Ultrafast vector imaging of plasmonic skyrmion dynamics with deep subwavelength resolution

Acoustic Skyrmionic Mode Coupling and Transferring in a Chain of Subwavelength Metastructures

Skyrmions, a stable topological vectorial textures characteristic with skyrmionic number, hold promise for advanced applications in information storage and transmission. While the dynamic motion control of skyrmions has been realized with various techniques in magnetics and optics, the manipulation of acoustic skyrmion has not been done. Here, the propagation and control of acoustic skyrmion along a chain of metastructures are shown. In coupled acoustic resonators made with Archimedes spiral channel, the skyrmion hybridization is found giving rise to bonding and antibonding skyrmionic modes. Furthermore, it is experimentally observed that the skyrmionic mode of acoustic velocity field distribution can be robustly transferred covering a long distance and almost no distortion of the skyrmion textures in a chain of metastructures, even if a structure defect is introduced in the travel path. The proposed localized acoustic skyrmionic mode coupling and propagating is expected in future applications for manipulating acoustic information storage and transfer.

Topological Structures of Energy Flow: Poynting Vector Skyrmions

Topological properties of energy flow of light are fundamentally interesting and may introduce novel physical phenomena associated with directional light scattering and optical trapping. In this Letter, skyrmionlike structures formed by Poynting vectors are unveiled in the focal region of two pairs of counterpropagating cylindrical vector vortex beams in free space. The appearance of local phase singularities, and the distinct traveling and standing wave modes of different field components passing through the focal spot lead to a Néel-Bloch-Néel transition of Poynting vector skyrmion textures along the light propagating direction. By shaping the wave front of the incident beams with patterned amplitudes, the topological invariant of the Poynting vector skyrmions can be further tuned in a prospective area. This work expands the family of optical skyrmions and holds great potential in energy flow associated applications.

Probing the Polarization of Low-Energy Excitations in 2D Materials from Atomic Crystals to Nanophotonic Arrays Using Momentum-Resolved Electron Energy Loss Spectroscopy

Spectroscopies utilizing free electron beams as probes offer detailed information on the reciprocal-space excitations of 2D materials such as graphene and transition metal dichalcogenide monolayers. Yet, despite the attention paid to such quantum materials, less consideration has been given to the electron-beam characterization of 2D periodic nanostructures such as photonic crystals, metasurfaces, and plasmon arrays, which can exhibit the same lattice and excitation symmetries as their atomic analogues albeit at drastically different length, momentum, and energy scales. Because of their lack of covalent bonding and influence of retarded electromagnetic interactions, important physical distinctions arise that complicate interpretation of scattering signals. Here we present a fully-retarded theoretical framework for describing the inelastic scattering of wide-field electron beams from 2D materials and apply it to investigate the complementarity in sample excitation information gained in the measurement of a honeycomb plasmon array versus angle-resolved optical spectroscopy in comparison to single monolayer graphene.

Temporal Dynamics of Collective Resonances in Periodic Metasurfaces

Temporal dynamics of confined optical fields can provide valuable insights into light-matter interactions in complex optical systems, going beyond their frequency-domain description. Here, we present a new experimental approach based on interferometric autocorrelation (IAC) that reveals the dynamics of optical near-fields enhanced by collective resonances in periodic metasurfaces. We focus on probing the resonances known as waveguide-plasmon polaritons, which are supported by plasmonic nanoparticle arrays coupled to a slab waveguide. To probe the resonant near-field enhancement, our IAC measurements make use of enhanced two-photon excited luminescence (TPEL) from semiconductor quantum dots deposited on the nanoparticle arrays. Thanks to the incoherent character of TPEL, the measurements are only sensitive to the fundamental optical fields and therefore can reveal clear signatures of their coherent temporal dynamics. In particular, we show that the excitation of a high-Q collective resonance gives rise to interference fringes at time delays as large as 500 fs, much greater than the incident pulse duration (150 fs). Based on these signatures, the basic characteristics of the resonances can be determined, including their Q factors, which are found to exceed 200. Furthermore, the measurements also reveal temporal beating between two different resonances, providing information on their frequencies and their relative contribution to the field enhancement. Finally, we present an approach to enhance the visibility of the resonances hidden in the IAC curves by converting them into spectrograms, which greatly facilitates the analysis and interpretation of the results. Our findings open up new perspectives on time-resolved studies of collective resonances in metasurfaces and other multiresonant systems.

Observation of an acoustic topological Euler insulator with meronic waves

Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian topologies that thrive on involving multiple gaps were studied, unveiling a new horizon in topological physics beyond the conventional paradigm. Here, we report on the first experimental realization of a topological Euler insulator phase with unique meronic characterization in an acoustic metamaterial. We demonstrate that this topological phase has several nontrivial features: First, the system cannot be described by conventional topological band theory, but has a nontrivial Euler class that captures the unconventional geometry of the Bloch bands in the Brillouin zone. Second, we uncover in theory and probe in experiments a meronic configuration of the bulk Bloch states for the first time. Third, using a detailed symmetry analysis, we show that the topological Euler insulator evolves from a non-Abelian topological semimetal phase via. the annihilation of Dirac points in pairs in one of the band gaps. With these nontrivial properties, we establish concretely an unconventional bulk-edge correspondence which is confirmed by directly measuring the edge states via. pump-probe techniques. Our work thus unveils a nontrivial topological Euler insulator phase with a unique meronic pattern and paves the way as a platform for non-Abelian topological phenomena.

Nondiffracting supertoroidal pulses and optical "Kármán vortex streets"

Supertoroidal light pulses, as space-time nonseparable electromagnetic waves, exhibit unique topological properties including skyrmionic configurations, fractal-like singularities, and energy backflow in free space, which however do not survive upon propagation. Here, we introduce the non-diffracting supertoroidal pulses (NDSTPs) with propagation-robust skyrmionic and vortex field configurations that persists over arbitrary propagation distances. Intriguingly, the field structure of NDSTPs has a similarity with the von Kármán vortex street, a pattern of swirling vortices in fluid and gas dynamics with staggered singularities that can stably propagate forward. NDSTPs will be of interest as directed channels for information and energy transfer applications.

