Particle-like topologies in light

Formation and Controlling of Optical Hopfions in High Harmonic Generation

Toroidal vortex is a kind of novel and exotic structured light with potential applications in photonic topology and quantum information. Here, we present the study on high harmonic generation from the interaction of the intense toroidal vortices with atoms. We show that the spatial distribution of harmonic spectra reveal unique structures, which are kinds of high-order topological toroidal vortex because of the rotating of the driving fields with transverse orbital angular momentum. Then we show that, by synthesizing the toroidal vortices and optical vortices with longitudinal orbital angular momentum, it is able to generate the optical hopfions in the extreme ultraviolet range, which exhibit a completely different topological property compared with both the driving fields. Harnessing the spin angular momentum selection rules, we further show that one can control the topological texture and channel each harmonic into a single mode of controllable Hopf invariant.

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.

Optical skyrmions in the Bessel profile

Optical skyrmions formed in terms of polarization are topological quasi-particles, and they have garnered much interest in the optical community owing to their unique inhomogeneous polarization structure and simplicity in their experimental realization. These structures belong to the Poincaré beams satisfying the stable topology. We theoretically investigated the non-diffracting and self-healing Poincaré beams based on the superposition of two orthogonal Bessel modes by the longitudinal mode matching technique. These Poincaré beams are topologically protected, and we suggest them as optical skyrmions in the corresponding Stokes vector fields. These optical skyrmions are quasi-skyrmions, and their range of propagation depends on the range of superposed Bessel modes. We have shown longitudinal mode matching of superposed Bessel beams is a necessary condition for the generation of propagation-invariant and non-diffracting skyrmions. The proposed longitudinal mode matching technique facilitates the generation of skyrmions with tunable position and range without any on-axis intensity modulations along the propagation axis. A suitable experimental configuration is suggested to realize variable order skyrmions in Bessel modes. The suggested experimental configuration can produce optical skyrmions even in ultra-short laser pulses with high mode conversion efficacy. This work can provide a new direction for the generation of skyrmions with completely new textures and features with reference to existing skyrmions originating from Laguerre-Gaussian modes.

Controlling the Polarization of Nitrogen Ion Lasing

Air lasing provides a promising technique to remotely produce coherent radiation in the atmosphere and has attracted continuous attention. However, the polarization properties of N2+ lasing with seeding have not been understood since it was discovered 10 years ago, in which the polarization behaviors appear disordered and confusing. Here, we performed an experimental and theoretical investigation of the polarization properties of N2+ lasing and successfully revealed its underlying physical mechanism. We found that the optical gain is anisotropic, owing to the permanent alignment of N2+ induced by the preferential ionization of the pump light. As a result, the polarization of the N2+ lasing tends to align with that of the pump light after amplification, which becomes more pronounced as the amplification factor increases. Based on the permanent alignment of N2+, we built a theoretical model that analytically interpreted and numerically reproduced the experimental observations, which points out the key factors for controlling the polarization of N2+ lasing.

Generation for high-dimensional caustics and artificially tailored structured caustic beams

We theoretically propose and demonstrate topological parabolic umbilic beams (PUBs) with high-dimensional caustic by mapping catastrophe theory into optics. The PUBs are first experimentally observed via dimensionality reduction. Due to the high-dimensionality, such light beams exhibit rich caustic structures characterized by optical singularities where the high-intensity gradient appears. Further, we propose an improved caustic approach to artificially tailored structured beams which exhibit significant intensity gradient and phase gradient. The properties can trap and drive particles to move along the predesigned trajectory, respectively. The advantages for structured caustic beams likely enable new applications in flexible particle manipulation, light-sheet microscopy, and micromachining.

Non-Gaussian anomalous diffusion of optical vortices

Anomalous diffusion of different particlelike entities, the deviation from typical Brownian motion, is ubiquitous in complex physical and biological systems. While optical vortices move randomly in evolving speckle fields, optical vortices have only been observed to exhibit pure Brownian motion in random speckle fields. Here we present direct experimental evidence of the anomalous diffusion of optical vortices in temporally varying speckle patterns from multiple-scattering viscoelastic media. Moreover, we observe two characteristic features, i.e., the self-similarity and the antipersistent correlation of the optical vortex motion, indicating that the mechanism of the observed subdiffusion of optical vortices can only be attributed to fractional Brownian motion (FBM). We further demonstrate that the vortex displacements exhibit a non-Gaussian heavy-tailed distribution. Additionally, we modulate the extent of subdiffusion, such as diffusive scaling exponents, and the non-Gaussianity of optical vortices by altering the viscoelasticity of samples. The discovery of the complex FBM but non-Gaussian subdiffusion of optical vortices may not only offer insight into certain fundamental physics, including the anomalous diffusion of vortices in fluids and the decoupling between Brownianity and Gaussianity, but also suggest a strong potential for utilizing optical vortices as tracers in microrheology instead of the introduced exogenous probe particles in particle tracking microrheology.

