Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Second-harmonic generation of 2D materials excited by the Laguerre-Gaussian beam

We theoretically study the second-harmonic generation (SHG) of two-dimensional (2D) materials excited by a Laguerre-Gaussian (LG) beam at normal incidence and provide a method to distinguish SHG induced by the electric dipole (ED) interaction and SHG induced by the electric quadrupole and magnetic dipole (EQ-MD) interaction by their different dependence on the LG beam parameters, including the effective spot area v02 and the order of orbital angular momentum (OAM) m. In an approximation of neglecting reflection and taking a beam radius to infinity, the intensity of the ED induced SHG is proportional to F m/v02 with Fm = 2-2|m|(2|m|)!/(π(|m|!)2), while the EQ-MD induced one is proportional to (4|m|+2)F m/v04. An in-plane isotropic substrate can strongly affect the signal amplitude but slightly change the v0 and m dependence. Our results provide an all-optical way to detect the OAM by SHG, as well as a theoretical basis for studying the EQ-MD induced SHG by the LG beams.

Deep learning facilitated superhigh-resolution recognition of structured light ellipticities

Elliptical beams (EBs), an essential family of structured light, have been investigated theoretically due to their intriguing mathematical properties. However, their practical application has been significantly limited due to the inability to determine all their physical quantities, particularly the ellipticity factor, a unique parameter for EBs of different families. In this paper, to our knowledge, we proposed the first high-accuracy approach that can effectively distinguish EBs with an ellipticity factor difference of 0.01, equivalent to 99.9% field similarities. The method is based on a transformer deep learning (DL) network, and the accuracy has reached 99% for two distinct families of exemplified EBs. To prove that the high performance of this model can dramatically extend the practical aspect of EBs, we used EBs as information carriers in free-space optical communication for an image transmission task, and an error bit rate as low as 0.22% is achieved. Advancing the path of such a DL approach will facilitate the research of EBs for many practical applications such as optical imaging, optical sensing, and quantum-related systems.

Ultrahigh-channel-count OAM mode conversion utilizing a hybrid few-mode fiber configuration

We propose and demonstrate a hybrid few-mode fiber configuration (HFMFC) that enables ultrahigh-channel-count orbital angular momentum (OAM) mode conversion. The HFMFC consists of periodically twisted graded-index few-mode fiber segments and a step-index few-mode fiber segment. Our proposed HFMFC-based multichannel OAM mode converter (OAM-MC) offers an exceptionally high channel count in a wide bandwidth, with customizable channel spacing down to 50 GHz (∼0.4 nm), achieved through optimization of the structural parameters of the HFMFC. By employing this methodology, we have successfully demonstrated 10, 32, 117, and 233 channel OAM mode conversions covering the entire C + L band, representing the highest performance among all reported fiber-based multichannel OAM-MCs to date, for the first time to the best of our knowledge. The suggested ultrahigh-channel-count OAM-MC exhibits promising potential for applications in various fields such as OAM fiber communication, OAM holography, OAM information processing, and OAM metrology.

Cascaded partitioned phase modulation for cross-connection of orbital angular momentum mode and polarization multiplexing channels

Multi-dimensional orbital angular momentum (OAM) mode multiplexing provides a promising route for enlarging communication capacity and establishing comprehensive networks. While multi-dimensional multiplexing has gained advancements, the cross-connection of these multiplexed channels, especially involving modes and polarizations, remains challenging due to the needs for multi-mode interconversion and on-demand polarization control. Herein, we propose an OAM mode-polarization cross-transformation solution via cascaded partitioned phase modulation, which enables the divergently separated OAM modes to be independently phase-imposed within distinct spatial regions, leading to the synergistic conversion operation of mode and polarization channels. In demonstrations, we implemented the cross-connection of three OAM modes and two polarization multiplexed channels, achieving the mode purity that exceeds 0.951 and polarization contrast up to 0.947. The measured mode insertion losses and polarization conversion losses are below 3.42 and 3.54 dB, respectively. Consequently, 1.2 Tbit/s quadrature phase shift keying signals were successfully exchanged, yielding the bit-error-rates close to 10-6. Incorporating with increased partitioned phase treatments, this approach shows promise in accommodating massive mode-polarization multiplexed channels, which hold the potential to augment networking capability of large-scale OAM mode multiplexing communication networks.