An Ultra-broadband Metallic Plasmonic Antenna for Ultrasensitive Molecular Fingerprint Identification

Near-field enhanced mid-infrared light-matter interactions via metallic plasmonic antennae (PA) have attracted much attention but are inevitably limited by the detuning between their narrow band and the broad applied spectral range. Here, we develop a new low-temperature incubation synthetic method to acquire uniform Ag microparticles (MPs) with numerous hotspots. Their plasmonic band is remarkably extended by the plasmonic coupling of numerous hotspots and covers the entire mid-infrared range (400-4000 cm-1). Hence, the almost complete molecular fingerprint of 4-mercaptobenzonitrile was successfully probed for the first time via resonant surface-enhanced infrared absorption (rSEIRA), and the rSEIRA spectra of different essential amino acids were further detected and exhibit a high spectral identification degree assisted by machine learning. This work changes the inertia perception of "narrow band and large size but small hotspot area" of mid-infrared metallic PA and paves the way for the ultrasensitive mid-infrared optical sensing.

Large area single crystal gold of single nanometer thickness for nanophotonics

Two-dimensional single crystal metals, in which the behavior of highly confined optical modes is intertwined with quantum phenomena, are highly sought after for next-generation technologies. Here, we report large area (>104 μm2), single crystal two-dimensional gold flakes (2DGFs) with thicknesses down to a single nanometer level, employing an atomic-level precision chemical etching approach. The decrease of the thickness down to such scales leads to the quantization of the electronic states, endowing 2DGFs with quantum-confinement-augmented optical nonlinearity, particularly leading to more than two orders of magnitude enhancement in harmonic generation compared with their thick polycrystalline counterparts. The nanometer-scale thickness and single crystal quality makes 2DGFs a promising platform for realizing plasmonic nanostructures with nanoscale optical confinement. This is demonstrated by patterning 2DGFs into nanoribbon arrays, exhibiting strongly confined near infrared plasmonic resonances with high quality factors. The developed 2DGFs provide an emerging platform for nanophotonic research and open up opportunities for applications in ultrathin plasmonic, optoelectronic and quantum devices.

Real-time tracking of coherent oscillations of electrons in a nanodevice by photo-assisted tunnelling

Coherent collective oscillations of electrons excited in metallic nanostructures (localized surface plasmons) can confine incident light to atomic scales and enable strong light-matter interactions, which depend nonlinearly on the local field. Direct sampling of such collective electron oscillations in real-time is crucial to performing petahertz scale optical modulation, control, and readout in a quantum nanodevice. Here, we demonstrate real-time tracking of collective electron oscillations in an Au bowtie nanoantenna, by recording photo-assisted tunnelling currents generated by such oscillations in this quantum nanodevice. The collective electron oscillations show a noninstantaneous response to the driving laser fields with a T2 decay time of nearly 8 femtoseconds. The contributions of linear and nonlinear electron oscillations in the generated tunnelling currents were precisely determined. A phase control of electron oscillations in the nanodevice is illustrated. Functioning in ambient conditions, the excitation, phase control, and read-out of coherent electron oscillations pave the way toward on-chip light-wave electronics in quantum nanodevices.

Topological state transitions of skyrmionic beams under focusing configurations

The recent emerging appearance of optical analogs of magnetic quasiparticles, i.e., optical skyrmions constructed via spin, field, and Stokes vectors, has garnered substantial interest from deep-subwavelength imaging and quantum entanglement. Here, we investigate systematically the topological state transitions of skyrmionic beams constructed by the Stokes vectors in the focusing configuration. We theoretically demonstrated that in the weak focusing, the skyrmion topological number is protected. Whereas, in the tight focusing, a unique topological transformation with skyrmion number variation is exhibited for the optical skyrmion, anti-skyrmion, and 2nd-order skyrmion structures. The significant difference between the topological state transitions of these two cases originates from the transformation from the paraxial optical system to the nonparaxial optical system, and the approximate two-dimensional polarization structure to the three-dimensional polarization structure. The results provide new insights into the topological state transitions in topological structures, which promote applications in information processing, data storage, and free-space optical communications.

Dynamical Control of Topology in Polar Skyrmions via Twisted Light

Twisted light carries a nonzero orbital angular momentum, that can be transferred from light to electrons and particles ranging from nanometers to micrometers. Up to now, the interplay between twisted light with dipolar systems has scarcely been explored, though the latter bear abundant forms of topologies such as skyrmions and embrace strong light-matter coupling. Here, using first-principles-based simulations, we show that twisted light can excite and drive dynamical polar skyrmions and transfer its nonzero winding number to ferroelectric ultrathin films. The skyrmion is successively created and annihilated alternately at the two interfaces, and experiences a periodic transition from a markedly "Bloch" to "Néel" character, accompanied with the emergence of a "Bloch point" topological defect with vanishing polarization. The dynamical evolution of skyrmions is connected to a constant jump of topological number between "0" and "1" over time. These intriguing phenomena are found to have an electrostatic origin. Our study thus demonstrates that, and explains why this unique light-matter interaction can be very powerful in creating and manipulating topological solitons in functional materials.

Nanoparticle Deep-Subwavelength Dynamics Empowered by Optical Meron-Antimeron Topology

Optical meron is a type of nonplanar topological texture mainly observed in surface plasmon polaritons and highly symmetric points of photonic crystals in the reciprocal space. Here, we report Poynting-vector merons formed at the real space of a photonic crystal for a Γ-point illumination. Optical merons can be utilized for subwavelength-resolution manipulation of nanoparticles, resembling a topological Hall effect on electrons via magnetic merons. In particular, staggered merons and antimerons impose strong radiation pressure on large gold nanoparticles (AuNPs), while focused hot spots in antimerons generate dominant optical gradient forces on small AuNPs. Synergistically, differently sized AuNPs in a still environment can be trapped or orbit in opposite directions, mimicking a coupled galaxy system. They can also be separated with a 10 nm precision when applying a flow velocity of >1 mm/s. Our study unravels a novel way to exploit topological textures for optical manipulation with deep-subwavelength precision and switchable topology in a lossless environment.

