological system

Nonlinear sum frequency generation (SFG) and difference frequency generation (DFG) are fundamental methods to obtain new light sources for various applications. However, most of the on-chip SFG and DFG are based on conventional resonators, lacking robustness against fabrication defects. Here, we demonstrate topologically protected SFG and DFG in a second-order topological photonic system. The mechanism is based on the nonlinear interaction between three high-Q corner modes inside dual topological band gaps. The frequency matching condition for SFG and DFG is precisely satisfied by designing a valley-photonic-crystal-like topological system, which provides more freedoms to tune the corner modes. The topological SFG and DFG are achieved with high conversion efficiency, and the underlying topological physics is revealed. This work opens up avenues toward topologically protected nonlinear frequency conversion, and can find applications in the fields of on-chip single-photon detections and optical quantum memories with robustness against defects.

Bound-Extended Mode Transition in Type-II Synthetic Photonic Weyl Heterostructures

Photonic structures with Weyl points (WPs), including type I and type II, promise nontrivial surface modes and intriguing light manipulations for their three-dimensional topological bands. While previous studies mainly focus on exploring WPs in a uniform Weyl structure, here we establish Weyl heterostructures (i.e., a nonuniform Weyl lattice) with different rotational orientations in the synthetic dimension by nanostructured photonic waveguides. In this work, we unveil a transition between bound and extended modes on the interface of type-II Weyl heterostructures by tuning their rotational phases, despite the reversed topological order across the interface. This mode transition is also manifested from the total transmission to total reflection at the interface. All of these unconventional effects are attributed to the tilted dispersion of type-II Weyl band structure that can lead to mismatched bands and gaps across the interface. As a comparison, the type-I Weyl heterostructures lack the phase transition due to the untilted band structure. This work establishes a flexible scheme of artificial Weyl heterostructures that opens a new avenue toward high-dimensional topological effects and significantly enhances our capabilities in on-chip light manipulations.

Local Markers for Crystalline Topology

Over the last few years, crystalline topology has been used in photonic crystals to realize edge- and corner-localized states that enhance light-matter interactions for potential device applications. However, the band-theoretic approaches currently used to classify bulk topological crystalline phases cannot predict the existence, localization, or spectral isolation of any resulting boundary-localized modes. While interfaces between materials in different crystalline phases must have topological states at some energy, these states need not appear within the band gap, and thus may not be useful for applications. Here, we derive a class of local markers for identifying material topology due to crystalline symmetries, as well as a corresponding measure of topological protection. As our real-space-based approach is inherently local, it immediately reveals the existence and robustness of topological boundary-localized states, yielding a predictive framework for designing topological crystalline heterostructures. Beyond enabling the optimization of device geometries, we anticipate that our framework will also provide a route forward to deriving local markers for other classes of topology that are reliant upon spatial symmetries.

Deep learning improves performance of topological bending waveguides

This study introduced design informatics using deep learning in a topological photonics system and applied it to a topological waveguide with a sharp bending structure to further reduce propagation loss. The sharp bend in the topological waveguide composed of two photonic crystals wherein dielectrics having C6v symmetry were arranged in triangle lattices of hexagons, and the designing of parameters individually for 6 × 6 unit cells near the bending region using deep learning resulted in an output improvement of 60% compared to the initial structure. The proposed structural design method has high versatility and applicability for various topological photonic structures.

Creating pairs of exceptional points for arbitrary polarization control: asymmetric vectorial wavefront modulation

Exceptional points (EPs) can achieve intriguing asymmetric control in non-Hermitian systems due to the degeneracy of eigenstates. Here, we present a general method that extends this specific asymmetric response of EP photonic systems to address any arbitrary fully-polarized light. By rotating the meta-structures at EP, Pancharatnam-Berry (PB) phase can be exclusively encoded on one of the circular polarization-conversion channels. To address any arbitrary wavefront, we superpose the optical signals originating from two orthogonally polarized -yet degenerate- EP eigenmodes. The construction of such orthogonal EP eigenstates pairs is achieved by applying mirror-symmetry to the nanostructure geometry flipping thereby the EP eigenmode handedness from left to right circular polarization. Non-Hermitian reflective PB metasurfaces designed using such EP superposition enable arbitrary, yet unidirectional, vectorial wavefront shaping devices. Our results open new avenues for topological wave control and illustrate the capabilities of topological photonics to distinctively operate on arbitrary polarization-state with enhanced performances.

