Multidimensional phase singularities in nanophotonics

Dipolar Huygens-Kerker radiation for surface waves

Exotic dipolar radiation with zero light emission in one direction but maximal light emission in the opposite direction was envisioned by Huygens in 1690, and it could emerge in vacuum if the ratio between the source's electric and magnetic dipole moments fulfills the Kerker condition as revealed by Kerker in 1983. Due to its intricate connection with both the Huygens principle and Kerker condition, this radiation phenomenon is suggested to be termed as dipolar Huygens-Kerker radiation, and at this moment, the ratio is termed as the Huygens-Kerker ratio. However, the dipolar Huygens-Kerker radiation remains underexplored in non-vacuum matters, inside which the source locates, especially for surface waves. Here we find that the dipolar Huygens-Kerker radiation of surface waves in principle could occur in non-vacuum matters and is essentially featured with the same normalized radiation pattern, which is closely related to the inclination factor that appears in the Fresnel-Kirchhoff diffraction theory. Moreover, the corresponding Huygens-Kerker ratio is intrinsically determined by the phase velocity of excited surface waves. To be specific, the Huygens-Kerker ratio is proportional to the phase velocity for transverse-magnetic surface waves but becomes inversely proportional to the phase velocity for transverse-electric surface waves.

Optical vortex-antivortex crystallization in free space

Stable vortex lattices are basic dynamical patterns which have been demonstrated in physical systems including superconductor physics, Bose-Einstein condensates, hydrodynamics and optics. Vortex-antivortex (VAV) ensembles can be produced, self-organizing into the respective polar lattices. However, these structures are in general highly unstable due to the strong VAV attraction. Here, we demonstrate that multiple optical VAV clusters nested in the propagating coherent field can crystallize into patterns which preserve their lattice structures over distance up to several Rayleigh lengths. To explain this phenomenon, we present a model for effective interactions between the vortices and antivortices at different lattice sites. The observed VAV crystallization is a consequence of the globally balanced VAV couplings. As the crystallization does not require the presence of nonlinearities and appears in free space, it may find applications to high-capacity optical communications and multiparticle manipulations. Our findings suggest possibilities for constructing VAV complexes through the orbit-orbit couplings, which differs from the extensively studied spin-orbit couplings.

Highly efficient vortex generation at the nanoscale

Control of the angular momentum of light at the nanoscale is critical for many applications of subwavelength photonics, such as high-capacity optical communications devices, super-resolution imaging and optical trapping. However, conventional approaches to generate optical vortices suffer from either low efficiency or relatively large device footprints. Here we show a new strategy for vortex generation at the nanoscale that surpasses single-pixel phase control. We reveal that interaction between neighbouring nanopillars of a meta-quadrumer can tailor both the intensity and phase of the transmitted light. Consequently, a subwavelength nanopillar quadrumer is sufficient to cover a 2lπ phase change, thus efficiently converting incident light into high-purity optical vortices with different topological charges l. Benefiting from the nanoscale footprint of the meta-quadrumers, we demonstrate high-density vortex beam arrays and high-dimensional information encryption, bringing a new degree of freedom to many designs of meta-devices.

On-chip photodetection of angular momentums of vortex structured light

Structured vortex light with orbital angular momentum (OAM) shows great promise for high-bandwidth optical communications, quantum information and computing, optical tweezers, microscopy, astronomy, among others. Generating, controlling, and detecting of vortex light by all-electrical means is at the heart of next generation nanophotonic platforms. However, on-chip electrical photodetection of structured vortex light remains challenging. Here, we propose an on-chip photodetector based on 2D broadband thermoelectric material (PdSe2) with a well-designed spin-Hall couplers to directly characterize angular momentum modes of vortex structured light. Photothermoelectric responses in the PdSe2 nanoflake, excited by the focusing surface plasmons, show a magnitude proportional to the total angular momentum modes of the infrared vortex beams, thereby achieving direct detection of spin and orbital angular momentum, as well as the chirality and ellipticity of scalar vortex lights. Our works provide a promising strategy for developing on-chip angular momentum optoelectronic devices, which play a key role in the next-generation high-capacity optical communications, quantum information and computing, imaging, and other photonic systems.

Multifunctional Meta-Devices for Full-Polarization Rotation and Focusing in the Near-Infrared

The creation of multi-channel focused beams with arbitrary polarization states and their corresponding optical torques finds effective applications in the field of optical manipulation at the micro-nanoscale. The existing metasurface-based technologies for polarization rotation have made some progress, but they have been limited to single functions and have not yet achieved the generation of full polarization. In this work, we propose a multi-channel and spatial-multiplexing interference strategy for the generation of multi-channel focusing beams with arbitrary polarization rotation based on all-dielectric birefringent metasurfaces via simultaneously regulating the propagation phase and the geometric phase and independently controlling the wavefronts at different circular polarizations. For the proof of concept, we demonstrate highly efficient multi-channel polarization rotation meta-devices. The meta-devices demonstrate ultra-high polarization extinction ratios and high focusing efficiencies at each polarization channel. Our work provides a compact and versatile wavefront-shaping methodology for full-polarization control, paving a new path for planar multifunctional meta-optical devices in optical manipulation at micro-nano dimensions.