Photonic Spin Hopfions and Monopole Loops

Spin textures with various topological orders are of great theoretical and practical interest. Hopfion, a spin texture characterized by a three-dimensional topological order was recently realized in electronic spin systems. Here, we show that monochromatic light can be structured such that its photonic spin exhibits a hopfion texture in the three-dimensional real space. We also provide ways to construct spin textures of arbitrary Hopf charges. When extending the system to four dimensions by introducing a parameter dimension, a new type of topological defect in the form of a monopole loop in photonic spin is encountered. Each point on the loop is a topological spin defect in three dimensions, and the loop itself carries quantized Hopf charges. Such photonic spin texture and defect may find application in control and sensing of nanoparticles, and optical generation of topological texture in motions of particles or fluids.

Ultrafast Time Dynamics of Plasmonic Fractional Orbital Angular Momentum

The creation and manipulation of optical vortices, both in free space and in two-dimensional systems such as surface plasmon polaritons (SPPs), has attracted widespread attention in nano-optics due to their robust topological structure. Coupled with strong spatial confinement in the case of SPPs, these plasmonic vortices and their underlying orbital angular momentum (OAM) have promise in novel light-matter interactions on the nanoscale with applications ranging from on-chip particle manipulation to tailored control of plasmonic quasiparticles. Until now, predominantly integer OAM values have been investigated. Here, we measure and analyze the time evolution of fractional OAM SPPs using time-resolved two-photon photoemission electron microscopy and near-field optical microscopy. We experimentally show the field's complex rotational dynamics and observe the beating of integer OAM eigenmodes at fractional OAM excitations. With our ability to access the ultrafast time dynamics of the electric field, we can follow the buildup of the plasmonic fractional OAM during the interference of the converging surface plasmons. By adiabatically increasing the phase discontinuity at the excitation boundary, we track the total OAM, leading to plateaus around integer OAM values that arise from the interplay between intrinsic and extrinsic OAM.

Impact of the geometry of the excitation structure on optical skyrmion

Optical skyrmions have attracted great attention for the potential applications in novel information storage and communication. It is of great significance to get insight into the generation of optical skyrmions by surface waves. Here, we have paid greater emphasis on the influence of the geometry of the coupling structure on the formation of optical skyrmions. Optical skyrmions are constructed from the superposition of the interfering surface plasmons excited by polygon trenches on Ag film. The results show the field texture of optical skyrmions is mainly determined by the excitation structure, with distinct properties revealed with various closed and non-closed geometries. Moreover, the ratio between the electric field strengths of the optical skyrmions can be larger than 4 between the optimized and unoptimized coupling structures. The pattern of the optical skyrmion shows a strong dependence on the excitation structure, implying the significant role in skyrmion topology it plays.

Angle-resolved photoelectron spectroscopy in a low-energy electron microscope

Spectroscopic photoemission microscopy is a well-established method to investigate the electronic structure of surfaces. In modern photoemission microscopes, the electron optics allow imaging of the image plane, momentum plane, or dispersive plane, depending on the lens setting. Furthermore, apertures allow filtering of energy-, real-, and momentum space. Here, we describe how a standard spectroscopic and low-energy electron microscope can be equipped with an additional slit at the entrance of the already present hemispherical analyzer to enable an angle- and energy-resolved photoemission mode with micrometer spatial selectivity. We apply a photogrammetric calibration to correct for image distortions of the projective system behind the analyzer and present spectra recorded on Au(111) as a benchmark. Our approach makes data acquisition in energy-momentum space more efficient, which is a necessity for laser-based pump-probe photoemission microscopy with femtosecond time resolution.

Lorentz microscopy of optical fields

In electron microscopy, detailed insights into nanoscale optical properties of materials are gained by spontaneous inelastic scattering leading to electron-energy loss and cathodoluminescence. Stimulated scattering in the presence of external sample excitation allows for mode- and polarization-selective photon-induced near-field electron microscopy (PINEM). This process imprints a spatial phase profile inherited from the optical fields onto the wave function of the probing electrons. Here, we introduce Lorentz-PINEM for the full-field, non-invasive imaging of complex optical near fields at high spatial resolution. We use energy-filtered defocus phase-contrast imaging and iterative phase retrieval to reconstruct the phase distribution of interfering surface-bound modes on a plasmonic nanotip. Our approach is universally applicable to retrieve the spatially varying phase of nanoscale fields and topological modes.

Scalar topological photonic nested meta-crystals and skyrmion surface states in the light cone continuum

Topological photonics is rapidly expanding. However, discovering three-dimensional topological electromagnetic systems can be more challenging than electronic systems for two reasons. First, the vectorial nature of electromagnetic waves results in complicated band dispersions, and simple tight-binding-type predictions usually fail. Second, topological electromagnetic surface modes inside the light cone have very low quality factors (Q factors). Here, we propose the concept of scalar topological photonics to address these challenges. Our approach is experimentally validated by employing a nested meta-crystal configuration using connected coaxial waveguides. They exhibit scalar-wave-like band dispersions, making the search for photonic topological phases an easier task. Their surface states have skyrmion-like electric field distributions, resulting in a whole, bright surface state band inside the light cone continuum. As such, the topological surface states in our three-dimensional nested crystals can be exposed to air, making such systems well-suited for practical applications.

Dynamic manipulation of graphene plasmonic skyrmions

With the characteristics of ultrasmall, ultrafast, and topological protection, optical skyrmions are great prospects for applications in high intensity data stroage, high resolution microscopic imaging, and polarization sensing. Flexible control over the topology of optical skyrmions is required for practical implementation/application. At present, the manipulation of optical skyrmions usually relies upon the change of spatial structure, which results in a limited-tuning range and a discontinuous control in the parameter space. Here, we propose continuous manipulation of the graphene plasmon skyrmions based on the electrotunable properties of graphene. By changing the Fermi energy of one pair of the standing waves or the phase of incident light, one can achieve topological state transformation of graphene plasmon skyrmions, which is evident by the change of skyrmion number from 1 to 0.5. The direct manipulation of the graphene plasmon skyrmions is demonstrated by simulation results based on the finite element method. Our work suggests a feasible way to flexibly control the topology of an optical skyrmionic field, which can be used for novel integrated photonic devices in the future.