Demonstration of a highly efficient topological vertical coupler

A defect structure is proposed for enhancing the coupling efficiency of vertically incident circularly polarized light in a topological waveguide. In the topological edge-state waveguide based on triangle lattices of hexagons consisting of six nanoholes respecting C6v symmetry in a silicon optical circuit, the vertical coupling rate is improved by removing the nanoholes from one hexagonal cell near the line. The coupling efficiency was evaluated with and without the defect structure. The introduced defect structure operates suitably for focused beams of left- and right-handed circularly polarized light, enhancing the optical communication wavelength bandwidth by up to 10 dB.

Enhancing Up-Conversion Luminescence Using Dielectric Metasurfaces: Role of the Quality Factor of Resonance at a Pumping Wavelength

Photonic applications of up-conversion luminescence (UCL) suffer from poor external quantum yield owing to a low absorption cross-section of UCL nanoparticles (UCNPs) doped with lanthanide ions. In this regard, plasmonic nanostructures have been proposed for enhancing UCL intensity through strong electromagnetic local-field enhancement; however, their intrinsic ohmic loss opens additional nonradiative decay channels. Herein, we demonstrate that dielectric metasurfaces can overcome this disadvantage. A periodic array of amorphous-silicon nanodisks serves as a metasurface on which a layer of UCNPs is self-assembled. Sharp resonances supported by the metasurface overlap the absorption wavelength (λ = 980 nm) of UCNPs to excite them, resulting in the enhancement of UCL intensity. We further sharpen the resonances through rapid thermal annealing (RTA) of the metasurface, crystallizing silicon to reduce intrinsic optical losses. By optimizing the RTA condition (at 1000 °C for 20 min in N2/H2 (3 vol %) atmosphere), the resonance quality factor improves from 17.2 to 32.9, accompanied by an increase in the enhancement factor of the UCL intensity from 86- to over 600-fold. Moreover, a reduction in the intrinsic optical losses mitigates the UCL thermal quenching under a high excitation density. These findings provide a strategy for increasing light-matter interactions in nanophotonic composite systems and promote UCNP applications.

Topologically enhanced nonlinear optical response of graphene nanoribbon heterojunctions

We study the nonlinear optical properties of heterojunctions made of graphene nanoribbons (GNRs) consisting of two segments with either the same or different topological properties. By utilizing a quantum mechanical approach that incorporates distant-neighbor interactions, we demonstrate that the presence of topological interface states significantly enhances the second- and third-order nonlinear optical response of GNR heterojunctions that are created by merging two topologically inequivalent GNRs. Specifically, GNR heterojunctions with topological interface states display third-order harmonic hyperpolarizabilities that are more than two orders of magnitude larger than those of their similarly sized counterparts without topological interface states, whereas the second-order harmonic hyperpolarizabilities exhibit a more than ten-fold contrast between heterojunctions with and without topological interface states. Additionally, we find that the topological state at the interface between two topologically distinct GNRs can induce a noticeable red-shift of the quantum plasmon frequency of the heterojunctions. Our results reveal a general and profound connection between the existence of topological states and an enhanced nonlinear optical response of graphene nanostructures and possible other photonic systems.

Absence of Topological Protection of the Interface States in Z_{2} Photonic Crystals

Inspired from electronic systems, topological photonics aims to engineer new optical devices with robust properties. In many cases, the ideas from topological phases protected by internal symmetries in fermionic systems are extended to those protected by crystalline symmetries. One such popular photonic crystal model was proposed by Wu and Hu in 2015 for realizing a bosonic Z_{2} topological crystalline insulator with robust topological edge states, which led to intense theoretical and experimental studies. However, a rigorous relationship between the bulk topology and edge properties for this model, which is central to evaluating its advantage over traditional photonic designs, has never been established. In this Letter, we revisit the expanded and shrunken honeycomb lattice structures proposed by Wu and Hu and show that they are topologically trivial in the sense that symmetric, localized Wannier functions can be constructed. We show that the Z and Z_{2} type classifications of the Wu-Hu model are equivalent to the C_{2}T protected Euler class and the second Stiefel-Whitney class, respectively, with the latter characterizing the full valence bands of the Wu-Hu model, indicating only a higher order topological insulator. Additionally, we show that the Wu-Hu interface states can be gapped by a uniform topology preserving C_{6} and T symmetric perturbation, which demonstrates the trivial nature of the interface. Our result reveals that topology is not a necessary condition for the reported helical edge states in many photonics systems and opens new possibilities for interface engineering that may not be constrained by topological considerations.