Stable Vortex Solitons Sustained by Localized Gain in a Cubic Medium

We propose a simple dissipative system with purely cubic defocusing nonlinearity and nonuniform linear gain that can support stable localized dissipative vortex solitons with high topological charges without the utilization of competing nonlinearities and nonlinear gain or losses. Localization of such solitons is achieved due to an intriguing mechanism when defocusing nonlinearity stimulates energy flow from the ringlike region with linear gain to the periphery of the medium where energy is absorbed due to linear background losses. Vortex solitons bifurcate from linear gain-guided vortical modes with eigenvalues depending on topological charges that become purely real only at specific gain amplitudes. Increasing gain amplitude leads to transverse expansion of vortex solitons, but simultaneously it usually also leads to stability enhancement. Increasing background losses allows creation of stable vortex solitons with high topological charges that are usually prone to instabilities in conservative and dissipative systems. Propagation of the perturbed unstable vortex solitons in this system reveals unusual dynamical regimes, when instead of decay or breakup, the initial state transforms into stable vortex solitons with lower or sometimes even with higher topological charge. Our results suggest an efficient mechanism for the formation of nonlinear excited vortex-carrying states with suppressed destructive azimuthal modulational instabilities in a simple setting relevant to a wide class of systems, including polaritonic systems, structured microcavities, and lasers.

Analytic ellipsometric measurement for materials under bulk encapsulation

Accurate measurement of the dielectric functions of emerging optical materials is of great importance for advancements in solid-state physics. However, it is rather challenging since most materials are highly active in ambient conditions, which makes in-situ measurements tough. Here, we report an analytical ellipsometry method (AEM) accessible in ambient conditions for measuring the dielectric functions of chemically reactive materials under bulk encapsulation. Taking the highly pursued low-loss plasmonic materials, such as sodium films, as an example, the effectiveness and measuring errors of the proposed AEM have been systematically demonstrated. This verifies AEM's superiority in overcoming the limitations of traditional spectroscopic ellipsometry methodologies, which include complex multi-parameter fitting procedures and the issue of potentially unphysical results, especially in newly developed low-loss materials. Our results will provide a generalized and convenient ellipsometric measurement strategy for sensitive materials under bulk encapsulation.

Visualizing a single wavefront dislocation induced by orbital angular momentum in graphene

Phase singularities are phase-indeterminate points where wave amplitudes are zero, which manifest as phase vertices or wavefront dislocations. In the realm of optical and electron beams, the phase singularity has been extensively explored, demonstrating a profound connection to orbital angular momentum. Direct local imaging of the impact of orbital angular momentum on phase singularities at the nanoscale, however, remains challenging. Here, we study the role of orbital angular momentum in phase singularities in graphene, particularly at the atomic level, through scanning tunneling microscopy and spectroscopy. Our experiments demonstrate that the scatterings between different orbital angular momentum states, which are induced by local rotational symmetry-breaking potentials, can generate additional phase singularities, and result in robust single-wavefront dislocations in real space. Our results pave the way for exploring the effects of orbital degree of freedom on quantum phases in quasiparticle interference processes.

Nanostructure-based orbital angular momentum encryption and multiplexing

The orthogonality among the OAM modes provides a new degree of freedom for optical multiplexing communications. So far, traditional Dammann gratings and spatial light modulators (SLMs) have been widely used to generate OAM beams by modulating electromagnetic waves at each pixel. However, such architectures suffer from limitations in terms of having a resolution of only a few microns and the bulkiness of the entire optical system. With the rapid development of the electromagnetic theory and advanced nanofabrication methods, artificial nanostructures, especially optical metasurfaces, have been introduced which greatly shrink the size of OAM multiplexing devices while increasing the level of integration. This review focuses on the study of encryption, multiplexing and demultiplexing of OAM beams based on nanostructure platforms. After introducing the focusing characteristics of OAM beams, the interaction mechanism between OAM beams and nanostructures is discussed. The physical phenomena of helical dichroism response and spatial separation of OAM beams achieved through nanostructures, setting the stage for OAM encryption and multiplexing, are reviewed. Afterward, the further advancements and potential applications of nanophotonics-based OAM multiplexing are deliberated. Finally, the challenges of conventional design methods and dynamic tunable techniques for nanostructure-based OAM multiplexing technology are addressed.

Experimental realization of a transmissive microwave metasurface for dual vector vortex beams generation

This work presents a theoretical design and experimental demonstration of a transmissive microwave metasurface for generating dual-vector vortex beams (VVBs). The proposed metasurface consists of an array of pixelated dartboard discretization meta-atoms. By rotating the meta-atoms from 0° to 180°, a Pancharatnam-Barry (P-B) phase covering the full 360° range is achieved, with a transmittance exceeding 90% over the frequency range from 9.7 to 10.2 GHz. The measured results demonstrate that when a linearly polarized microwave normally impinges on the metasurface, the transmitted beams correspond to the dual VVBs with different directions. A good agreement among Poincaré sphere theory, full-wave simulation, and experimental measurement is observed. This proposed transmissive microwave metasurface for VVBs may offer promising applications in communications and radar detection.

Spatiotemporal beating and vortices of van der Waals hyperbolic polaritons

In conventional thin materials, the diffraction limit of light constrains the number of waveguide modes that can exist at a given frequency. However, layered van der Waals (vdW) materials, such as hexagonal boron nitride (hBN), can surpass this limitation due to their dielectric anisotropy, exhibiting positive permittivity along one optic axis and negativity along the other. This enables the propagation of hyperbolic rays within the material bulk and an unlimited number of subdiffractional modes characterized by hyperbolic dispersion. By employing time-domain near-field interferometry to analyze ultrafast hyperbolic ray pulses in thin hBN, we showed that their zigzag reflection trajectories bound within the hBN layer create an illusion of backward-moving and leaping behavior of pulse fringes. These rays result from the coherent beating of hyperbolic waveguide modes but could be mistakenly interpreted as negative group velocities and backward energy flow. Moreover, the zigzag reflections produce nanoscale (60 nm) and ultrafast (40 fs) spatiotemporal optical vortices along the trajectory, presenting opportunities to chiral spatiotemporal control of light-matter interactions. Supported by experimental evidence, our simulations highlight the potential of hyperbolic ray reflections for molecular vibrational absorption nanospectroscopy. The results pave the way for miniaturized, on-chip optical spectrometers, and ultrafast optical manipulation.

