Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing

Flexible self-supporting photonic crystals: Fabrications and responsive structural colors

Photonic crystals (PCs) play an increasingly significant role in anti-counterfeiting, sensors, displays, and other fields due to their tunable structural colors produced by light manipulation of photonic stop bands. Flexible self-supporting photonic crystals (FSPCs) eliminate the requirement for conventional structures to rely on the existence of hard substrates, as well as the problem of poor mechanical qualities caused by the stiffness of the building blocks. Meanwhile, diverse production techniques and materials provide FSPCs with varied stimulus-responsive color-changing capacities, thus they have received an abundance of focus. This review summarizes the preparation strategies and variable structural colors of FSPCs. First, a series of preparation strategies by integrating polymers with PCs are summarized, including assembly of colloidal spheres on flexible substrates, polymer packaging, polymer-based direct assembly, nanoimprinting, and 3D printing. Subsequently, variable structural colors of FSPCs with different stimulations, such as viewing angle, chemical stimulation (solvents, ions, pH, biomolecules, etc.), temperature, mechanical/magnetic stress, and light, are described in detail. Finally, the outlook and challenges regarding FSPCs are presented, and several potential directions for their fabrication and application are discussed. It's believed that FSPCs will be a valuable platform for advancing the practical implementation of optical metamaterials.

Parity-Frequency-Space Elastic Spin Control of Wave Routing in Topological Phononic Circuits

Topological phononic cavities, such as ring resonators with topological whispering gallery modes (TWGMs), offer a flexible platform for the realization of robust phononic circuits. However, the chiral mechanism governing TWGMs and their selective routing in integrated phononic circuits remain unclear. This work reveals, both experimentally and theoretically, that at a phononic topological interface, the elastic spin texture is intricately linked to, and can be explained through a knowledge of, the phonon eigenmodes inside each unit cell. Furthermore, for paired, counterpropagating TWGMs based on such interfaces in a waveguide resonator, this study demonstrates that the elastic spin exhibits locking at discrete frequencies. Backed up by theory, experiments on kHz TWGMs in thin honeycomb-lattice aluminum plates bored with clover-leaf shaped holes show that together with this spin-texture related angular-momentum locking mechanism at a single topological interface, there are triplicate parity-frequency-space selective wave routing mechanisms. In the future, these mechanisms can be harnessed for the versatile manipulation of elastic-spin based routing in phononic topological insulators.

Photonic topological phase transition induced by material phase transition

Photonic topological insulators (PTIs) have been proposed as an analogy to topological insulators in electronic systems. In particular, two-dimensional PTIs have gained attention for the integrated circuit applications. However, controlling the topological phase after fabrication is difficult because the photonic topology requires the built-in specific structures. This study experimentally demonstrates the band inversion in two-dimensional PTI induced by the phase transition of deliberately designed nanopatterns of a phase change material, Ge2Sb2Te5 (GST), which indicates the first observation of the photonic topological phase transition in two-dimensional PTI with changes in the Chern number. This approach allows us to directly alter the topological invariants, which is achieved by symmetry-breaking perturbation through GST nanopatterns with different symmetry from original PTI. The success of our scheme is attributed to the ultrafine lithographic alignment technologies of GST nanopatterns. These results demonstrate how to control photonic topological properties in a reconfigurable manner, providing insight into the possibilities for reconfigurable photonic processing circuits.

Local control of polarization and geometric phase in thermal metasurfaces

Thermal emission from a hot body is inherently challenging to control due to its incoherent nature. Recent advances have shown that patterned surfaces can transform thermal emission into partially coherent beams with tailored directionality and frequency selectivity. Here we experimentally demonstrate polarization-selective, unidirectional and narrowband thermal emission using single-layer metasurfaces. By implementing polarization gradients across the surface, we unveil a generalization of the photonic Rashba effect from circular polarizations to any pair of orthogonal polarizations and apply it to thermal emission. Leveraging pointwise specification of arbitrary elliptical polarization, we implement a thermal geometric phase and leverage it to prove previous theoretical predictions that asymmetric chiral emission is possible without violating reciprocity. This general platform can be extended to other frequency regimes in efforts to compactify metasurface optics technologies without the need for external coherent sources.