Néel-type optical target skyrmions inherited from evanescent electromagnetic fields with rotational symmetry

Optical skyrmions have recently attracted growing interest due to their potential applications in deep-subwavelength imaging and nanometrology. While optical skyrmions have been successfully demonstrated using different field vectors, the study of their generation and control, as well as their general correlation with electromagnetic (EM) fields, is still in its infancy. Here, we theoretically propose that evanescent transverse-magnetic-polarized (TM-polarized) EM fields with rotational symmetry are actually Néel-type optical target skyrmions of the electric field vectors. Such optical target skyrmions are independent of the operation frequency and medium. Our proposal was verified by numerical simulations and real-space nano-imaging experiments performed on a graphene monolayer, where the target skyrmions could be as small as ∼100 nm in diameter. The results can therefore not only further our understanding of the formation mechanisms of EM topological textures, but also provide guidelines for the facile construction of EM skyrmions that may impact future information technologies.

Revealing low-loss dielectric near-field modes of hexagonal boron nitride by photoemission electron microscopy

Low-loss dielectric modes are important features and functional bases of fundamental optical components in on-chip optical devices. However, dielectric near-field modes are challenging to reveal with high spatiotemporal resolution and fast direct imaging. Herein, we present a method to address this issue by applying time-resolved photoemission electron microscopy to a low-dimensional wide-bandgap semiconductor, hexagonal boron nitride (hBN). Taking a low-loss dielectric planar waveguide as a fundamental structure, static vector near-field vortices with different topological charges and the spatiotemporal evolution of waveguide modes are directly revealed. With the lowest-order vortex structure, strong nanofocusing in real space is realized, while near-vertical photoemission in momentum space and narrow spread in energy space are simultaneously observed due to the atomically flat surface of hBN and the small photoemission horizon set by the limited photon energies. Our approach provides a strategy for the realization of flat photoemission emitters.

Attosecond electron microscopy of sub-cycle optical dynamics

The primary step of almost any interaction between light and materials is the electrodynamic response of the electrons to the optical cycles of the impinging light wave on sub-wavelength and sub-cycle dimensions¹. Understanding and controlling the electromagnetic responses of a material^2-11 is therefore essential for modern optics and nanophotonics^12-19. Although the small de Broglie wavelength of electron beams should allow access to attosecond and ångström dimensions²⁰, the time resolution of ultrafast electron microscopy²¹ and diffraction²² has so far been limited to the femtosecond domain^16-18, which is insufficient for recording fundamental material responses on the scale of the cycles of light^1,2,10. Here we advance transmission electron microscopy to attosecond time resolution of optical responses within one cycle of excitation light²³. We apply a continuous-wave laser²⁴ to modulate the electron wave function into a rapid sequence of electron pulses, and use an energy filter to resolve electromagnetic near-fields in and around a material as a movie in space and time. Experiments on nanostructured needle tips, dielectric resonators and metamaterial antennas reveal a directional launch of chiral surface waves, a delay between dipole and quadrupole dynamics, a subluminal buried waveguide field and a symmetry-broken multi-antenna response. These results signify the value of combining electron microscopy and attosecond laser science to understand light-matter interactions in terms of their fundamental dimensions in space and time.

Plate-Like Colloidal Metal Nanoparticles

The pseudo-two-dimensional (2D) morphology of plate-like metal nanoparticles makes them one of the most anisotropic, mechanistically understood, and tunable structures available. Although well-known for their superior plasmonic properties, recent progress in the 2D growth of various other materials has led to an increasingly diverse family of plate-like metal nanoparticles, giving rise to numerous appealing properties and applications. In this review, we summarize recent progress on the solution-phase growth of colloidal plate-like metal nanoparticles, including plasmonic and other metals, with an emphasis on mechanistic insights for different synthetic strategies, the crystallographic habits of different metals, and the use of nanoplates as scaffolds for the synthesis of other derivative structures. We additionally highlight representative self-assembly techniques and provide a brief overview on the attractive properties and unique versatility benefiting from the 2D morphology. Finally, we share our opinions on the existing challenges and future perspectives for plate-like metal nanomaterials.

Tunable photon-induced spatial modulation of free electrons

Spatial modulation of electron beams is an essential tool for various applications such as nanolithography and imaging, yet its conventional implementations are severely limited and inherently non-tunable. Conversely, proposals of light-driven electron spatial modulation promise tunable electron wavefront shaping, for example, using the mechanism of photon-induced near-field electron microscopy. Here we present tunable photon-induced spatial modulation of electrons through their interaction with externally controlled surface plasmon polaritons (SPPs). Using recently developed methods of shaping SPP patterns, we demonstrate a dynamic control of the electron beam with a variety of electron distributions and verify their coherence through electron diffraction. Finally, the nonlinearity stemming from energy post-selection provides us with another avenue for controlling the electron shape, generating electron features far below the SPP wavelength. Our work paves the way to on-demand electron wavefront shaping at ultrafast timescales, with prospects for aberration correction, nanofabrication and material characterization.

Three-dimensional topological magnetic monopoles and their interactions in a ferromagnetic meta-lattice

Topological magnetic monopoles (TMMs), also known as hedgehogs or Bloch points, are three-dimensional (3D) non-local spin textures that are robust to thermal and quantum fluctuations due to the topology protection^1-4. Although TMMs have been observed in skyrmion lattices^1,5, spinor Bose-Einstein condensates^6,7, chiral magnets⁸, vortex rings^2,9 and vortex cores¹⁰, it has been difficult to directly measure the 3D magnetization vector field of TMMs and probe their interactions at the nanoscale. Here we report the creation of 138 stable TMMs at the specific sites of a ferromagnetic meta-lattice at room temperature. We further develop soft X-ray vector ptycho-tomography to determine the magnetization vector and emergent magnetic field of the TMMs with a 3D spatial resolution of 10 nm. This spatial resolution is comparable to the magnetic exchange length of transition metals¹¹, enabling us to probe monopole-monopole interactions. We find that the TMM and anti-TMM pairs are separated by 18.3 ± 1.6 nm, while the TMM and TMM, and anti-TMM and anti-TMM pairs are stabilized at comparatively longer distances of 36.1 ± 2.4 nm and 43.1 ± 2.0 nm, respectively. We also observe virtual TMMs created by magnetic voids in the meta-lattice. This work demonstrates that ferromagnetic meta-lattices could be used as a platform to create and investigate the interactions and dynamics of TMMs. Furthermore, we expect that soft X-ray vector ptycho-tomography can be broadly applied to quantitatively image 3D vector fields in magnetic and anisotropic materials at the nanoscale.