Three-Dimensional Reconfigurable Optical Singularities in Bilayer Photonic Crystals

Metasurfaces and photonic crystals have revolutionized classical and quantum manipulation of light and opened the door to studying various optical singularities related to phases and polarization states. However, traditional nanophotonic devices lack reconfigurability, hindering the dynamic switching and optimization of optical singularities. This paper delves into the underexplored concept of tunable bilayer photonic crystals (BPhCs), which offer rich interlayer coupling effects. Utilizing silicon nitride-based BPhCs, we demonstrate tunable bidirectional and unidirectional polarization singularities, along with spatiotemporal phase singularities. Leveraging these tunable singularities, we achieve dynamic modulation of bound-state-in-continuum states, unidirectional guided resonances, and both longitudinal and transverse orbital angular momentum. Our work paves the way for multidimensional control over polarization and phase, inspiring new directions in ultrafast optics, optoelectronics, and quantum optics.

Orbital angular momentum-mediated machine learning for high-accuracy mode-feature encoding

Machine learning with optical neural networks has featured unique advantages of the information processing including high speed, ultrawide bandwidths and low energy consumption because the optical dimensions (time, space, wavelength, and polarization) could be utilized to increase the degree of freedom. However, due to the lack of the capability to extract the information features in the orbital angular momentum (OAM) domain, the theoretically unlimited OAM states have never been exploited to represent the signal of the input/output nodes in the neural network model. Here, we demonstrate OAM-mediated machine learning with an all-optical convolutional neural network (CNN) based on Laguerre-Gaussian (LG) beam modes with diverse diffraction losses. The proposed CNN architecture is composed of a trainable OAM mode-dispersion impulse as a convolutional kernel for feature extraction, and deep-learning diffractive layers as a classifier. The resultant OAM mode-dispersion selectivity can be applied in information mode-feature encoding, leading to an accuracy as high as 97.2% for MNIST database through detecting the energy weighting coefficients of the encoded OAM modes, as well as a resistance to eavesdropping in point-to-point free-space transmission. Moreover, through extending the target encoded modes into multiplexed OAM states, we realize all-optical dimension reduction for anomaly detection with an accuracy of 85%. Our work provides a deep insight to the mechanism of machine learning with spatial modes basis, which can be further utilized to improve the performances of various machine-vision tasks by constructing the unsupervised learning-based auto-encoder.

Generation of Spatiotemporal Vortex Pulses by Resonant Diffractive Grating

Spatiotemporal vortex pulses are wave packets that carry transverse orbital angular momentum, exhibiting exotic structured wave fronts that can twist through space and time. Existing methods to generate these pulses require complex setups like spatial light modulators or computer-optimized structures. Here, we demonstrate a new approach to generate spatiotemporal vortex pulses using just a simple diffractive grating. The key is constructing a phase vortex in frequency-momentum space by leveraging symmetry, resonance, and diffraction. Our approach is applicable to any wave system. We use a liquid surface wave (gravity wave) platform to directly demonstrate and observe the real-time generation and evolution of spatiotemporal vortex pulses. This straightforward technique provides opportunities to explore pulse dynamics and potential applications across different disciplines.

Exploiting Topological Darkness in Photonic Crystal Slabs for Spatiotemporal Vortex Generation

Spatiotemporal optical vortices (STOVs) with swirling phase singularities in space and time hold great promise for a wide range of applications across diverse fields. However, current approaches to generate STOVs lack integrability and rely on bulky free-space optical components. Here, we demonstrate routine STOV generation by harnessing the topological darkness phenomenon of a photonic crystal slab. Complete polarization conversion enforced by symmetry enables topological darkness to arise from photonic bands of guided resonances, imprinting vortex singularities onto an ultrashort reflected pulse. Utilizing time-resolved spatial mapping, we provide the first observation of STOV generation using a photonic crystal slab, revealing the imprinted STOV structure manifested as a curved vortex line in the pulse profile in space and time. Our work establishes photonic crystal slabs as a versatile and accessible platform for engineering STOVs and harnessing the topological darkness in nanophotonics.

Ultracompact Single-Photon Sources of Linearly Polarized Vortex Beams

Ultracompact chip-integrated single-photon sources of collimated beams with polarization-encoded states are crucial for integrated quantum technologies. However, most of currently available single-photon sources rely on external bulky optical components to shape the polarization and phase front of emitted photon beams. Efficient integration of quantum emitters with beam shaping and polarization encoding functionalities remains so far elusive. Here, ultracompact single-photon sources of linearly polarized vortex beams based on chip-integrated quantum emitter-coupled metasurfaces are presented, which are meticulously designed by fully exploiting the potential of nanobrick-arrayed metasurfaces. The authors first demonstrate on-chip single-photon generation of high-purity linearly polarized vortex beams with prescribed topological charges of 0, - 1, and +1. The multiplexing of single-photon emission channels with orthogonal linear polarizations carrying different topological charges are further realized and their entanglement is demonstarated. The work illustrates the potential and feasibility of ultracompact quantum emitter-coupled metasurfaces as a new quantum optics platform for realizing chip-integrated high-dimensional single-photon sources.