Symmetry-Guided Engineering of Polarization by 2D Moiré Metasurfaces

Cylindrical vector (CV) beams exhibit spatially varying polarization important in optical communication, super-resolution microscopy, and high-throughput information processing. Compared to radially or azimuthally polarized CV beams that are cylindrically symmetric, hybrid-electric (HE) beams offer increased optical tunability because of their polygonally symmetric polarizations. However, efforts to generate and isolate HE beams have relied on bulky optical assemblies or devices with complex and stringent fabrication requirements. Here, we report a moiré-based metasurface approach to engineer HE polarization states with high degrees of rotational symmetry. Importantly, polarization symmetries can be tailored based only on the reciprocal lattice of the metasurface and not the real-space patterns. Our modular method outlines important design principles for shaping light at the nanoscale.

SU(N) symmetry of coherent photons controlled by rotated waveplates

The coherent state from a laser source has spin and orbital degrees of freedom, which allow an arbitrary superposition state among orthogonal states with varying amplitudes and phases. Here, we theoretically show coherent photons with SU(N) symmetry are characterised by expectation values of angular momentum shown on a hypersphere in SO(N 2 - 1 ) space. To demonstrate expected unitary transformations in experiments, we have constructed generators of transformations in the Lie group simply by combining widely available optical components such as waveplates and vortex lenses. We show a superposition state between twisted and Gaussian states is characterised by the dynamics of the topological charge upon the transformation in SU(3) states. We also realised photonic singlet and triplet states corresponding to SU(4) states, which were projected to SU(2)×SU(2) states upon passing through a rotated polariser.

Generation and applications of x-ray and extreme ultraviolet beams carrying orbital angular momentum

In addition to spin angular momentum, light can carry orbital angular momentum. The orbital angular momentum degree of freedom in the extreme ultraviolet and x-ray regimes enables fundamental studies of light-matter interactions and new methods to study materials. Advances in x-ray optics, as well as undulator radiation and high harmonic generation techniques, lead to the creation of beams with non-trivial phase structure, such as a helical phase structure, creating new possibilities for the use of extreme ultraviolet and x-ray photons with orbital angular momentum in probing complex electronic structures in matter. In this article, we review the generation and applications of orbital angular momentum beams in the x-ray and extreme ultraviolet regime. We discuss several recent works that exploit the orbital angular momentum degree of freedom and showcase the potential advantages of using these beams.

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.

Achromatic CMOS-Integrated Four-Bit Orbital Angular Momentum Mode Detector at Three Wavelengths

The simultaneous detection of the orbital angular momentum (OAM) and wavelength offers new opportunities for optical multiplexing. However, because of the dispersion of lens functions for Fourier transformation, the mode conversions at distinct wavelengths cannot be achieved in the same plane. Here we propose an ultracompact achromatic complementary metal oxide semiconductor (CMOS)-integrated OAM mode detector. Specifically, a spatial multiplexed scheme, randomly interleaving the phase distributions for distributing the superposed OAM modes into preset positions at distinct wavelengths, is presented. In addition, such a nanoprinted achromatic OAM detector featuring a microscale size and a short focal length can be integrated onto a CMOS chip. Consequently, the four-bit incident light beams at three discrete wavelengths (633, 532, and 488 nm) can be distinguished with a high degree of accuracy evaluated by the average standardized Euclidean distance of ∼0.75 between the analytical and target results. Our results showcase a miniaturized platform for achieving high-capacity information processing.

Coherent beam combining of optical vortices

We experimentally demonstrate the power scaling of optical vortices using the coherent beam combining technique, encompassing topological charges ranging from ℓ = 1 to ℓ = 5 realized on the basis of a Yb-doped fiber short-pulsed laser system. The combining efficiency varies from 83.2 to 96.9% depending on the topological charge and beam pattern quality generated by the spatial light modulators. This work is a proof of concept for using a coherent beam combining technique to surpass the physical power/energy limitation of any single source of optical vortices, regardless of the generation methods employed. These results open a pathway to power scaling of optical vortices with diverse applications in science and industry by utilizing advances in light-matter interactions.

Structured electrons with chiral mass and charge

Chirality is a phenomenon with widespread relevance in fundamental physics, material science, chemistry, optics, and spectroscopy. In this work, we show that a free electron can be converted by the field cycles of laser light into a right-handed or left-handed coil of mass and charge. In contrast to phase-vortex beams, our electrons maintained a flat de Broglie wave but obtained their chirality from the shape of their expectation value in space and time. Measurements of wave function densities by attosecond gating revealed the three-dimensional shape of coils and double coils with left-handed or right-handed pitch. Engineered elementary particles with such or related chiral geometries should be useful for applications in chiral sensing, free-electron quantum optics, particle physics or electron microscopy.