Observation of phononic skyrmions based on hybrid spin of elastic waves

Skyrmions with topologically stable configuration have shown a promising route toward high-density magnetic and photonic information processing due to their defect-immune and low-driven energy. Here, we experimentally report and observe the existence of phononic skyrmions as new topological structures formed by the three-dimensional hybrid spin of elastic waves. We demonstrate that the frequency-independent spin configuration leads to ultra-broadband feature of phononic skyrmions, which can be produced in any solid structure, including chip-scale ones. We further experimentally show the excellent robustness of the flexibly movable phononic skyrmion lattices against local defects of disorder, sharp corners, and even rectangular holes. Our research opens a vibrant horizon toward an unprecedented way for elastic wave manipulation and structuration by spin configuration and offers a promising lever for alternative phononic technologies, including information processing, biomedical testing, and wave engineering.

Metastability of photonic spin meron lattices in the presence of perturbed spin-orbit coupling

Photonic skyrmions and merons are topological quasiparticles characterized by nontrivial electromagnetic textures, which have received increasing research attention recently, providing novel degree of freedom to manipulate light-matter interactions and exhibiting excellent potential in deep-subwavelength imaging and nanometrology. Here, the topological stability of photonic spin meron lattices, which indicates the invariance of skyrmion number and robustness of spin texture under a continuous deformation of the field configuration, is demonstrated by inducing a perturbation to break the C₄ symmetry in the presence spin-orbit coupling in an optical field. We revealed that amplitude perturbation would result in an amplitude-dependent shift of spin center, while phase perturbation leads to the deformation of domain walls, manifesting the metastability of photonic meron. Such spin topology is verified through the interference of plasmonic vortices with a broken rotational symmetry. The results provide new insights on optical topological quasiparticles, which may pave the way towards applications in topological photonics, optical information storage and transfer.

Disorder-Induced Topological State Transition in the Optical Skyrmion Family

Skyrmions endowed with topological protection have been extensively investigated in various platforms including magnetics, ferroelectrics, and liquid crystals, stimulating applications such as memories, logic devices, and neuromorphic computing. While the optical counterpart has been proposed and realized recently, the study of optical skyrmions is still in its infancy. Among the unexplored questions, the investigation of the topology induced robustness against disorder is of substantial importance on both fundamental and practical sides but remains elusive. In this Letter, we manage to generate optical skyrmions numerically in real space with different topological features at will, providing a unique platform to investigate the robustness of various optical skyrmions. A disorder-induced topological state transition is observed for the first time in a family of optical skyrmions composed of six classes with different skyrmion numbers. Intriguingly, the optical skyrmions produced from a vectorial hologram are exceptionally robust against scattering from a random medium, shedding light on topological photonic devices for the generation and manipulation of robust states for applications including imaging and communication.

Observation of localized magnetic plasmon skyrmions

Optical skyrmions have recently been constructed by tailoring vectorial near-field distributions through the interference of multiple surface plasmon polaritons, offering promising features for advanced information processing, transport and storage. Here, we provide experimental demonstration of electromagnetic skyrmions based on magnetic localized spoof plasmons (LSP) showing large topological robustness against continuous deformations, without stringent external interference conditions. By directly measuring the spatial profile of all three vectorial magnetic fields, we reveal multiple π-twist target skyrmion configurations mapped to multi-resonant near-equidistant LSP eigenmodes. The real-space skyrmion topology is robust against deformations of the meta-structure, demonstrating flexible skyrmionic textures for arbitrary shapes. The observed magnetic LSP skyrmions pave the way to ultra-compact and robust plasmonic devices, such as flexible sensors, wearable electronics and ultra-compact antennas.

Measuring the magnetic topological spin structure of light using an anapole probe

Topological spin structures of light, including the Skyrmion, Meron, and bi-Meron, are intriguing optical phenomena that arise from spin-orbit coupling. They have promising potential applications in nano-metrology, data storage, super-resolved imaging and chiral detection. Aside from the electric part of optical spin, of equal importance is the magnetic part, particularly the H-type electromagnetic modes for which the spin topological properties of the field are dominated by the magnetic field. However, their observation and measurement remains absent and faces difficult challenges. Here, we design a unique type of anapole probe to measure specifically the photonic spin structures dominated by magnetic fields. The probe is composed of an Ag-core and Si-shell nanosphere, which manifests as a pure magnetic dipole with no electric response. The effectiveness of the method was validated by characterizing the magnetic field distributions of various focused vector beams. It was subsequently employed to measure the magnetic topological spin structures, including individual Skyrmions and Meron/Skyrmion lattices for the first time. The proposed method may be a powerful tool to characterize the magnetic properties of optical spin and valuable in advancing spin photonics.

Towards higher-dimensional structured light

Structured light refers to the arbitrarily tailoring of optical fields in all their degrees of freedom (DoFs), from spatial to temporal. Although orbital angular momentum (OAM) is perhaps the most topical example, and celebrating 30 years since its connection to the spatial structure of light, control over other DoFs is slowly gaining traction, promising access to higher-dimensional forms of structured light. Nevertheless, harnessing these new DoFs in quantum and classical states remains challenging, with the toolkit still in its infancy. In this perspective, we discuss methods, challenges, and opportunities for the creation, detection, and control of multiple DoFs for higher-dimensional structured light. We present a roadmap for future development trends, from fundamental research to applications, concentrating on the potential for larger-capacity, higher-security information processing and communication, and beyond.