Possible gapless helical edge states in hydrogenated graphene

Electronic band structures in hydrogenated graphene are theoretically investigated by means of first-principle calculations and an effective tight-binding model. It is shown that regularly designed hydrogenation to graphene gives rise to a large band gap about 1 eV. Remarkably, by changing the spatial pattern of the hydrogenation, topologically distinct states can be realized, where the topological nontriviality is detected by C 2 parity indices in bulk and confirmed by the existence of gapless edge/interface states as protected by the mirror and sublattice symmetries. The analysis of the wave functions reveals that the helical edge states in hydrogenated graphene with the appropriate design carry pseudospin currents that are reminiscent of the quantum spin Hall effect. Our work shows the potential of hydrogenated graphene in pseudospin-based device applications.

Terahertz flexible multiplexing chip enabled by synthetic topological phase transitions

Flexible multiplexing chips that permit reconfigurable multidimensional channel utilization are indispensable for revolutionary 6G terahertz communications, but the insufficient manipulation capability of terahertz waves prevents their practical implementation. Herein, we propose the first experimental demonstration of a flexible multiplexing chip for terahertz communication by revealing the unique mechanism of topological phase (TP) transition and perseveration in a heterogeneously coupled bilayer valley Hall topological photonic system. The synthetic and individual TPs operated in the coupled and decoupled states enable controllable on-chip modular TP transitions and subchannel switching. Two time-frequency interleaved subchannels support 10- and 12-Gbit/s QAM-16 high-speed data streams along corresponding paths over carriers of 120 and 130 GHz with 2.5- and 3-GHz bandwidths, respectively. This work unlocks interlayer heterogeneous TPs for inspiring ingenious on-chip terahertz-wave regulation, allowing functionality-reconfigurable, compactly integrated and CMOS-compatible chips.

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.

Dynamic Optical Encryption Fueled via Tunable Mechanical Composite Micrograting Systems

Optical grating devices based on micro/nanostructured functional surfaces are widely employed to precisely manipulate light propagation, which is significant for information technologies, optical data storage, and light sensors. However, the parameters of rigid periodic structures are difficult to tune after manufacturing, which seriously limits their capacity for in situ light manipulation. Here, a novel anti-eavesdropping, anti-damage, and anti-tamper dynamic optical encryption strategy are reported via tunable mechanical composite wrinkle micrograting encryption systems (MCWGES). By mechanically composing multiple in-situ tunable ordered wrinkle gratings, the dynamic keys with large space capacity are generated to obtain encrypted diffraction patterns, which can provide a higher level of security for the encrypted systems. Furthermore, a multiple grating cone diffraction model is proposed to reveal the dynamic optical encryption principle of MCWGES. Optical encryption communication using dynamic keys has the effect of preventing eavesdropping, damage, and tampering. This dynamic encryption method based on optical manipulation of wrinkle grating demonstrates the potential applications of micro/nanostructured functional surfaces in the field of information security.

Photonic Molecule Approach to Multiorbital Topology

The concepts of topology provide a powerful tool to tailor the propagation and localization of the waves. While electrons have only two available spin states, engineered degeneracies of photonic modes provide novel opportunities resembling spin degrees of freedom in condensed matter. Here, we tailor such degeneracies for the array of femtosecond laser written waveguides in the optical range exploiting the idea of photonic molecules: clusters of strongly coupled waveguides. In our experiments, we observe unconventional topological modes protected by the Z3 invariant arising due to the interplay of interorbital coupling and geometric dimerization mechanism. We track multiple topological transitions in the system with the change in the lattice spacings and excitation wavelength. This strategy opens an avenue for designing novel types of photonic topological phases and states.