Spin-dependent properties of optical modes guided by adiabatic trapping potentials in photonic Dirac metasurfaces

The Dirac-like dispersion in photonic systems makes it possible to mimic the dispersion of relativistic spin-1/2 particles, which led to the development of the concept of photonic topological insulators. Despite recent demonstrations of various topological photonic phases, the full potential offered by Dirac photonic systems, specifically their ability to emulate the spin degree of freedom-referred to as pseudo-spin-beyond topological boundary modes has remained underexplored. Here we demonstrate that photonic Dirac metasurfaces with smooth one-dimensional trapping gauge potentials serve as effective waveguides with modes carrying pseudo-spin. We show that spatially varying gauge potentials act unevenly on the two pseudo-spins due to their different field distributions, which enables control of guided modes by their spin, a property that is unattainable with conventional optical waveguides. Silicon nanophotonic metasurfaces are used to experimentally confirm the properties of these guided modes and reveal their distinct spin-dependent radiative character; modes of opposite pseudo-spin exhibit disparate radiative lifetimes and couple differently to incident light. The spin-dependent field distributions and radiative lifetimes of their guided modes indicate that photonic Dirac metasurfaces could be used for spin-multiplexing, controlling the characteristics of optical guided modes, and tuning light-matter interactions with photonic pseudo-spins.

Simultaneous manipulation of spatial fundamental and harmonic electromagnetic waves by microwave nonlinear metasurfaces

In the area of manipulating the spatial electromagnetic (EM) waves fields, the metasurfaces have become much more attractive and powerful in recent years. Here, we propose a design to realize the simultaneous control of spatial fundamental and harmonic EM waves applying nonlinear metasurfaces in microwave band. The proposed meta-atom composed of three topological layers which are transmitting antenna, nonlinear wave guiding and receiving antenna respectively. And the critical factor of generating the harmonic is the nonlinear chip which is integrated into the middle layer. The microstrip power divider and phase shifter in each meta-atom are preciously tailored to actualize the spatial control of the fundamental and harmonic transmission beams in the far field. One prototype of the nonlinear metasurfaces is fabricated and corresponding radiation patterns of fundamental and harmonic modes are observed very well in the experience that can verify the validity of our proposed method.

Exceptional points and non-Hermitian photonics at the nanoscale

Exceptional points (EPs) arising in non-Hermitian systems have led to a variety of intriguing wave phenomena, and have been attracting increased interest in various physical platforms. In this Review, we highlight the latest fundamental advances in the context of EPs in various nanoscale systems, and overview the theoretical progress related to EPs, including higher-order EPs, bulk Fermi arcs and Weyl exceptional rings. We peek into EP-associated emerging technologies, in particular focusing on the influence of noise for sensing near EPs, improving the efficiency in asymmetric transmission based on EPs, optical isolators in nonlinear EP systems and novel concepts to implement EPs in topological photonics. We also discuss the constraints and limitations of the applications relying on EPs, and offer parting thoughts about promising ways to tackle them for advanced nanophotonic 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.

Second harmonic generation by matching the phase distributions of topological corner and edge states

Second harmonic generation (SHG) in topological photonic crystals is chiefly concerned with frequency conversion between the same topological states. However, little attention has been paid to the effect of coupling between different topological states on the SHG. In this study, we propose a method for achieving optimal SHG in a topological cavity by matching the phase distributions of the electric fields of the topological corner state (TCS) and topological edge state (TES). Our results show that the intrinsic efficiency can be improved when the phase distributions of the fundamental wave within the TCS and the second harmonic wave within the TES have the same symmetry. Otherwise, conversion efficiency will be greatly inhibited. With this method, we achieved an optimal intrinsic efficiency of 0.165%. Such a platform may enable the development of integrated nanoscale light sources and on-chip frequency converters.