Non-convex optimization for inverse problem solving in computer-generated holography

Computer-generated holography is a promising technique that modulates user-defined wavefronts with digital holograms. Computing appropriate holograms with faithful reconstructions is not only a problem closely related to the fundamental basis of holography but also a long-standing challenge for researchers in general fields of optics. Finding the exact solution of a desired hologram to reconstruct an accurate target object constitutes an ill-posed inverse problem. The general practice of single-diffraction computation for synthesizing holograms can only provide an approximate answer, which is subject to limitations in numerical implementation. Various non-convex optimization algorithms are thus designed to seek an optimal solution by introducing different constraints, frameworks, and initializations. Herein, we overview the optimization algorithms applied to computer-generated holography, incorporating principles of hologram synthesis based on alternative projections and gradient descent methods. This is aimed to provide an underlying basis for optimized hologram generation, as well as insights into the cutting-edge developments of this rapidly evolving field for potential applications in virtual reality, augmented reality, head-up display, data encryption, laser fabrication, and metasurface design.

Orbital Hall diffraction and its application for vortex measurement

We observe significant orbital angular momentum (OAM)-helicity-dependent centroid shifts in the Fraunhofer patterns for the far-field diffraction of optical vortex beams passing through a thin single wire, thus suggesting the orbital Hall effect (OHE) of light in diffraction. Based on the OHE with a thin cross wire, we further experimentally develop a compact and robust alignment-free method to measure the OAM states of light. These findings indicate that not only does the OHE of light offer insights into vortex diffraction with broken rotational symmetry, it may also provide a reliable and efficient way to simplify the vortex measurement for waves of different natures.

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.

Wigner distribution and entropy of partially coherent light generated by perfect optical vortices

We developed analytical expressions for the Wigner distribution function of partially coherent fields generated by the scattering of beams with a particular phase structure, namely perfect optical vortex beams. In addition, we provide the modal decomposition of the field correlations and evaluate the evolution of Shannon entropy associated with the partially coherent field.

Scanning Electrochemical Probe Lithography for Ultra-Precision Machining of Micro-Optical Elements with Freeform Curved Surface

Two challenges should be overcome for the ultra-precision machining of micro-optical element with freeform curved surface: one is the intricate geometry, the other is the hard-to-machining optical materials due to their hardness, brittleness or flexibility. Here scanning electrochemical probe lithography (SECPL) is developed, not only to meet the machining need of intricate geometry by 3D direct writing, but also to overcome the above mentioned mechanical properties by an electrochemical material removal mode. Through the electrochemical probe a localized anodic voltage is applied to drive the localized corrosion of GaAs. The material removal rate is obtained as a function of applied voltage, motion rate, scan segment, etc. Based on the material removal function, an arbitrary geometry can be converted to a spatially distributed voltage. Thus, a series of micro-optical element are fabricated with a machining accuracy in the scale of 100 s of nanometers. Notably, the spiral phase plate shows an excellent performance to transfer parallel light to vortex beam. SECPL demonstrates its excellent controllability and accuracy for the ultra-precision machining of micro-optical devices with freeform curved surface, providing an alternative chemical approach besides the physical and mechanical techniques.

Achromatic and Coma-Corrected Hybrid Meta-Optics for High-Performance Thermal Imaging

Long-wave infrared (LWIR) imaging, or thermal imaging, is widely applied in night vision and security monitoring. However, the widespread use of LWIR imagers is impeded by their bulky size, considerable weight, and high cost. While flat meta-optics present a potential solution to these limitations, existing pure LWIR meta-optics face constraints such as severe chromatic or coma aberrations. Here, we introduce an approach utilizing large-scale hybrid meta-optics to address these challenges and demonstrate the achromatic, coma-corrected, and polarization-insensitive thermal imaging. The hybrid metalens doublet is composed of a metasurface corrector and a refractive lens, featuring a full field-of-view angle surpassing 20° within the 8-12 μm wavelength range. Employing this hybrid metalens doublet, we showcase high-performance thermal imaging capabilities both indoors and outdoors, effectively capturing ambient thermal radiation. The proposed hybrid metalens doublet holds considerable promise for advancing miniaturized, lightweight, and cost-effective LWIR optical imaging systems.