Pseudo-spin switches and Aharonov-Bohm effect for topological boundary modes

Topological boundary modes in electronic and classical-wave systems exhibit fascinating properties. In photonics, topological nature of boundary modes can make them robust and endows them with an additional internal structure-pseudo-spins. Here, we introduce heterogeneous boundary modes, which are based on mixing two of the most widely used topological photonics platforms-the pseudo-spin-Hall-like and valley-Hall photonic topological insulators. We predict and confirm experimentally that transformation between the two, realized by altering the lattice geometry, enables a continuum of boundary states carrying both pseudo-spin and valley degrees of freedom (DoFs). When applied adiabatically, this leads to conversion between pseudo-spin and valley polarization. We show that such evolution gives rise to a geometrical phase associated with the synthetic gauge fields, which is confirmed via an Aharonov-Bohm type experiment on a silicon chip. Our results unveil a versatile approach to manipulating properties of topological photonic states and envision topological photonics as a powerful platform for devices based on synthetic DoFs.

Topological photonic crystal nanowire array laser with bulk states

A topological photonic crystal InGaAsP/InP core-shell nanowire array laser with bulk states operating in the 1550 nm band is proposed and simulated. By optimizing the structure parameters, high Q factor of 1.2 × 105 and side-mode suppression ratio of 13.2 dB are obtained, which are 28.6 and 4.6 times that of a uniform nanowire array, respectively. The threshold and maximum output are 17% lower and 613% higher than that of the uniform nanowire array laser, respectively, due to the narrower nanowire slits and stronger optical confinement. In addition, a low beam divergence angle of 2° is obtained due to the topological protection. This work may pave the way for the development of high-output, low-threshold, low-beam-divergence nanolasers.

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

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

Topological electronic states in holey graphyne

We unveil that the holey graphyne (HGY), a two-dimensional carbon allotrope where benzene rings are connected by two -C≡C- bonds fabricated recently in a bottom-up way, exhibits topological electronic states. Using first-principles calculations and Wannier tight-binding modeling, we discover a higher-order topological invariant associated withC2symmetry of the material, and show that the resultant corner modes appear in nanoflakes matching to the structure of precursor reported previously, which are ready for direct experimental observations. In addition, we find that a band inversion between emergentg-like andh-like orbitals gives rise to a nontrivial topology characterized byZ2invariant protected by an energy gap as large as 0.52 eV, manifesting helical edge states mimicking those in the prominent quantum spin Hall effect, which can be accessed experimentally after hydrogenation in HGY. We hope these findings trigger interests towards exploring the topological electronic states in HGY and related future electronics applications.

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.

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.

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.

Fermi Arc Reconstruction in Synthetic Photonic Lattice

The chiral surface states of Weyl semimetals have an open Fermi surface called a Fermi arc. At the interface between two Weyl semimetals, these Fermi arcs are predicted to hybridize and alter their connectivity. In this Letter, we numerically study a one-dimensional (1D) dielectric trilayer grating where the relative displacements between adjacent layers play the role of two synthetic momenta. The lattice emulates 3D crystals without time-reversal symmetry, including Weyl semimetal, nodal line semimetal, and Chern insulator. Besides showing the phase transition between Weyl semimetal and Chern insulator at telecom wavelength, this system allows us to observe the Fermi arc reconstruction between two Weyl semimetals, confirming the theoretical predictions.

Adiabatic topological photonic interfaces

Topological phases of matter have been attracting significant attention across diverse fields, from inherently quantum systems to classical photonic and acoustic metamaterials. In photonics, topological phases offer resilience and bring novel opportunities to control light with pseudo-spins. However, topological photonic systems can suffer from limitations, such as breakdown of topological properties due to their symmetry-protected origin and radiative leakage. Here we introduce adiabatic topological photonic interfaces, which help to overcome these issues. We predict and experimentally confirm that topological metasurfaces with slowly varying synthetic gauge fields significantly improve the guiding features of spin-Hall and valley-Hall topological structures commonly used in the design of topological photonic devices. Adiabatic variation in the domain wall profiles leads to the delocalization of topological boundary modes, making them less sensitive to details of the lattice, perceiving the structure as an effectively homogeneous Dirac metasurface. As a result, the modes showcase improved bandgap crossing, longer radiative lifetimes and propagation distances.