Smooth Sidewalls on Crystalline Gold through Facet-Selective Anisotropic Reactive Ion Etching: Toward Low-Loss Plasmonic Devices

Quantum plasmonics aims to harness the deeply subwavelength confinement provided by plasmonic devices to engineer more efficient interfaces to quantum systems in particular single emitters. Realizing this vision is hampered by the roughness-induced scattering and loss inherent in most nanofabricated devices. In this work, we show evidence of a reactive ion etching process to selectively etch gold along select crystalline facets. Since the etch is facet selective, the sidewalls of fabricated devices are smoother than the lithography induced line-edge roughness with the prospect of achieving atomic smoothness by further optimization of the etch chemistry. This opens up a route toward fabricating integrated plasmonic circuits that can achieve loss metrics close to fundamental bounds.

Intrinsic Spin-Momentum Dynamics of Surface Electromagnetic Waves in Dispersive Interfaces

Intrinsic spin-momentum locking is an inherent property of surface electromagnetic fields and its study has led to the discovery of phenomena such as unidirectional guided waves and photonic spin lattices. Previously, dispersion was ignored in spin-momentum locking, resulting in anomalies contradicting the apparent physical reality. Here, we formulate four dispersive spin-momentum equations, revealing in theory that transverse spin is locked with kinetic momentum. Moreover, in dispersive metal or magnetic materials spin-momentum locking obeys the left-hand screw rule. In addition to dispersion, structural features can affect substantially this locking. Remarkably, an extraordinary spin originating from coupling polarization ellipticities is uncovered that depends on the symmetry of the field modes. We further identify the properties of this spin-momentum locking with diverse photonic topological lattices by engineering their rotational symmetry akin to that in solid-state physics. The concept of spin-momentum locking based on photon flow properties translates easily to other classical wave fields.

Observation of localized magnetic plasmon skyrmions

Optical skyrmions have recently been constructed by tailoring vectorial near-field distributions through the interference of multiple surface plasmon polaritons, offering promising features for advanced information processing, transport and storage. Here, we provide experimental demonstration of electromagnetic skyrmions based on magnetic localized spoof plasmons (LSP) showing large topological robustness against continuous deformations, without stringent external interference conditions. By directly measuring the spatial profile of all three vectorial magnetic fields, we reveal multiple π-twist target skyrmion configurations mapped to multi-resonant near-equidistant LSP eigenmodes. The real-space skyrmion topology is robust against deformations of the meta-structure, demonstrating flexible skyrmionic textures for arbitrary shapes. The observed magnetic LSP skyrmions pave the way to ultra-compact and robust plasmonic devices, such as flexible sensors, wearable electronics and ultra-compact antennas.

Photonic Spin Lattices: Symmetry Constraints for Skyrmion and Meron Topologies

Symmetry and topology govern many electronic, magnetic, and photonic phenomena in condensed matter physics and optics, resulting in counterintuitive skyrmion, meron, and other phenomena important for modern technologies. Here we demonstrate photonic spin lattices as a new topological construct governed by the spin-orbit coupling in an optical field. The symmetry of the electromagnetic field in the presence of the spin-orbit interaction may result in only two types of photonic spin lattices: either hexagonal spin-skyrmion or square spin-meron lattices. We show that these spin structures correspond to the lowest energy of the electromagnetic field configuration, therefore, energetically stable. We further show that in the absence of spin-orbit coupling these spin topologies are degenerated in dynamic field skyrmions, unifying the description of electromagnetic field topologies. The results provide a new understanding of electromagnetic field topology and its transformations as well as new opportunities for applications in quantum technologies, spin optics, and topological photonics.

Particle-like topologies in light

Three-dimensional (3D) topological states resemble truly localised, particle-like objects in physical space. Among the richest such structures are 3D skyrmions and hopfions, that realise integer topological numbers in their configuration via homotopic mappings from real space to the hypersphere (sphere in 4D space) or the 2D sphere. They have received tremendous attention as exotic textures in particle physics, cosmology, superfluids, and many other systems. Here we experimentally create and measure a topological 3D skyrmionic hopfion in fully structured light. By simultaneously tailoring the polarisation and phase profile, our beam establishes the skyrmionic mapping by realising every possible optical state in the propagation volume. The resulting light field's Stokes parameters and phase are synthesised into a Hopf fibration texture. We perform volumetric full-field reconstruction of the [Formula: see text] mapping, measuring a quantised topological charge, or Skyrme number, of 0.945. Such topological state control opens avenues for 3D optical data encoding and metrology. The Hopf characterisation of the optical hypersphere endows a fresh perspective to topological optics, offering experimentally-accessible photonic analogues to the gamut of particle-like 3D topological textures, from condensed matter to high-energy physics.

Polaritonic Vortices with a Half-Integer Charge

Topological spin textures are field arrangements that cannot be continuously deformed to a fully polarized state. In particular, merons are topological textures characterized by half-integer topological charge ±1/2 and vortex-like swirling patterns at large distances. Merons have been studied previously in the context of cosmology, fluid dynamics, condensed matter physics and plasmonics. Here, we visualized optical spin angular momentum of phonon polaritons that resembles nanoscale meron spin textures. Phonon polaritons, hybrids of infrared photons and phonons in hexagonal boron nitride, were excited by circularly polarized light incident on a ring-shaped antenna and imaged using infrared near-field techniques. The polariton field reveals a half-integer topological charge determined by the handedness of the incident beam. Our phonon polaritonic platform opens up new pathways to create, control, and visualize topological textures.

Supertoroidal light pulses as electromagnetic skyrmions propagating in free space

Topological complex transient electromagnetic fields give access to nontrivial light-matter interactions and provide additional degrees of freedom for information transfer. An important example of such electromagnetic excitations are space-time non-separable single-cycle pulses of toroidal topology, the exact solutions of Maxwell's equations described by Hellwarth and Nouchi in 1996 and recently observed experimentally. Here we introduce an extended family of electromagnetic excitation, the supertoroidal electromagnetic pulses, in which the Hellwarth-Nouchi pulse is just the simplest member. The supertoroidal pulses exhibit skyrmionic structure of the electromagnetic fields, multiple singularities in the Poynting vector maps and fractal-like distributions of energy backflow. They are of interest for transient light-matter interactions, ultrafast optics, spectroscopy, and toroidal electrodynamics.