Photonic Dirac cavities with spatially varying mass term

In recent years, photonics has proven itself as an excellent platform for emulation of relativistic phenomena. Here, we show an example of relativistic-like trapping in photonic system that realizes Dirac-like dispersion with spatially inhomogeneous mass term. The modes trapped by such cavities, their energy levels, and corresponding orbitals are then characterized through optical imaging in real and momentum space. The fabricated cavities host a hierarchy of photonic modes with distinct radiation profiles directly analogous to various atomic orbitals endowed with unique characteristics, such as pseudo-particle-hall symmetry and spin degeneracy, and they carry topological charge which gives rise to radiative profiles with angular momentum. We demonstrate that these modes can be directionally excited by pseudo-spin-polarized boundary states. In addition to the fundamental interest in the structure of these pseudo-relativistic orbitals, the proposed system offers a route for designing new types of nanophotonic devices, spin-full resonators and topological light sources compatible with integrated photonics platforms.

Coherent Control of Topological States in an Integrated Waveguide Lattice

Topological photonics holds the promise for enhanced robustness of light localization and propagation enabled by the global symmetries of the system. While traditional designs of topological structures rely on lattice symmetries, there is an alternative strategy based on accidentally degenerate modes of the individual meta-atoms. Using this concept, we experimentally realize topological edge state in an array of silicon nanostructured waveguides, each hosting a pair of degenerate modes at telecom wavelengths. Exploiting the hybrid nature of the topological mode, we implement its coherent control by adjusting the phase between the degenerate modes and demonstrating selective excitation of bulk or edge states. The resulting field distribution is imaged via third harmonic generation showing the localization of topological modes as a function of the relative phase of the excitations. Our results highlight the impact of engineered accidental degeneracies on the formation of topological phases, extending the opportunities stemming from topological nanophotonic systems.

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.

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.

Topologically tuned terahertz confinement in a nonlinear photonic chip

Compact terahertz (THz) functional devices are greatly sought after for high-speed wireless communication, biochemical sensing, and non-destructive inspection. However, controlled THz generation, along with transport and detection, has remained a challenge especially for chip-scale devices due to low-coupling efficiency and unavoidable absorption losses. Here, based on the topological protection of electromagnetic waves, we demonstrate nonlinear generation and topologically tuned confinement of THz waves in an engineered lithium niobate chip forming a wedge-shaped Su-Schrieffer-Heeger lattice. Experimentally measured band structures provide direct visualization of the THz localization in the momentum space, while robustness of the confined mode against chiral perturbations is also analyzed and compared for both topologically trivial and nontrivial regimes. Such topological control of THz waves may bring about new possibilities in the realization of THz integrated circuits, promising for advanced photonic applications.

Engineering Plasmonic Environments for 2D Materials and 2D-Based Photodetectors

Two-dimensional layered materials are considered ideal platforms to study novel small-scale optoelectronic devices due to their unique electronic structures and fantastic physical properties. However, it is urgent to further improve the light–matter interaction in these materials because their light absorption efficiency is limited by the atomically thin thickness. One of the promising approaches is to engineer the plasmonic environment around 2D materials for modulating light–matter interaction in 2D materials. This method greatly benefits from the advances in the development of nanofabrication and out-plane van der Waals interaction of 2D materials. In this paper, we review a series of recent works on 2D materials integrated with plasmonic environments, including the plasmonic-enhanced photoluminescence quantum yield, strong coupling between plasmons and excitons, nonlinear optics in plasmonic nanocavities, manipulation of chiral optical signals in hybrid nanostructures, and the improvement of the performance of optoelectronic devices based on composite systems.

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.

Extended topological valley-locked surface acoustic waves

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

Highly efficient vertical coupling to a topological waveguide with defect structure

In this study, we propose a defect structure that enhances the vertical coupling efficiency of circularly polarized light incident on topological waveguides consisting of triangle nanoholes with C_6v symmetry arranged in honeycomb lattice. The defect structure was formed by removing triangle nanoholes from a certain hexagonal unit cell around the topological waveguide. As a result of comparing the coupling efficiency with and without the defect structure through three-dimensional finite-difference time-domain analysis, significant improvement in the vertical coupling efficiency was observed over the entire telecom C band (4460%@1530 nm). In addition, it was also found that the wavelength showing maximum coupling efficiency can be controlled over the entire C band by changing the arrangement of the dielectric around the defect structure.