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.

Unique Huygens-Fresnel electromagnetic transportation of chiral Dirac wavelet in topological photonic crystal

Light propagates in various ways depending on environment, including uniform medium, surface/interface and photonic crystals, which appears ubiquitously in daily life and has been exploited for advanced optics technology. We unveiled that a topological photonic crystal exhibits unique electromagnetic (EM) transport properties originating from the Dirac frequency dispersion and multicomponent spinor eigenmodes. Measuring precisely local Poynting vectors in microstrips of honeycomb structure where optics topology emerges upon a band gap opening in the Dirac dispersion and a p-d band inversion induced by a Kekulé-type distortion respecting C_6v symmetry, we showed that a chiral wavelet induces a global EM transportation circulating in the direction counter to the source, which is intimately related to the topological band gap specified by a negative Dirac mass. This brand-new Huygens-Fresnel phenomenon can be considered as the counterpart of negative refraction of EM plane waves associated with upwardly convex dispersions of photonic crystals, and our present finding is expected to open a new window for photonic innovations.

Photonic-crystal-based high-performance ring resonator using a topological interface state: design and analysis

We propose a photonic crystal ring resonator for the enhancement of quality factor that supports two-dimensionally bounded topological edge states. Crystal parameters are obtained through finite-difference time-domain numerical simulation to get the enhanced quality factor using the topological properties of the photonic crystal. Topological edge states are created when two regions with dissimilar band topologies come together at an interface and are contained within a slab of dielectric material. These edge states can move along sharp edges without backscattering. The transmission dropout issue arises whenever the quality factor is enhanced in a conventional photonic system and is eliminated remarkably by employing the present approach. Such nanoscale photonic crystal structures promote robust interactions between quantum emitters and photonic edge states.

Angle-insensitive topological interface states in hybrid one-dimensional photonic crystal heterostructures containing all-dielectric metamaterials

Topological interface states (TISs) in conventional one-dimensional (1D) photonic crystal (PhC) heterostructures strongly shift toward higher frequencies as the incident angle increases. This strong blueshift property of TISs intensively limits the operating angle ranges of TISs. Herein, we design two angle-insensitive photonic bandgaps (PBGs) in two hybrid 1D PhCs containing all-dielectric metamaterials. By cascading these two hybrid 1D PhCs to construct a hybrid 1D PhC heterostructure, we achieve an angle-insensitive TIS under transverse magnetic polarization. Empowered by the angle-insensitive property of the PBGs, the angular tolerance of the TIS reaches 69.65°, which is much higher than those of the TISs in conventional 1D PhC heterostructures. In addition, the angle-insensitive property of the TIS is robust against the layer thickness. Our work provides a viable route to achieving TISs with high angular tolerances and would facilitate the applications of photonic topological states.

Topological Photonic Lattice for Uniform Beam Splitting, Robust Routing, and Sensitive Far-Field Steering

Far-field optical beam steering is a fast-growing technology for communications, spatial ranging, and detections. Nonmechanical optical phased arrays based on straight waveguides have been studied recently, where the beam emission angle to the propagation axis can be scanned by conveniently tuning the wavelength. However, the dispersion of the waveguide limits the wavelength sensitivity of beam steering and the deliberately created emitters inevitably introduce in-line backscattering on-chip. To overcome these limitations, here, we report a robust and back-reflection-free topological photonic integrated circuit, where different functionalities, such as beam splitting, routing, and far-field steering, are defined by strategic arrangements of lattices with different topological modulations simply controlled by a single lattice deformation parameter. Benefiting from the robust topological scheme, an extra band flattening is applied to achieve far-field steering with high wavelength sensitivity.

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.