Metafiber transforming arbitrarily structured light

Structured light has proven useful for numerous photonic applications. However, the current use of structured light in optical fiber science and technology is severely limited by mode mixing or by the lack of optical elements that can be integrated onto fiber end-faces for wavefront engineering, and hence generation of structured light is still handled outside the fiber via bulky optics in free space. We report a metafiber platform capable of creating arbitrarily structured light on the hybrid-order Poincaré sphere. Polymeric metasurfaces, with unleashed height degree of freedom and a greatly expanded 3D meta-atom library, were 3D laser nanoprinted and interfaced with polarization-maintaining single-mode fibers. Multiple metasurfaces were interfaced on the fiber end-faces, transforming the fiber output into different structured-light fields, including cylindrical vector beams, circularly polarized vortex beams, and arbitrary vector field. Our work provides a paradigm for advancing optical fiber science and technology towards fiber-integrated light shaping, which may find important applications in fiber communications, fiber lasers and sensors, endoscopic imaging, fiber lithography, and lab-on-fiber technology.

High-Purity Generation and Switching of Twisted Single Photons

Quantum technologies, if scaled into a high-dimensional Hilbert space, can dramatically enhance connection capabilities with supporting higher bit rates and ultrasecure information transfer. Twisted single photons, carrying orbital angular momentum (OAM) as an unbounded dimension, could address the growing demand for high-dimensional quantum information encoding and transmission. By hybrid integration of two-dimensional semiconductor WSe_{2} with a spin-orbit-coupled microring resonator, we demonstrate an integrated tunable twisted single photon source with the ability to precisely define and switch between highly pure spin-OAM states. Our results feature a single photon purity of g^{(2)}(0)∼0.13 with a cavity-enhanced quantum yield of 76% and a high OAM mode purity up to 96.9%. Moreover, the demonstrated quantum-chiral control can also enable new quantum functionality such as single photon routing for efficient quantum information processing on chip.

Multichannel Quantum Emission with On-Chip Emitter-Coupled Holographic Metasurfaces

Multichannel quantum emission is in high demand for advanced quantum photonic applications such as quantum communications, quantum computing, and quantum cryptography. However, to date, the most common way for shaping photon emission from quantum emitters (QEs) is to utilize free-standing (external) bulky optical components. Here, we develop the multichannel holography approach for flexibly designing on-chip QE-coupled metasurfaces that make use of nonradiatively QE-excited surface plasmon polaritons for generating far-field quantum emission, which propagates in designed directions carrying specific spin and orbital angular momenta (SAM and OAM, respectively). We further design, fabricate, and characterize on-chip quantum light sources of multichannel quantum emission encoded with different SAMs and OAMs. The holography-based inverse design approach developed and demonstrated on-chip quantum light sources with multiple degrees of freedoms, thereby enabling a powerful platform for quantum nanophotonics, especially relevant for advanced quantum photonic applications, e.g., high-dimensional quantum information processing.

Topological Darkness in Optical Heterostructures: Prediction and Confirmation

Topological darkness is a new phenomenon that guarantees zero reflection/transmission of light from an optical sample and hence provides topologically nontrivial phase singularities. Here we consider topological darkness in an optical heterostructure that consists of an (unknown) layer placed on a composite substrate and suggest an algorithm that can be used to predict and confirm the presence of topological darkness. The algorithm is based on a combination of optical measurements and the Fresnel equations. We apply this algorithm to ultrathin Pd films fabricated on a Si/SiO2/Cr substrate and extract four different points of topological darkness. Our results will be useful for topological photonics and label-free optical biosensing based on phase interrogation.

Cascaded metasurfaces for high-purity vortex generation

We introduce a new paradigm for generating high-purity vortex beams with metasurfaces. By applying optical neural networks to a system of cascaded phase-only metasurfaces, we demonstrate the efficient generation of high-quality Laguerre-Gaussian (LG) vortex modes. Our approach is based on two metasurfaces where one metasurface redistributes the intensity profile of light in accord with Rayleigh-Sommerfeld diffraction rules, and then the second metasurface matches the required phases for the vortex beams. Consequently, we generate high-purity LGp,l optical modes with record-high Laguerre polynomial orders p = 10 and l = 200, and with the purity in p, l and relative conversion efficiency as 96.71%, 85.47%, and 70.48%, respectively. Our engineered cascaded metasurfaces suppress greatly the backward reflection with a ratio exceeding -17 dB. Such higher-order optical vortices with multiple orthogonal states can revolutionize next-generation optical information processing.

Excitons Enabled Topological Phase Singularity in a Single Atomic Layer

The nontrivial and rigorous Heaviside phase jump behavior of phase singularities (PSs) empowers exotic topological modes and widely divergent nature compared to neighboring points, which has attracted great attention in condensed matter physics as well as applications in photonics and ultrasensitive sensors. Here we demonstrate the universal existence of a family of topologically protected PSs generated from exciton resonances of single-atom layers. We obtain the PSs by coating the transition metal dichalcogenide (TMDC) monolayers on a nonabsorptive semi-infinite substrate without surface plasmon effect or other assisted resonators, which exploits the benefits of both exciton-dominated enhancement and peculiarities of the singular phase. We show that a refractive indices matched transparent substrate enables TMDC monolayers to exhibit topologically protected zero reflection accompanied by a perfect Heaviside π-phase jump at strong light adsorptions, which can be utilized to radically reduce the thickness of PS-based devices to a single atomic layer. By using the TMDC monolayer-based PSs for refractive index biosensors, we demonstrate its superior phase sensitivity at a level of 104 degrees per refractive index unit and detection of bioactive bacteria, respectively, which is comparable to the cutting-edge surface plasmon and Fabry-Perot resonance sensors. Our proof-of-concept results offer experimental and theoretical insights into a single atomic playground for flat singular optics and label-free biosensing technologies.