Second harmonic generation enhancement and directional emission from topological corner state based on the quantum spin Hall effect

Topological corner state has attracted much research interests since it does not obey the conventional bulk-edge correspondence and enables tightly confined light within small volumes. In this work, we demonstrate an enhanced second harmonic generation (SHG) from a topological corner state and its directional emission. To this end, we design an all-dielectric topological photonic crystal based on optical quantum spin Hall effect. In this framework, pseudospin states of photons, topological phase, and topological corner state are subsequently constructed by engineering the structures. It is shown that a high Q-factor of 3.66×10¹¹ can be obtained at the corner state, showing strong confinement of light at the corner. Consequently, SHG is significantly boosted and manifests directional out-of-plane emission. More importantly, the enhanced SHG has robustness against a broad class of defects. These demonstrated properties offer practical advantages for integrated optical circuits.

Probing Rotated Weyl Physics on Nonlinear Lithium Niobate-on-Insulator Chips

Topological photonics, featured by stable topological edge states resistant to perturbations, has been utilized to design robust integrated devices. Here, we present a study exploring the intriguing topological rotated Weyl physics in a 3D parameter space based on quaternary waveguide arrays on lithium niobate-on-insulator (LNOI) chips. Unlike previous works that focus on the Fermi arc surface states of a single Weyl structure, we can experimentally construct arbitrary interfaces between two Weyl structures whose orientations can be freely rotated in the synthetic parameter space. This intriguing system was difficult to realize in usual 3D Weyl semimetals due to lattice mismatch. We found whether the interface can host gapless topological interface states or not is determined by the relative rotational directions of the two Weyl structures. In the experiment, we have probed the local characteristics of the TISs through linear optical transmission and nonlinear second harmonic generation. Our study introduces a novel path to explore topological photonics on LNOI chips and various applications in integrated nonlinear and quantum optics.

Nonlinear Imaging of Nanoscale Topological Corner States

Topological states of light represent counterintuitive optical modes localized at boundaries of finite-size optical structures that originate from the properties of the bulk. Being defined by bulk properties, such boundary states are insensitive to certain types of perturbations, thus naturally enhancing robustness of photonic circuitries. Conventionally, the N-dimensional bulk modes correspond to (N - 1)-dimensional boundary states. The higher-order bulk-boundary correspondence relates N-dimensional bulk to boundary states with dimensionality reduced by more than 1. A special interest lies in miniaturization of such higher-order topological states to the nanoscale. Here, we realize nanoscale topological corner states in metasurfaces with C₆-symmetric honeycomb lattices. We directly observe nanoscale topology-empowered edge and corner localizations of light and enhancement of light-matter interactions via a nonlinear imaging technique. Control of light at the nanoscale empowered by topology may facilitate miniaturization and on-chip integration of classical and quantum photonic devices.

Dynamically reconfigurable topological states in photonic crystals with liquid crystals

Dynamically tunable and reconfigurable topological states are realized in higher-order topological insulators with the liquid crystal (LC). By changing the loading voltage of the LC, the eigenfrequency of the edge and corner states can be tuned, but even more important is that the edge state and corner state with the same frequency are realized. Based on this reconfigurability of topological states, optical routers and lasers with multiple topological states can be realized. Our results may be applied to topological optical circuits and provide new ideas for optical field localization and manipulation.

Probing Band Topology Using Modulational Instability

We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations of the nonlinear Bloch waves are sensitive to topological band inversions. At longer timescales, nonlinear wave mixing induces spreading of energy through the entire band and spontaneous creation of wave polarization singularities determined by the band Chern number. Our analytical and numerical results establish modulational instability as a tool to probe bulk topological invariants and create topologically nontrivial wave fields.