Exploiting Oriented Field Projectors to Open Topological Gaps in Plasmonic Nanoparticle Arrays

In the last years there have been multiple proposals in nanophotonics to mimic topological condensed matter systems. However, nanoparticles have degrees of freedom that atoms lack of, like dimensions or shape, which can be exploited to explore topology beyond electronics. Elongated nanoparticles can act like projectors of the electric field in the direction of the major axis. Then, by orienting them in an array the coupling between them can be tuned, allowing to open a gap in an otherwise gapless system. As a proof of the potential of the use of orientation of nanoparticles for topology, we study 1D chains of prolate spheroidal silver nanoparticles. We show that in these arrays spatial modulation of the polarization allows to open gaps, engineer hidden crystalline symmetries and to switch on/off or left/right edge states depending on the polarization of the incident electric field. This opens a path toward exploiting features of nanoparticles for topology to go beyond analogues of condensed matter systems.

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

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

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

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

Observation of intrinsic chiral bound states in the continuum

Photons with spin angular momentum possess intrinsic chirality, which underpins many phenomena including nonlinear optics¹, quantum optics², topological photonics³ and chiroptics⁴. Intrinsic chirality is weak in natural materials, and recent theoretical proposals^5-7 aimed to enlarge circular dichroism by resonant metasurfaces supporting bound states in the continuum that enhance substantially chiral light-matter interactions. Those insightful works resort to three-dimensional sophisticated geometries, which are too challenging to be realized for optical frequencies⁸. Therefore, most of the experimental attempts^9-11 showing strong circular dichroism rely on false/extrinsic chirality by using either oblique incidence^9,10 or structural anisotropy¹¹. Here we report on the experimental realization of true/intrinsic chiral response with resonant metasurfaces in which the engineered slant geometry breaks both in-plane and out-of-plane symmetries. Our result marks, to our knowledge, the first observation of intrinsic chiral bound states in the continuum with near-unity circular dichroism of 0.93 and a high quality factor exceeding 2,663 for visible frequencies. Our chiral metasurfaces may lead to a plethora of applications in chiral light sources and detectors, chiral sensing, valleytronics and asymmetric photocatalysis.

Direct Observation of Spin-Orbit Interaction of Light via Chiroptical Responses

The spin-orbit interaction of light is a fundamental manifestation of controlling its angular momenta with numerous applications in photonic spin Hall effects and chiral quantum optics. However, observation of an optical spin Hall effect, which is normally very weak with subwavelength displacements, needs quantum weak measurements or sophisticated metasurfaces. Here, we theoretically and experimentally demonstrate the spin-orbit interaction of light in the form of strong chiroptical responses by breaking the in-plane inversion symmetry of a dielectric substrate. The chiroptical signal is observed at the boundary of a microdisk illuminated by circularly polarized vortex beams at normal incidence. The generated chiroptical spectra are tunable for different photonic orbital angular momenta and microdisk diameters. Our findings, correlating photonic spin-orbit interaction with chiroptical responses, may provide a route for exploiting optical information processing, enantioselective sensing, and chiral metrology.

Topological photonics by breaking the degeneracy of line node singularities in semimetal-like photonic crystals

Degeneracy is an omnipresent phenomenon in various physical systems, which has its roots in the preservation of geometrical symmetry. In electronic and photonic crystal systems, very often this degeneracy can be broken by virtue of strong interactions between photonic modes of the same energy, where the level repulsion and the hybridization between modes causes the emergence of photonic bandgaps. However, most often this phenomenon does not lead to a complete and inverted bandgap formation over the entire Brillouin zone. Here, by systematically breaking the symmetry of a two-dimensional square photonic crystal, we investigate the formation of Dirac points, line node singularities, and inverted bandgaps. The formation of this complete bandgap is due to the level repulsion between degenerate modes along the line nodes of a semimetal-like photonic crystal, over the entire Brillouin zone. Our numerical experiments are performed by a home-build numerical framework based on a multigrid finite element method. The developed numerical toolbox and our observations pave the way towards designing complete bandgap photonic crystals and exploring the role of symmetry on the optical behaviour of even more complicated orders in photonic crystal systems.