Observation of Acoustic Skyrmions

Despite a long history of studies, acoustic waves are generally regarded as spinless scalar waves, until recent research revealed their rich structures. Here, we report the experimental observation of skyrmion configurations in acoustic waves. We find that surface acoustic waves trapped by a designed hexagonal acoustic metasurface give rise to skyrmion lattice patterns in the dynamic acoustic velocity fields (i.e., the oscillating acoustic air flows). Using an acoustic velocity sensing technique, we directly visualize a Néel-type skyrmion configuration of the acoustic velocity fields. We further demonstrate, respectively, the controllability and robustness of the acoustic skyrmion lattices by tuning the phase differences between the acoustic sources and by introducing local perturbations in our setup. Our study unveils a fundamental acoustic phenomenon that may enable unprecedented manipulation of acoustic waves and may inspire future technologies including advanced acoustic tweezers for the control of small particles.

Nonlinear Tunable Vibrational Response in Hexagonal Boron Nitride

Nonlinear light-matter interactions in structured materials are the source of exciting properties and enable vanguard applications in photonics. However, the magnitude of nonlinear effects is generally small, thus requiring high optical intensities for their manifestation at the nanoscale. Here, we reveal a large nonlinear response of monolayer hexagonal boron nitride (hBN) in the mid-infrared phonon-polariton region, triggered by the strongly anharmonic potential associated with atomic vibrations in this material. We present robust first-principles theory predicting a threshold light field ∼24 MV/m to produce order-unity effects in Kerr nonlinearities and harmonic generation, which are made possible by a combination of the long lifetimes exhibited by optical phonons and the strongly asymmetric landscape of the configuration energy in hBN. We further foresee polariton blockade at the few-quanta level in nanometer-sized structures. In addition, by mixing static and optical fields, the strong nonlinear response of monolayer hBN gives rise to substantial frequency shifts of optical phonon modes, exceeding their spectral width for in-plane DC fields that are attainable using lateral gating technology. We therefore predict a practical scheme for electrical tunability of the vibrational modes with potential interest in mid-infrared optoelectronics. The strong nonlinear response, low damping, and robustness of hBN polaritons set the stage for the development of applications in light modulation, sensing, and metrology, while triggering the search for an intense vibrational nonlinear response in other ionic materials.

Topological bimeronic beams

This Letter proposes a family of structured light, called bimeronic beams, that characterize topological structures of bimeron (the quasiparticle homeomorphic to skyrmion). The polarization Stokes vectors of bimeronic beams emulate bimeron structures, which are reconfigurable to form various topological textures by tuning mode parameters. The bimeronic beams unveil a mechanism to transform diverse topological states of light, similar to the skyrmionic transformations among Néel, Bloch, and anti-skyrmion types. Moreover, bimeronic transformations are more generalized to include skyrmionic transformations as special cases.

Orbital angular momentum multiplication in plasmonic vortex cavities

Orbital angular momentum of light is a core feature in photonics. Its confinement to surfaces using plasmonics has unlocked many phenomena and potential applications. Here, we introduce the reflection from structural boundaries as a new degree of freedom to generate and control plasmonic orbital angular momentum. We experimentally demonstrate plasmonic vortex cavities, generating a succession of vortex pulses with increasing topological charge as a function of time. We track the spatiotemporal dynamics of these angularly decelerating plasmon pulse train within the cavities for over 300 femtoseconds using time-resolved photoemission electron microscopy, showing that the angular momentum grows by multiples of the chiral order of the cavity. The introduction of this degree of freedom to tame orbital angular momentum delivered by plasmonic vortices could miniaturize pump probe-like quantum initialization schemes, increase the torque exerted by plasmonic tweezers, and potentially achieve vortex lattice cavities with dynamically evolving topology.

The 2021 ultrafast spectroscopic probes of condensed matter roadmap

In the 60 years since the invention of the laser, the scientific community has developed numerous fields of research based on these bright, coherent light sources, including the areas of imaging, spectroscopy, materials processing and communications. Ultrafast spectroscopy and imaging techniques are at the forefront of research into the light-matter interaction at the shortest times accessible to experiments, ranging from a few attoseconds to nanoseconds. Light pulses provide a crucial probe of the dynamical motion of charges, spins, and atoms on picosecond, femtosecond, and down to attosecond timescales, none of which are accessible even with the fastest electronic devices. Furthermore, strong light pulses can drive materials into unusual phases, with exotic properties. In this roadmap we describe the current state-of-the-art in experimental and theoretical studies of condensed matter using ultrafast probes. In each contribution, the authors also use their extensive knowledge to highlight challenges and predict future trends.

Optical Excitations with Electron Beams: Challenges and Opportunities

Free electron beams such as those employed in electron microscopes have evolved into powerful tools to investigate photonic nanostructures with an unrivaled combination of spatial and spectral precision through the analysis of electron energy losses and cathodoluminescence light emission. In combination with ultrafast optics, the emerging field of ultrafast electron microscopy utilizes synchronized femtosecond electron and light pulses that are aimed at the sampled structures, holding the promise to bring simultaneous sub-Å-sub-fs-sub-meV space-time-energy resolution to the study of material and optical-field dynamics. In addition, these advances enable the manipulation of the wave function of individual free electrons in unprecedented ways, opening sound prospects to probe and control quantum excitations at the nanoscale. Here, we provide an overview of photonics research based on free electrons, supplemented by original theoretical insights and discussion of several stimulating challenges and opportunities. In particular, we show that the excitation probability by a single electron is independent of its wave function, apart from a classical average over the transverse beam density profile, whereas the probability for two or more modulated electrons depends on their relative spatial arrangement, thus reflecting the quantum nature of their interactions. We derive first-principles analytical expressions that embody these results and have general validity for arbitrarily shaped electrons and any type of electron-sample interaction. We conclude with some perspectives on various exciting directions that include disruptive approaches to noninvasive spectroscopy and microscopy, the possibility of sampling the nonlinear optical response at the nanoscale, the manipulation of the density matrices associated with free electrons and optical sample modes, and appealing applications in optical modulation of electron beams, all of which could potentially revolutionize the use of free electrons in photonics.