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.

On-chip generation of single-photon circularly polarized single-mode vortex beams

Generation of single photons carrying spin and orbital angular momenta (SAM and OAM) opens enticing perspectives for exploiting multiple degrees of freedom for high-dimensional quantum systems. However, on-chip generation of single photons encoded with single-mode SAM-OAM states has been a major challenge. Here, by using carefully designed anisotropic nanodimers fabricated atop a substrate, supporting surface plasmon polariton (SPP) propagation, and accurately positioned around a quantum emitter (QE), we enable nonradiative QE-SPP coupling and the SPP outcoupling into free-space propagating radiation featuring the designed SAM and OAM. We demonstrate on-chip room-temperature generation of well-collimated (divergence < 7.5°) circularly polarized (chirality > 0.97) single-mode vortex beams with different topological charges (𝓁 = 0, 1, and 2) and high single-photon purity, g(2)(0) < 0.15. The developed approach can straightforwardly be extended to produce multiple, differently polarized, single-mode single-photon radiation channels and enable thereby realization of high-dimensional quantum sources for advanced quantum photonic technologies.

Structured light enhanced entoptic stimuli for vision science applications

The dichroic macular pigment in the Henle fiber layer in the fovea enables humans to perceive entoptic phenomena when viewing polarized blue light. In the standard case of linearly polarized stimuli, a faint bowtie-like pattern known as the Haidinger's brush appears in the central point of fixation. As the shape and clarity of the perceived signal is directly related to the health of the macula, Haidinger's brush has been used as a diagnostic marker in studies of early stage macular degeneration and central field visual dysfunction. However, due to the weak nature of the perceived signal the perception of the Haidinger's brush has not been integrated with modern clinical methods. Recent attempts have been made to increase the strength of the perceived signal by employing structured light with spatially varying polarization profiles. Here we review the advancements with the structured light stimuli and describe the current challenges and future prospects.

Topological Metamaterials

The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

Efficient ultrafast laser writing with appropriate polarization

Appropriate polarization utilization makes the electric field vector direction and the statistically oriented localized states suitable for enhancing light-matter interactions so as to improve the efficiency of ultrafast laser writing, which will remarkably reduce the pulse energy and increase the processing speed for high density optical data storage, as well as manufacturing three-dimensional integrated optics and geometric phase optical elements.

Structured transverse orbital angular momentum probed by a levitated optomechanical sensor

The momentum carried by structured light fields exhibits a rich array of surprising features. In this work, we generate transverse orbital angular momentum (TOAM) in the interference field of two parallel and counter-propagating linearly-polarised focused beams, synthesising an array of identical handedness vortices carrying intrinsic TOAM. We explore this structured light field using an optomechanical sensor, consisting of an optically levitated silicon nanorod, whose rotation is a probe of the optical angular momentum, which generates an exceptionally large torque. This simple creation and direct observation of TOAM will have applications in studies of fundamental physics, the optical manipulation of matter and quantum optomechanics.

Broadband 2D phase-gradient metasurface for linearly-polarized waves by suppressing Lorentz resonance of meta-atoms

Metasurfaces have exhibited versatile capacities of controlling electromagnetic (EM) waves due to the high degree of freedom of designing artificially engineered meta-atoms. For circular polarization (CP), broadband phase gradient metasurfaces (PGMs) can be realized based on P-B geometric phase by rotating meta-atoms; while for linear polarization (LP), realization of broadband phase gradients has to resort to P-B geometric phase during polarization conversion and polarization purity has to be sacrificed for broadband properties. It is still challenging to obtain broadband PGMs for LP waves without polarization conversion. In this paper, we propose the design of 2D PGMs by combining the inherently wideband geometric phases and non-resonant phases of meta-atom, under the philosophy of suppressing Lorentz resonances that usually bring about abrupt phase changes. To this end, an anisotropic meta-atom is devised which can suppress abrupt Lorentz resonances in 2D for both x- and y-polarized waves. For y-polarized waves, the central straight wire is in perpendicular to electric vector Ein of incident waves, Lorentz resonance cannot be excited although the electrical length approaches or even exceeds half a wavelength. For x-polarized waves, the central straight wire is in parallel with Ein, a split gap is opened on the center of the straight wire so as to avoid Lorentz resonance. In this way, the abrupt Lorentz resonances are suppressed in 2D and the wideband geometric phase and the gradual non-resonant phase are left for broadband PGM design. As a proof of concept, a 2D PGM prototype for LP waves was designed, fabricated and measured in microwave regime. Both simulated and measured results show that the PGM can achieve broadband beam deflection for reflected waves for both x- and y-polarized waves in broadband, without changing the LP state. This work provides a broadband route to 2D PGMs for LP waves and can be readily extended to higher frequencies such as terahertz and infrared regimes.

Meta-optics empowered vector visual cryptography for high security and rapid decryption

Optical encryption is a promising approach to protecting secret information owing to the advantages of low-power consumption, parallel, high-speed, and multi-dimensional processing capabilities. Nevertheless, conventional strategies generally suffer from bulky system volume, relatively low security level, redundant measurement, and/or requirement of digital decryption algorithms. Here, we propose a general optical security strategy dubbed meta-optics-empowered vector visual cryptography, which fully exploits the abundant degrees of freedom of light as well as the spatial dislocation as key parameters, significantly upgrading the security level. We also demonstrate a decryption meta-camera that can implement the reversal coding procedure for real-time imaging display of hidden information, avoiding redundant measurement and digital post-processing. Our strategy features the merits of a compact footprint, high security, and rapid decryption, which may open an avenue for optical information security and anti-counterfeiting.