Menezes L, Tittl A, Ren H, Maier SA. Optical Metasurfaces for Energy Conversion

Nanostructured surfaces with designed optical functionalities, such as metasurfaces, allow efficient harvesting of light at the nanoscale, enhancing light-matter interactions for a wide variety of material combinations. Exploiting light-driven matter excitations in these artificial materials opens up a new dimension in the conversion and management of energy at the nanoscale. In this review, we outline the impact, opportunities, applications, and challenges of optical metasurfaces in converting the energy of incoming photons into frequency-shifted photons, phonons, and energetic charge carriers. A myriad of opportunities await for the utilization of the converted energy. Here we cover the most pertinent aspects from a fundamental nanoscopic viewpoint all the way to applications.

Metamaterial-enabled asymmetric negative refraction of GHz mechanical waves

Wave refraction at an interface between different materials is a basic yet fundamental phenomenon, transversal to several scientific realms - electromagnetism, gas and fluid acoustics, solid mechanics, and possibly also matter waves. Under specific circumstances, mostly enabled by structuration below the wavelength scale, i.e., through the metamaterial approach, waves undergo negative refraction, eventually enabling superlensing and transformation optics. However, presently known negative refraction systems are symmetric, in that they cannot distinguish between positive and negative angles of incidence. Exploiting a metamaterial with an asymmetric unit cell, we demonstrate that the aforementioned symmetry can be broken, ultimately relying on the specific shape of the Bloch mode isofrequency curves. Our study specialized upon a mechanical metamaterial operating at GHz frequency, which is by itself a building block for advanced technologies such as chip-scale hybrid optomechanical and electromechanical devices. However, the phenomenon is based on general wave theory concepts, and it applies to any frequency and time scale for any kind of linear waves, provided that a suitable shaping of the isofrequency contours is implemented.

Three-dimensional photonic topological insulator without spin-orbit coupling

Spin-orbit coupling, a fundamental mechanism underlying topological insulators, has been introduced to construct the latter's photonic analogs, or photonic topological insulators (PTIs). However, the intrinsic lack of electronic spin in photonic systems leads to various imperfections in emulating the behaviors of topological insulators. For example, in the recently demonstrated three-dimensional (3D) PTI, the topological surface states emerge, not on the surface of a single crystal as in a 3D topological insulator, but along an internal domain wall between two PTIs. Here, by fully abolishing spin-orbit coupling, we design and demonstrate a 3D PTI whose topological surface states are self-guided on its surface, without extra confinement by another PTI or any other cladding. The topological phase follows the original Fu's model for the topological crystalline insulator without spin-orbit coupling. Unlike conventional linear Dirac cones, a unique quadratic dispersion of topological surface states is directly observed with microwave measurement. Our work opens routes to the topological manipulation of photons at the outer surface of photonic bandgap materials.

Energy density as a probe of band representations in photonic crystals

Topological quantum chemistry (TQC) has recently emerged as an instrumental tool to characterize the topological nature of both fermionic and bosonic band structures. TQC is based on the study of band representations and the localization of maximally localized Wannier functions. In this article, we study various two-dimensional photonic crystal structures analyzing their topological character through a combined study of TQC, their Wilson-loop (WL) spectra and the electromagnetic energy density. Our study demonstrates that the analysis of the spatial localization of the energy density complements the study of the topological properties in terms of the spectrum of the WL operator and TQC.

Breakdown of Spin-to-Helicity Locking at the Nanoscale in Topological Photonic Crystal Edge States

We measure the local near-field spin in topological edge state waveguides that emulate the quantum spin Hall effect. We reveal a highly structured spin density distribution that is not linked to a unique pseudospin value. From experimental near-field real-space maps and numerical calculations, we confirm that this local structure is essential in understanding the properties of optical edge states and light-matter interactions. The global spin is reduced by a factor of 30 in the near field and, for certain frequencies, flipped compared to the pseudospin measured in the far field. We experimentally reveal the influence of higher-order Bloch harmonics in spin inhomogeneity, leading to a breakdown in the coupling between local helicity and global spin.