Mapping the Magnetic Field Intensity of Light with the Nonlinear Optical Emission of a Silicon Nanoparticle

To detect the magnetic component of arbitrary unknown optical fields, a candidate probe must meet a list of demanding requirements, including a spatially isotropic magnetic response, suppressed electric effect, and wide operating bandwidth. Here, we show that a silicon nanoparticle satisfies all these requirements, and its optical magnetism driven multiphoton luminescence enables direct mapping of the magnetic field intensity distribution of a tightly focused femtosecond laser beam with varied polarization orientation and spatially overlapped electric and magnetic components. Our work establishes a powerful nonlinear optics paradigm for probing unknown optical magnetic fields of arbitrary electromagnetic structures, which is not only essential for realizing subwavelength-scale optical magnetometry but also facilitates nanophotonic research in the magnetic light-matter interaction regime.

Emulating spin transport with nonlinear optics, from high-order skyrmions to the topological Hall effect

Exploring material magnetization led to countless fundamental discoveries and applications, culminating in the field of spintronics. Recently, research effort in this field focused on magnetic skyrmions – topologically robust chiral magnetization textures, capable of storing information and routing spin currents via the topological Hall effect. In this article, we propose an optical system emulating any 2D spin transport phenomena with unprecedented controllability, by employing three-wave mixing in 3D nonlinear photonic crystals. Precise photonic crystal engineering, as well as active all-optical control, enable the realization of effective magnetization textures beyond the limits of thermodynamic stability in current materials. As a proof-of-concept, we theoretically design skyrmionic nonlinear photonic crystals with arbitrary topologies and propose an optical system exhibiting the topological Hall effect. Our work paves the way towards quantum spintronics simulations and novel optoelectronic applications inspired by spintronics, for both classical and quantum optical information processing.

Control of effective magnetization textures like skyrmions is limited by the thermodynamic stability in current materials. Here, the authors propose a 3D nonlinear photonic crystal to emulate 2D spin transport phenomena with excellent controllability.

Transverse spin dynamics in structured electromagnetic guided waves

We formulate and experimentally validate a set of spin–momentum equations which are analogous to the Maxwell’s equations and govern spin–orbit coupling in electromagnetic guided waves. The Maxwell-like spin–momentum equations reveal the spin–momentum locking, the chiral spin texture of the field, Berry phase, and the spin–orbit interaction in the optical near field. The observed spin–momentum behavior can be extended to other classical waves, such as acoustic, fluid, gas, and gravitational waves.

Spin–momentum locking, a manifestation of topological properties that governs the behavior of surface states, was studied intensively in condensed-matter physics and optics, resulting in the discovery of topological insulators and related effects and their photonic counterparts. In addition to spin, optical waves may have complex structure of vector fields associated with orbital angular momentum or nonuniform intensity variations. Here, we derive a set of spin–momentum equations which describes the relationship between the spin and orbital properties of arbitrary complex electromagnetic guided modes. The predicted photonic spin dynamics is experimentally verified with four kinds of nondiffracting surface structured waves. In contrast to the one-dimensional uniform spin of a guided plane wave, a two-dimensional chiral spin swirl is observed for structured guided modes. The proposed framework opens up opportunities for designing the spin structure and topological properties of electromagnetic waves with practical importance in spin optics, topological photonics, metrology and quantum technologies and may be used to extend the spin-dynamics concepts to fluid, acoustic, and gravitational waves.

Plasmonic topological quasiparticle on the nanometre and femtosecond scales

At the interface of classical and quantum physics, the Maxwell and Schrödinger equations describe how optical fields drive and control electronic phenomena to enable lightwave electronics at terahertz or petahertz frequencies and on ultrasmall scales^1-5. The electric field of light striking a metal interacts with electrons and generates light-matter quasiparticles, such as excitons⁶ or plasmons⁷, on an attosecond timescale. Here we create and image a quasiparticle of topological plasmonic spin texture in a structured silver film. The spin angular momentum components of linearly polarized light interacting with an Archimedean coupling structure with a designed geometric phase generate plasmonic waves with different orbital angular momenta. These plasmonic fields undergo spin-orbit interaction and their superposition generates an array of plasmonic vortices. Three of these vortices can form spin textures that carry non-trivial topological charge⁸ resembling magnetic meron quasiparticles⁹. These spin textures are localized within a half-wavelength of light, and exist on the timescale of the plasmonic field. We use ultrafast nonlinear coherent photoelectron microscopy to generate attosecond videos of the spatial evolution of the vortex fields; electromagnetic simulations and analytic theory confirm the presence of plasmonic meron quasiparticles. The quasiparticles form a chiral field, which breaks the time-reversal symmetry on a nanometre spatial scale and a 20-femtosecond timescale (the 'nano-femto scale'). This transient creation of non-trivial spin angular momentum topology pertains to cosmological structure creation and topological phase transitions in quantum matter^10-12, and may transduce quantum information on the nano-femto scale^13,14.

Plasmonic Skyrmion Lattice Based on the Magnetoelectric Effect

The physical mechanism of the plasmonic skyrmion lattice formation in a magnetic layer deposited on a metallic substrate is studied theoretically. The optical lattice is the essence of the standing interference pattern of the surface plasmon polaritons created through coherent or incoherent laser sources. The nodal points of the interference pattern play the role of lattice sites where skyrmions are confined. The confinement appears as a result of the magnetoelectric effect and the electric field associated with the plasmon waves. The proposed model is applicable to yttrium iron garnet and single-phase multiferroics and combines plasmonics and skyrmionics.

On the pole expansion of electromagnetic fields

In several publications, it has been shown how to calculate the near- or far-field properties for a given source or incident field using the resonant states, also known as quasi-normal modes. As previously noted, this pole expansion is not unique, and there exist many equivalent formulations with dispersive expansion coefficients. Here, we approach the pole expansion of the electromagnetic fields using the Mittag-Leffler theorem and obtain another set of formulations with constant weight factors for each pole. We compare the performance and applicability of these formulations using analytical and numerical examples. It turns out that the accuracy of all approaches is rather comparable with a slightly better global convergence of the approach based on a formulation with dispersive expansion coefficients. However, other expansions can be superior locally and are typically faster. Our work will help with selecting appropriate formulations for an efficient description of the electromagnetic response in terms of the resonant states.