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.

Trapped atoms in spatially-structured vector light fields

Spatially-structured laser beams, eventually carrying orbital angular momentum, affect electronic transitions of atoms and their motional states in a complex way. We present a general framework, based on the spherical tensor decomposition of the interaction Hamiltonian, for computing atomic transition matrix elements for light fields of arbitrary spatial mode and polarization structures. We study both the bare electronic matrix elements, corresponding to transitions with no coupling to the atomic center-of-mass motion, as well as the matrix elements describing the coupling to the quantized atomic motion in the resolved side-band regime. We calculate the spatial dependence of electronic and motional matrix elements for tightly focused Hermite-Gaussian, Laguerre-Gaussian and for radially and azimuthally polarized beams. We show that near the diffraction limit, all these beams exhibit longitudinal fields and field gradients, which strongly affect the selection rules and could be used to tailor the light-matter interaction. The presented framework is useful for describing trapped atoms or ions in spatially-structured light fields and therefore for designing new protocols and setups in quantum optics, -sensing and -information processing. We provide open code to reproduce our results or to evaluate interaction matrix elements for different transition types, beam structures and interaction geometries.

Vortex rings in paraxial laser beams

Interference of a fundamental vortex-free Gaussian beam with a co-propagating plane wave leads to nucleation of a series of vortex rings in the planes transverse to the optical axis; the number of rings grows with vanishing amplitude of the plane wave. In contrast, such interference with a beam carrying on-axis vortex with winding number l results in the formation of |l| rings elongated and gently twisted in propagation direction. The twist handedness of the vortex lines is determined by the interplay between dynamic and geometric phases of the Gaussian beam and the twist angle grows with vanishing amplitude of the plane wave. In the counter-propagating geometry the vortex rings nucleate and twist with half-wavelength period dominated by the interference grating in propagation direction.

Topological solitonic macromolecules

Being ubiquitous, solitons have particle-like properties, exhibiting behaviour often associated with atoms. Bound solitons emulate dynamics of molecules, though solitonic analogues of polymeric materials have not been considered yet. Here we experimentally create and model soliton polymers, which we call "polyskyrmionomers", built of atom-like individual solitons characterized by the topological invariant representing the skyrmion number. With the help of nonlinear optical imaging and numerical modelling based on minimizing the free energy, we reveal how topological point defects bind the solitonic quasi-atoms into polyskyrmionomers, featuring linear, branched, and other macromolecule-resembling architectures, as well as allowing for encoding data by spatial distributions of the skyrmion number. Application of oscillating electric fields activates diverse modes of locomotion and internal vibrations of these self-assembled soliton structures, which depend on symmetry of the solitonic macromolecules. Our findings suggest new designs of soliton meta matter, with a potential for the use in fundamental research and technology.

Topologically protected optical polarization singularities in four-dimensional space

Optical singularities play a major role in modern optics and are frequently deployed in structured light, super-resolution microscopy, and holography. While phase singularities are uniquely defined as locations of undefined phase, polarization singularities studied thus far are either partial, i.e., bright points of well-defined polarization, or are unstable for small field perturbations. We demonstrate a complete, topologically protected polarization singularity; it is located in the four-dimensional space spanned by the three spatial dimensions and the wavelength and is created in the focus of a cascaded metasurface-lens system. The field Jacobian plays a key role in the design of such higher-dimensional singularities, which can be extended to multidimensional wave phenomena, and pave the way for unconventional applications in topological photonics and precision sensing.

Synthetic spin dynamics with Bessel-Gaussian optical skyrmions

Skyrmions are topologically stable fields that cannot be smoothly deformed into any other field configuration that differs topologically, that is, one that possesses a different integer topological invariant called the Skyrme number. They have been studied as 3-dimensional and 2-dimensional skyrmions in both magnetic and, more recently, optical systems. Here, we introduce an optical analogy to magnetic skyrmions and demonstrate their dynamics within a magnetic field. Our optical skyrmions and synthetic magnetic field are both engineered using superpositions of Bessel-Gaussian beams, with time dynamics observed over the propagation distance. We show that the skyrmionic form changes during propagation, exhibiting controllable periodic precession over a well defined range, analogous to time varying spin precession in homogeneous magnetic fields. This local precession manifests as the global beating between skyrmion types, while still maintaining the invariance of the Skyrme number, which we monitor through a full Stokes analysis of the optical field. Finally, we outline, through numerical simulation, how this approach could be extended to create time varying magnetic fields, offering free-space optical control as a powerful analogue to solid state systems.