High-speed infrared photonic band microscope using hyperspectral Fourier image spectroscopy

In this study, we developed a photonic band microscope based on hyperspectral Fourier image spectroscopy. The developed device constructs an infrared photonic band structure from Fourier images for various wavelength obtained by hyperspectral imaging, which make it possible to speedily measure the dispersion characteristics of photonic nanostructures. By applying the developed device to typical photonic crystals and topological photonic crystals, we succeeded in obtaining band structures in good agreement with the theoretical prediction calculated by the finite element method. This device facilitates the evaluation of physical properties in various photonic nanostructures, and is expected to further promote related fields.

Ideal nodal rings of one-dimensional photonic crystals in the visible region

Three-dimensional (3D) artificial metacrystals host rich topological phases, such as Weyl points, nodal rings, and 3D photonic topological insulators. These topological states enable a wide range of applications, including 3D robust waveguides, one-way fiber, and negative refraction of the surface wave. However, these carefully designed metacrystals are usually very complex, hindering their extension to nanoscale photonic systems. Here, we theoretically proposed and experimentally realized an ideal nodal ring in the visible region using a simple 1D photonic crystal. The π-Berry phase around the ring is manifested by a 2π reflection phase's winding and the resultant drumhead surface states. By breaking the inversion symmetry, the nodal ring can be gapped and the π-Berry phase would diffuse into a toroidal-shaped Berry flux, resulting in photonic ridge states (the 3D extension of quantum valley Hall states). Our results provide a simple and feasible platform for exploring 3D topological physics and its potential applications in nanophotonics.

On-chip nanophotonic topological rainbow

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

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

Selective excitation of optical vortex modes with specific charge numbers in band-tuned topological waveguides

We propose a method for selectively propagating optical vortex modes with specific charge numbers in a photonic integrated circuit (PIC) by using a topological photonic system. Specifically, by performing appropriate band tuning in two photonic structures that comprise a topological waveguide, one specific electromagnetic mode at the Γ point of a band diagram can be excited. Based on theoretical analysis, we successfully propagated optical vortex modes with specific charge numbers over a wide range in the C band in the proposed topological waveguide. The proposed method could be useful in controlling optical vortex signals at the chip level in future orbital angular momentum multiplexing technologies.

Spin Hall effect of transmitted light through α-Li3N-type topological semimetals

The spin Hall effect of light occurring in topological semimetals provides unprecedented opportunities to exploit novel photonic properties and applications. In particular, pristine α-Li₃N-type crystal has recently been predicted to be a type-I nodal-line semimetal based on density functional theory. Herein, the spin Hall effect of transmitted light through thin films of α-Li₃N-type topological semimetals is investigated. We show that the prominent intense peak and dip emerging in the spectra of spin Hall shifts occur at the high-energy side of interband absorption of α-Li₃N-type semimetals and show redshifts with increasing the incident angle or permittivity of the exit medium. In addition, type-I nodal-line semimetal under a compressive lattice strain is transformed into a type-II one such that the main intense peak and dip show blueshifts. Inversely, the tensile strain induces the formation of a triply degenerate nodal point in α-Li₃N-type semimetals, causing the main intense peak and dip to show redshifts. Moreover, the influences of alloying and hole-doping in α-Li₃N-type semimetals on the spin Hall effect of light are also discussed. Our findings may provide clear strategies to accurately engineer and detect the structural or phase change in topological materials.

High-directionality spin-selective routing of photons in plasmonic nanocircuits

Efficient on-chip manipulation of photon spin is of crucial importance in developing future integrated nanophotonics as is electron spin in spintronics. The unidirectionality induced by the interaction between spin and orbital angular momenta suffers low efficiency in classical macroscopic optics, while it can be highly enhanced on subwavelength scales with suitable architectures. Here we propose and demonstrate a spin-sorting achiral split-ring coupler to unidirectionally excite dielectric-loaded plasmonic modes in two independent waveguides. We found experimentally that the impinging light with different spin can be selectively directed into one of two branching plasmonic waveguides with a directionality contrast up to 15.1 dB. A circular-helicity-independent compact beam splitter is also realized demonstrating great potential in designing complex interconnect nanocircuits. The illustrated approach is believed to open new avenues for developing advanced optical functionalities with a flexible degree of freedom in manipulation of on-chip chirality within chiral optics.