Longitudinal evolution from scalar to vector beams assembled from all-dielectric metasurfaces

Vector vortex beams (VVBs) with non-uniform polarization states have a wide range of applications, from particle capture to quantum information. Here, we theoretically demonstrate a generic design for all-dielectric metasurfaces operating in the terahertz (THz) band, characterized as a longitudinal evolution from scalar vortices carrying homogeneous polarization states to inhomogeneous vector vortices with polarization singularities. The order of the converted VVBs can be arbitrarily tailored by manipulating the topological charge embedded in two orthogonal circular polarization channels. The introduction of the extended focal length and the initial phase difference effectively guarantees the smoothness of the longitudinal switchable behavior. A generic design approach based on vector-generated metasurfaces can assist in the exploration of new singular properties of THz optical fields.

Scalable manufacturing of high-index atomic layer-polymer hybrid metasurfaces for metaphotonics in the visible

Metalenses are attractive alternatives to conventional bulky refractive lenses owing to their superior light-modulating performance and sub-micrometre-scale thicknesses; however, limitations in existing fabrication techniques, including high cost, low throughput and small patterning area, have hindered their mass production. Here we demonstrate low-cost and high-throughput mass production of large-aperture visible metalenses using deep-ultraviolet argon fluoride immersion lithography and wafer-scale nanoimprint lithography. Once a 12″ master stamp is imprinted, hundreds of centimetre-scale metalenses can be fabricated using a thinly coated high-index film to enhance light confinement, resulting in a substantial increase in conversion efficiency. As a proof of concept, an ultrathin virtual reality device created with the printed metalens demonstrates its potential towards the scalable manufacturing of metaphotonic devices.

Observation of Perfectly-Chiral Exceptional Point via Bound State in the Continuum

Chirality is one of the fundamentals of nature with strong ties to asymmetry. In wave physics, it is conventionally characterized by asymmetric scattering of circularly polarized waves but suffers from two-state polarization. To overcome the limitation, here we demonstrate the concept of extreme chirality regarding orbital angular momentum (OAM) helicity, originating from a chiral quasibound state in the continuum held by a mirror-symmetry-broken metasurface. Empowered by the intrinsic OAM-selective coupling nature of the metasurface, the system arrives at a peculiar state where the left-handed incident vortex is completely absorbed while the right-handed counterpart is totally reflected, namely, a perfectly-chiral exceptional point. The realization of asymmetric OAM modulation creates the possibility to explore chirality with unlimited states. Our work raises a new paradigm for the study of extreme OAM chirality and enriches the physics of chiral wave-matter interaction.

Rotary Structural Color Spindles from Droplet Confined Magnetic Self-Assembly

Structural colors materials are profoundly explored owing to their fantastic optical properties and widespread applications. Development of structural color materials bearing flexible morphologies and versatile functionalities is highly anticipated. Here, a droplet-confined, magnetic-induced self-assembly strategy for generating rotary structural color spindles (SCSPs) by fast solvent extraction is proposed. The as-prepared SCSPs exhibit an orderly close-packed lattice structure, thus appearing brilliant structural colors that serve as encoding tags for multiplexed bioassays. Besides, benefitting from the abundant specific surface area, biomarkers can be labeled on the SCSPs with high efficiency for specific detection of analytes in clinical samples. Moreover, the directional magnetic moment arrangement enables contactless magnetic manipulation of the SCSPs, and the resultant rotary motions of the SCSPs generates turbulence in the detection solution, thus significantly improving the detection efficiency and shortening the detection time. Based on these merits, a portable point-of-care-testing strip integrating the rotary SCSPs is further constructed and the capability and advantages of this platform for multiplexed detection of tumor-related exosomes in clinical samples are demonstrated. This study offers a new way for the control of bottom-up self-assembly and extends the configuration and application values of colloidal crystal structural colors materials.

Coloured vortex beams with incoherent white light illumination

The orbital angular momentum is a fundamental degree of freedom of light wavefronts, currently exploited in applications where information capacity is a key requirement, such as optical communication, super-resolution imaging and high-dimensional quantum computing. However, generating orbital angular momentum beams requires spatio-temporally coherent light sources (lasers or supercontinuum sources), because incoherent light would smear out the doughnut features of orbital angular momentum beams, forming polychromatic or obscured orbital angular momentum beams instead. Here we show generation of coloured orbital angular momentum beams using incoherent white light. Spatio-temporal coherence is achieved by miniaturizing spiral phase plates and integrating them with structural colour filters, three-dimensionally printed at the nanoscale. Our scheme can in principle generate multiple helical eigenstates and combine colour information into orbital angular momentum beams independently. These three-dimensional optical elements encoded with colour and orbital angular momentum information substantially increase the number of combinations for optical anti-counterfeiting and photonic lock-key devices in a pairwise fashion.

Topological Unidirectional Guided Resonances Emerged from Interband Coupling

Unidirectional guided resonances (UGRs) are optical modes in photonic crystal slabs that radiate toward one side without the need for mirrors on the other. In this Letter, we report a mechanism to realize UGRs by tuning the interband coupling effect originating from up-down symmetry breaking. We theoretically find that UGRs that reside along high-symmetric lines correspond to phase singularities of far-field radiation, depicted by phase winding numbers as a type of topological indices. We investigate the phase dislocation lines in three-dimensional parameter space and elaborate on the interplay between UGRs and non-Hermitian degeneracies accordingly. Our findings reveal the topological nature of UGRs about their generation, evolution, and annihilation in general parameter spaces, thus paving the way to new possibilities of light manipulation.