Critical couplings in topological-insulator waveguide-resonator systems observed in elastic waves

Waveguides and resonators are core components in the large-scale integration of electronics, photonics and phononics, both in existing and future scenarios. In certain situations, there is critical coupling of the two components; i.e. no energy passes through the waveguide after the incoming wave couples into the resonator. The transmission spectral characteristics resulting from this phenomenon are highly advantageous for signal filtering, switching, multiplexing and sensing. In the present study, adopting an elastic-wave platform, we introduce topological insulator (TI), a remarkable achievement in condensed matter physics over the past decade, into a classical waveguide-ring-resonator configuration. Along with basic similarities with classical systems, a TI system has important differences and advantages, mostly owing to the spin-momentum locked transmission states at the TI boundaries. As an example, a two-port TI waveguide resonator can fundamentally eliminate upstream reflections while completely retaining useful transmission spectral characteristics, and maximize the energy in the resonator, with possible applications being novel signal processing, gyro/sensing, lasering, energy harvesting and intense wave-matter interactions, using phonons, photons or even electrons. The present work further enhances confidence in using topological protection for practical device performance and functionalities, especially considering the crucial advantage of introducing (pseudo)spins to existing conventional configurations. More in-depth research on advancing phononics/photonics, especially on-chip, is foreseen.

Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths

Topological on-chip photonics based on tailored photonic crystals (PhCs) that emulate quantum valley-Hall effects has recently gained widespread interest owing to its promise of robust unidirectional transport of classical and quantum information. We present a direct quantitative evaluation of topological photonic edge eigenstates and their transport properties in the telecom wavelength range using phase-resolved near-field optical microscopy. Experimentally visualizing the detailed sub-wavelength structure of these modes propagating along the interface between two topologically non-trivial mirror-symmetric lattices allows us to map their dispersion relation and differentiate between the contributions of several higher-order Bloch harmonics. Selective probing of forward- and backward-propagating modes as defined by their phase velocities enables direct quantification of topological robustness. Studying near-field propagation in controlled defects allows us to extract upper limits of topological protection in on-chip photonic systems in comparison with conventional PhC waveguides. We find that protected edge states are two orders of magnitude more robust than modes of conventional PhC waveguides. This direct experimental quantification of topological robustness comprises a crucial step toward the application of topologically protected guiding in integrated photonics, allowing for unprecedented error-free photonic quantum networks.

Near- and Far-Field Excitation of Topological Plasmonic Metasurfaces

The breathing honeycomb lattice hosts a topologically non-trivial bulk phase due to the crystalline-symmetry of the system. Pseudospin-dependent edge states, which emerge at the interface between trivial and non-trivial regions, can be used for the directional propagation of energy. Using the plasmonic metasurface as an example system, we probe these states in the near- and far-field using a semi-analytical model. We provide the conditions under which directionality was observed and show that it is source position dependent. By probing with circularly-polarised magnetic dipoles out of the plane, we first characterise modes along the interface in terms of the enhancement of source emissions due to the metasurface. We then excite from the far-field with non-zero orbital angular momentum beams. The position-dependent directionality holds true for all classical wave systems with a breathing honeycomb lattice. Our results show that a metasurface in combination with a chiral two-dimensional material, could be used to guide light effectively on the nanoscale.

Nontrivial coupling of light into a defect: the interplay of nonlinearity and topology

The flourishing of topological photonics in the last decade was achieved mainly due to developments in linear topological photonic structures. However, when nonlinearity is introduced, many intriguing questions arise. For example, are there universal fingerprints of the underlying topology when modes are coupled by nonlinearity, and what can happen to topological invariants during nonlinear propagation? To explore these questions, we experimentally demonstrate nonlinearity-induced coupling of light into topologically protected edge states using a photonic platform and develop a general theoretical framework for interpreting the mode-coupling dynamics in nonlinear topological systems. Performed on laser-written photonic Su-Schrieffer-Heeger lattices, our experiments show the nonlinear coupling of light into a nontrivial edge or interface defect channel that is otherwise not permissible due to topological protection. Our theory explains all the observations well. Furthermore, we introduce the concepts of inherited and emergent nonlinear topological phenomena as well as a protocol capable of revealing the interplay of nonlinearity and topology. These concepts are applicable to other nonlinear topological systems, both in higher dimensions and beyond our photonic platform.

Room-temperature lasing from nanophotonic topological cavities

The study of topological phases of light underpins a promising paradigm for engineering disorder-immune compact photonic devices with unusual properties. Combined with an optical gain, topological photonic structures provide a novel platform for micro- and nanoscale lasers, which could benefit from nontrivial band topology and spatially localized gap states. Here, we propose and demonstrate experimentally active nanophotonic topological cavities incorporating III-V semiconductor quantum wells as a gain medium in the structure. We observe room-temperature lasing with a narrow spectrum, high coherence, and threshold behaviour. The emitted beam hosts a singularity encoded by a triade cavity mode that resides in the bandgap of two interfaced valley-Hall periodic photonic lattices with opposite parity breaking. Our findings make a step towards topologically controlled ultrasmall light sources with nontrivial radiation characteristics.