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.

Topological phonon-polariton funneling in midinfrared metasurfaces

[Figure: see text].

Exceptional topological insulators

We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the three-dimensional topological bulk embedding. We show how this phase can evolve from a Weyl semimetal or Hermitian three-dimensional topological insulator close to criticality when quasiparticles acquire a finite lifetime. The ETI does not require any symmetry to be stabilized. It is characterized by a bulk energy point gap, and exhibits robust surface states that cover the bulk gap as a single sheet of complex eigenvalues or with a single exceptional point. The ETI can be induced universally in gapless solid-state systems, thereby setting a paradigm for non-Hermitian topological matter.

Broadband Topological Slow Light through Brillouin Zone Winding

Topological photonic insulators have attracted significant attention for their robust transport of light, impervious to scattering and disorder. This feature is ideally suited for slow light applications, which are typically limited by disorder-induced attenuation. However, no practical approach to broadband topologically protected slow light has been demonstrated yet. In this work, we achieve slow light in topologically unidirectional waveguides based on periodically loading an edge termination with suitably tailored resonances. The resulting edge state dispersion can wind around the Brillouin zone multiple times sustaining broadband, topologically robust slow light, opening exciting opportunities in various photonic scenarios.

Modeling the optical properties of twisted bilayer photonic crystals

We demonstrate a photonic analog of twisted bilayer graphene that has ultra-flat photonic bands and exhibits extreme slow-light behavior. Our twisted bilayer photonic device, which has an operating wavelength in the C-band of the telecom window, uses two crystalline silicon photonic crystal slabs separated by a methyl methacrylate tunneling layer. We numerically determine the magic angle using a finite-element method and the corresponding photonic band structure, which exhibits a flat band over the entire Brillouin zone. This flat band causes the group velocity to approach zero and introduces light localization, which enhances the electromagnetic field at the expense of bandwidth. Using our original plane-wave continuum model, we find that the photonic system has a larger band asymmetry. The band structure can easily be engineered by adjusting the device geometry, giving significant freedom in the design of devices. Our work provides a fundamental understanding of the photonic properties of twisted bilayer photonic crystals and opens the door to the nanoscale-based enhancement of nonlinear effects.

Experimental observation of topological Z2 exciton-polaritons in transition metal dichalcogenide monolayers

The rise of quantum science and technologies motivates photonics research to seek new platforms with strong light-matter interactions to facilitate quantum behaviors at moderate light intensities. Topological polaritons (TPs) offer an ideal platform in this context, with unique properties stemming from resilient topological states of light strongly coupled with matter. Here we explore polaritonic metasurfaces based on 2D transition metal dichalcogenides (TMDs) as a promising platform for topological polaritonics. We show that the strong coupling between topological photonic modes of the metasurface and excitons in TMDs yields a topological polaritonic Z₂ phase. We experimentally confirm the emergence of one-way spin-polarized edge TPs in metasurfaces integrating MoSe₂ and WSe₂. Combined with the valley polarization in TMD monolayers, the proposed system enables an approach to engage the photonic angular momentum and valley and spin of excitons, offering a promising platform for photonic/solid-state interfaces for valleytronics and spintronics.

Topological Surface State in Epitaxial Zigzag Graphene Nanoribbons

Protected and spin-polarized transport channels are the hallmark of topological insulators, coming along with an intrinsic strong spin-orbit coupling. Here we identified such corresponding chiral states in epitaxially grown zigzag graphene nanoribbons (zz-GNRs), albeit with an extremely weak spin-orbit interaction. While the bulk of the monolayer zz-GNR is fully suspended across a SiC facet, the lower edge merges into the SiC(0001) substrate and reveals a surface state at the Fermi energy, which is extended along the edge and splits in energy toward the bulk. All of the spectroscopic details are precisely described within a tight binding model incorporating a Haldane term and strain effects. The concomitant breaking of time-reversal symmetry without the application of external magnetic fields is supported by ballistic transport revealing a conduction of G = e²/h.