Quantum vortex formation in the "rotating bucket" experiment with polariton condensates

The appearance of quantized vortices in the classical "rotating bucket" experiments of liquid helium and ultracold dilute gases provides the means for fundamental and comparative studies of different superfluids. Here, we realize the rotating bucket experiment for optically trapped quantum fluid of light based on exciton-polariton Bose-Einstein condensate in semiconductor microcavity. We use the beating note of two frequency-stabilized single-mode lasers to generate an asymmetric time-periodic rotating, nonresonant excitation profile that both injects and stirs the condensate through its interaction with a background exciton reservoir. The pump-induced external rotation of the condensate results in the appearance of a corotating quantized vortex. We investigate the rotation frequency dependence and reveal the range of stirring frequencies (from 1 to 4 GHz) that favors quantized vortex formation. We describe the phenomenology using the generalized Gross-Pitaevskii equation. Our results enable the study of polariton superfluidity on a par with other superfluids, as well as deterministic, all-optical control over structured nonlinear light.

Generation of spatiotemporal optical vortices in ultrashort laser pulses using rotationally interleaved multispirals

Ultrashort optical vortex pulses carrying spatiotemporal orbital angular momentum (OAM) have inspired versatile applications such as the micromachining of integrated quantum chips and discoveries such as optical toroidal structures and OAM-carrying X-waves. Generating high-quality ultrashort vortices with controllable topological charges remains a crucial issue. Thus, we propose a rotationally interleaved multispiral to generate such vortices. A multispiral comprises multiple identical spirals rotated around the center in the equal-azimuthal interval and interleaved in equal-radius increments; this structure overcomes the previous structural asymmetry of the single spiral and improves the vortex quality. Accordingly, we conducted theoretical analyses, numerical simulations, and experimental investigations that demonstrated the feasibility of multispirals in generating the ultrashort vortices with symmetric distributions and flexibly controlling the topological charges. The proposed study is significant for broader applications involving ultrashort vortices and extensive investigations in related areas such as research on electron vortices, plasmonic vortices, and other matter vortices.

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.

Experimental realization of neutron helical waves

Methods of preparation and analysis of structured waves of light, electrons, and atoms have been advancing rapidly. Despite the proven power of neutrons for material characterization and studies of fundamental physics, neutron science has not been able to fully integrate these techniques because of small transverse coherence lengths, the relatively poor resolution of spatial detectors, and low fluence rates. Here, we demonstrate methods that are practical with the existing technologies and show the experimental achievement of neutron helical wavefronts that carry well-defined orbital angular momentum values. We discuss possible applications and extensions to spin-orbit correlations and material characterization techniques.

Tailoring Nonlinear Metamaterials for the Controlling of Spatial Quantum Entanglement

The high designability of metamaterials has made them an attractive platform for devising novel optoelectronic devices. The demonstration of nonlinear metamaterials further indicates their potential in developing quantum applications. Here, we investigate designing nonlinear metamaterials consisting of the 3-fold (C3) rotationally symmetrical nanoantennas for generating and modulating entangled photons in the spatial degrees of freedom. Through tailoring the geometry and orientation of the nanoantennas, the parametric down conversion process inside the metamaterials can be locally engineered to generate entangled states with desired spatial properties. As the orbital angular momentum (OAM) states are valuable for enhancing the data capacity of quantum information systems, the photonic OAM entanglement is practically considered. With suitable nanostructure design, the generation of OAM entangled states is shown to be effectively realized in the discussed nonlinear metamaterial system. The nonlinear metamaterials present a perspective to provide a flexible platform for quantum photonic applications.

Efficient and High-Purity Sound Frequency Conversion with a Passive Linear Metasurface

Despite the significance for wave physics and potential applications, high-efficiency frequency conversion of low-frequency waves cannot be achieved with conventional nonlinearity-based mechanisms with poor mode purity, conversion efficiency, and real-time reconfigurability of the generated harmonic waves in both optics and acoustics. Rotational Doppler effect provides an intuitive paradigm to shifting the frequency in a linear system which, however, needs a spiral-phase change upon the wave propagation. Here a rotating passive linear vortex metasurface is numerically and experimentally presented with close-to-unity mode purity (>93%) and high conversion efficiency (>65%) in audible sound frequency as low as 3000 Hz. The topological charge of the transmitted sound is almost immune from the rotational speed and transmissivity, demonstrating the mechanical robustness and stability in adjusting the high-performance frequency conversion in situ. These features enable the researchers to cascade multiple vortex metasurfaces to further enlarge and diversify the extent of sound frequency conversion, which are experimentally verified. This strategy takes a step further toward the freewheeling sound manipulation at acoustic frequency domain, and may have far-researching impacts in various acoustic communications, signal processing, and contactless detection.

Topological polarization singular lasing with highly efficient radiation channel

Bound states in the continuum (BICs) in photonic crystals describe the originally leaky Bloch modes that can become bounded when their radiation fields carry topological polarization singularities. However, topological polarization singularities do not carry energy to far field, which limits radiation efficiencies of BICs for light emitting applications. Here, we demonstrate a topological polarization singular laser which has a topological polarization singular channel in the second Brillouin zone and a paired linearly polarized radiation channel in the first Brillouin zone. The presence of the singular channel enables the lasing mode with a higher quality factor than other modes for single mode lasing. In the meanwhile, the presence of the radiation channel secures the lasing mode with high radiation efficiency. The demonstrated topological polarization singular laser operates at room temperature with an external quantum efficiency exceeding 24%. Our work presents a new paradigm in eigenmode engineering for mode selection, exotic field manipulation and lasing.