Observation of Floquet solitons in a topological bandgap

Topological protection is a universal phenomenon that applies to electronic, photonic, ultracold atomic, mechanical, and other systems. The vast majority of research in these systems has explored the linear domain, where interparticle interactions are negligible. We experimentally observed solitons-waves that propagate without changing shape as a result of nonlinearity-in a photonic Floquet topological insulator. These solitons exhibited distinct behavior in that they executed cyclotron-like orbits associated with the underlying topology. Specifically, we used a waveguide array with periodic variations along the waveguide axis, giving rise to nonzero winding number, and the nonlinearity arose from the optical Kerr effect. This result applies to a range of bosonic systems because it is described by the focusing nonlinear Schrödinger equation (equivalently, the attractive Gross-Pitaevskii equation).

Enhanced Nonlinear Light Generation in Oligomers of Silicon Nanoparticles under Vector Beam Illumination

All-dielectric nanoparticle oligomers have recently emerged as promising candidates for nonlinear optical applications. Their highly resonant collective modes, however, are difficult to access by linearly polarized beams due to symmetry restraints. In this paper, we propose a new way to increase the efficiency of nonlinear processes in all-dielectric oligomers by tightly focused azimuthally polarized cylindrical vector beam illumination. We demonstrate two orders enhancement of the third-harmonic generation signal, governed by a collective optical mode represented by out-of-plane magnetic dipoles. Crucially, the collective mode is characterized by strong electromagnetic field localization in the bulk of the nonlinear material. For comparison, we measure third-harmonic generation in the same oligomer pumped with linearly and radially polarized fundamental beams, which both show significantly lower harmonic output. We also provide numerical analysis to describe and characterize the observed effect. Our findings open a new route to enhance and modulate the third-harmonic generation efficiency of Mie-resonant isolated nanostructures by tailoring the polarization of the pump beam.

Four-wave mixing of topological edge plasmons in graphene metasurfaces

We study topologically protected four-wave mixing (FWM) interactions in a plasmonic metasurface consisting of a periodic array of nanoholes in a graphene sheet, which exhibits a wide topological bandgap at terahertz frequencies upon the breaking of time reversal symmetry by a static magnetic field. We demonstrate that due to the significant nonlinearity enhancement and large life time of graphene plasmons in specific configurations, a net gain of FWM interaction of plasmonic edge states located in the topological bandgap can be achieved with a pump power of less than 10 nW. In particular, we find that the effective nonlinear edge-waveguide coefficient is about γ ≃ 1.1 × 10¹³ W^-1 m^-1, i.e., more than 10 orders of magnitude larger than that of commonly used, highly nonlinear silicon photonic nanowires. These findings could pave a new way for developing ultralow-power-consumption, highly integrated, and robust active photonic systems at deep-subwavelength scale for applications in quantum communications and information processing.

Z2 Photonic Topological Insulators in the Visible Wavelength Range for Robust Nanoscale Photonics

Topological photonics provides an ideal platform for demonstrating novel band topology concepts, which are also promising for robust waveguiding, communication, and computation applications. However, many challenges such as extremely large device footprint and functionality at short wavelengths remain to be solved which are required to make practical and useful devices that can also couple to electronic excitations in many important organic and inorganic semiconductors. In this letter, we report an experimental realization of Z₂ photonic topological insulators with their topological edge state energies spanning across the visible wavelength range including in the sub-500 nm regime, which requires highly optimized nanofabrication. The photonic structures are based on deformed hexagonal lattices with preserved 6-fold rotational symmetry patterned on suspended SiN_x membranes. The experimentally measured energy-momentum dispersion of the topological lattices directly shows topological band inversion by the swapping of the brightness of the bulk energy bands, and also the helical edge states when the measurement is taken near the topological interface. The robust topological transport of the helical edge modes in real space is demonstrated by successfully guiding circularly polarized light beams unidirectionally through sharp kinks without significant signal loss. This work paves the way for small footprint photonic topological devices working in the short wavelength range that can also be utilized to couple to excitons for unconventional light-matter interactions at the nanoscale.