Transverse energy flow in an optical Skyrmionic Hopfion

The energy flow of light represents a natural way of investigating complex light fields with respect to their applicability. With the generation of a three-dimensional Skyrmionic Hopfion structure in light, which is a topological 3D field configuration with particle-like nature, we paved the way to employ optical, topological constructs. In this work, we present an analysis of the transverse energy flow in the optical Skyrmionic Hopfion, showing the transfer of the topological properties to the mechanical attributes such as the optical angular momentum (OAM). Our findings thus prepare topological structures to be applied in optical traps and data storage or communication.

Spatiotemporal pulse weaving scalar optical hopfions

Scalar optical hopfions weaved by nested equiphase lines in the shape of a toroidal vortex are theoretically designed and experimentally demonstrated. This category of hopfions manifesting as a spatiotemporally structured pulse propagating in space-time may enable encoding and transferring optical topological information in an additional (temporal) dimension.

Accelerating Airy beams with particle-like polarization topologies and free-space bimeronic lattices

Phase and polarization singularities in electromagnetic waves are usually attributed to one-dimensional topologies-lines, knots, and braids. Recently, particle-like structures have been predicted and observed: optical Skyrmions, vortices with spherical polarization, etc. In this article, we devise vector Airy beams with point-like singularity in the focal plane, thus leading to the presence of a particle-like topology. We present an extensive analytical analysis of the spatial spectra and focal structure of such beams. We report on the presence of a free-space lattice of bimerons in such vector Airy beams.

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 Polarization Singularities and Topological Textures in Sound Waves

Polarization singularities and topological polarization structures are generic features of inhomogeneous vector wave fields of any nature. However, their experimental studies mostly remain restricted to optical waves. Here, we report the observation of polarization singularities, topological Möbius-strip structures, and skyrmionic textures in 3D polarization fields of inhomogeneous sound waves. Our experiments are made in the ultrasonic domain using nonparaxial propagating fields generated by space-variant 2D acoustic sources. We also retrieve distributions of the 3D spin density in these fields. Our results open the avenue to investigations and applications of topological features and nontrivial 3D vector properties of structured sound waves.

Topological near fields generated by topological structures

The central idea of metamaterials and metaoptics is that, besides their base materials, the geometry of structures offers a broad extra dimension to explore for exotic functionalities. Here, we discover that the topology of structures fundamentally dictates the topological properties of optical fields and offers a new dimension to exploit for optical functionalities that are irrelevant to specific material constituents or structural geometries. We find that the nontrivial topology of metal structures ensures the birth of polarization singularities (PSs) in the near field with rich morphologies and intriguing spatial evolutions including merging, bifurcation, and topological transition. By mapping the PSs to non-Hermitian exceptional points and using homotopy theory, we extract the core invariant that governs the topological classification of the PSs and the conservation law that regulates their spatial evolutions. The results bridge singular optics, topological photonics, and non-Hermitian physics, with potential applications in chiral sensing, chiral quantum optics, and beyond photonics in other wave systems.

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.

Multiple quasi-perfect vector vortex beams with arbitrary 3D position on focus

We show a method for creating multiple independent quasi-perfect vector vortex beams with real-time programmable radii, topological charges, polarization orders, and position in three dimensions using a device based on a phase-only liquid-crystal-on-silicon display. We achieved the simultaneous generation of up to seven independent beams, with topological charges from -3 to 3, and found great agreement between the simulated and the measured phases and polarization structures. Additionally, we used the same scheme for enhancing the depth of focus of a single beam, resulting in a "tube" beam that preserves its properties during propagation.

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.

Extreme Concentration and Nanoscale Interaction of Light

Concentrating light strongly calls for appropriate polarization patterns of the focused light beam and for up to a full 4π solid angle geometry. Focusing on the extreme requires efficient coupling to nanostructures of one kind or another via cylindrical vector beams having such patterns, the details of which depend on the geometry and property of the respective nanostructure. Cylindrical vector beams can not only be used to study a nanostructure, but also vice versa. Closely related is the discussion of topics such as the ultimate diffraction limit, a resonant field enhancement near nanoscopic absorbers, as well as speculations about nonresonant field enhancement, which, if it exists, might be relevant to pair production in vacuum. These cases do require further rigorous simulations and more decisive experiments. While there is a wide diversity of scenarios, there are also conceptually very different models offering helpful intuitive pictures despite this diversity.