Time diffraction-free transverse orbital angular momentum beams

The discovery of optical transverse orbital angular momentum (OAM) has broadened our understanding of light and is expected to promote optics and other physics. However, some fundamental questions concerning the nature of such OAM remain, particularly whether they can survive from observed mode degradation and hold OAM values higher than 1. Here, we show that the strong degradation actually origins from inappropriate time-delayed k_x–ω modulation, instead, for transverse OAM having inherent space-time coupling, immediate modulation is necessary. Thus, using immediate x–ω modulation, we demonstrate theoretically and experimentally degradation-free spatiotemporal Bessel (STB) vortices with transverse OAM even beyond 10². Remarkably, we observe a time-symmetrical evolution, verifying pure time diffraction on transverse OAM beams. More importantly, we quantify such nontrivial evolution as an intrinsic dispersion factor, opening the door towards time diffraction-free STB vortices via dispersion engineering. Our results may find analogues in other physical systems, such as surface plasmon-polaritons, superfluids, and Bose-Einstein condensates.

It remains unclear whether transverse orbital angular momentum beams can maintain OAM values above 1. Here the authors demonstrate the generation of beams with transverse OAM up to 100 by the inverse design of phase and find an intrinsic dispersion factor to describe the nontrivial evolution of such beams.

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.

Twisting Linear to Orbital Angular Momentum in an Ultrasonic Motor

An ultrasonic motor built with a contactless meta engine block (MEB) is designed and experimentally demonstrated for twisting the linear momentum of sound emanating from a Helmholtz resonator-based metasurface into orbital angular momentum (OAM). The MEB is capable of hosting highly efficient excitations of eigenmodes carrying desired OAM whose Bessel acoustic intensity patterns are enhanced by over ten times compared to the incident wave. Thanks to this efficiency, bidirectional ultrasonic OAM is capable of driving loads at speeds up to 1000 rpm at 4 W and remarkable sound radiation torque levels. Moreover, the possibility of using arbitrarily shaped MEBs is also demonstrated by engineering its physical boundary condition based on an analytically derived criterion to guarantee the high twisting efficiency of man-made OAM. The results show how noninvasive driving of an ultrasonic motor can be made possible through appropriately designed momentum twisting, which opens the door to a new class of integrated mechanical devices solely powered by sound.

Orbital Angular Momentum Multiplexing in Space-Time Thermoacoustic Metasurfaces

Multiplexing technology with increased information capacity plays a crucial role in the realm of acoustic communication. Different quantities of sound waves, including time, frequency, amplitude, phase, and orbital angular momentum (OAM), have been independently introduced as the physical multiplexing approach to allow for enhanced communication densities. An acoustic metasurface is decorated with carbon nanotube patches, which when electrically pumped and set to rotate, functions as a hybrid mode-frequency-division multiplexer with synthetic dimensions. Based on this spatiotemporal modulation, a superposition of vortex beams with orthogonal OAMs and symmetric harmonics are both numerically and experimentally demonstrated. Also, flexible combinations of OAM modes with diverse frequency shifts are obtained by transforming the azimuthal phase distributions, which inspires a mode-frequency-division multiplexing approach that significantly promotes the communication capacity.

Direct Light Orbital Angular Momentum Detection in Mid-Infrared Based on the Type-II Weyl Semimetal TaIrTe4

The direct photocurrent detection capability of light orbital angular momentum (OAM) has recently been realized with topological Weyl semimetals, but it is limited to the near-infrared wavelength range. The extension of the direct OAM detection capability to the mid-infrared band, which is a wave band that plays an important role in a vast range of applications, has not yet been realized. This is because the photocurrent responses of most photodetectors are neither sensitive to the phase information nor efficient in the mid-infrared region. In this study, a photodetector based on the type-II Weyl semimetal tantalum iridium telluride (TaIrTe₄ ) is designed with peculiar electrode geometries to directly detect the topological charge of the OAM using the orbital photogalvanic effect (OPGE). The results indicate that the helical phase gradient of light can be distinguished by a current winding around the optical beam axis, with a magnitude proportional to its quantized OAM mode number. The topologically enhanced responses in the mid-infrared region of TaIrTe₄ further help overcome the low responsivity issues and finally render direct OAM detection capability. This study enables on-chip-integrated OAM detection, and thus OAM-sensitive focal plane arrays in the mid-infrared region.

Wide-Angle Tunable Critical Coupling in Nanophotonic Optical Coatings with Low-Loss Phase Change Material

Realizing perfect light absorption in stacked thin films of dielectrics and metals through critical light coupling has recently received intensive research attention. In addition, realizing ultra-thin perfect absorber and tunable perfect absorber in the visible spectrum is essential for novel optoelectronics applications. However, the existing thin film stacks cannot show tunable perfect absorption in a wide-angle range. Here, a tunable perfect absorption from normal incidence to a wide-angle range (0° to 70°) by utilizing a two-layer stack consisting of a high refractive index low-loss dielectric on a high reflecting metal is proposed. This is experimentally demonstrated by depositing a thin layer of low-loss phase change material such as stibnite (Sb₂ S₃ ) on a thin layer of silver. This structure shows tunable perfect absorption with large spectral tunability in the visible wavelength. Furthermore, the absorption enhancement in 2D materials by transferring monolayer molybdenum disulfide on the stack, which shows 96% light absorption with enhanced photoluminescence, is demonstrated. In addition, the thin film stack can work as a scalable phase modulator offering a maximum phase tunability of ≈140° by changing the structural state of Sb₂ S₃ from amorphous to crystalline.