Tracking the transmission matrix of a moving fiber with the transmitted data

During data transmission, the dynamic change of a scattering medium will make the measured transmission matrix (TM) invalid, so it is necessary to repeatedly measure the TM to achieve a long-time data transmission, which requires stopping the data transmission process frequently to measure the TM and leads to a reduction in the communication capacity. To solve this problem, we propose a TM tracking method during data transmission. In the case of more than three discrete levels of phase modulation, this method can realize the calibration of the TM with the intensity pictures captured by the camera and the recovered data, so it does not require stopping the data transmission process to measure the TM and thus avoids the loss of communication capacity. We have proved the feasibility of this method through simulations and experiments and realized the continuous transmission of random data and image data through a moving fiber with high accuracy.

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.

Spatial and mode selective switch for orbital angular momentum mode division multiplexing

In analogy to a wavelength selective switch in wavelength-division multiplexing (WDM) optical fiber communication systems, a spatial and optical mode selective switch (SMSS) would be an important component in future ultrahigh capacity optical fiber communication systems based on space and mode division multiplexing. In this work, a free-space SMSS for orbital angular momentum (OAM) mode-division multiplexing (MDM) is proposed and experimentally demonstrated. The SMSS consists of a separating part for transforming OAM modes to spatial modes and a recombining part for selecting and recombining the modes to any spatial channel. The SMSS is able to implement strictly non-blocking switching between a total of 36 SDM/MDM channels configured as four spatial channels each supporting nine OAM mode channels.

Full C- and L-band covered second-order OAM mode generator based on a thinned helical long-period fiber grating

A full C- and L-band covered second-order orbital-angular-momentum (OAM) mode generator has been proposed and experimentally demonstrated, which is realized by using a helical long-period fiber grating (HLPG) but inscribed in a thinned four-mode fiber. By optimizing the design of grating period and fiber diameter of the proposed HLPG, an ultra-broadband rejection filter with a depth of ∼23 dB, a bandwidth of ∼156 nm @-10 dB (ranging from 1522 nm to 1678 nm) and a bandwidth of ∼58 nm @-20 dB (ranging from 1574 nm to 1632 nm), has been successfully obtained as a typical sample. To the best of our knowledge, this is the first demonstration of such ultra-broadband second-order OAM mode generator by using only one fiber component, i.e., the thinned HLPG. In addition, the proposed generator is less polarization-dependent and less temperature-sensitive than those of the conventional HLPGs, which is believed to be considerably helpful to find potential applications of the device itself in wavelength division multiplexing (WDM) and OAM mode division multiplexing (MDM) optical fiber communication systems.

Spatial-temporal optical vortex pendulum on a curved surface

Spatial-temporal optical vortices (STOVs) have recently become the focus of newly structured optical fields. In this paper, their propagation on a 2D curved surface named the constant Gaussian curvature surface (CGCS) is studied. Using the matrix optics approach, we provide the analytical solution of the STOV propagation under the paraxial approximation on the CGCS with positive curvature. One method of creating timers is made possible by the spatiotemporal distribution direction of STOV light intensity, which swings like a pendulum throughout the evolution, in contrast to propagation on a flat surface. This swing, however, stops when the curved surface's curvature radius matches the light's Rayleigh distance. Besides, the transverse orbital angular momentum of STOV is deduced, and we find that the intrinsic and extrinsic OAM periodically exchange, but the total transverse OAM is always zero during the propagation on CGCS. It aids in controlling the transverse extrinsic orbital angular momentum of STOV in nontrivial space.

Cavity soliton inhibition of extreme events in lasers with injection

Vortex mediated turbulence can be the key element in the generation of extreme events in spatially extended lasers with optical injection. Here, we study the interplay of vortex mediated turbulence and cavity solitons on the onset of extreme events in semiconductor lasers with injection. We first analyze and characterize these two features separately, spatiotemporal chaotic optical vortices for low values of the injection intensity and cavity solitons above the locking regime. In regimes where vortex mediated turbulence and cavity solitons coexist, localized peaks of light inhibit instead of enhancing the generation of rogue waves by locally regularizing the otherwise chaotic phase of the optical field. Cavity solitons can then be used to manipulate and control extreme events in systems displaying vortex mediated turbulence.

Enhanced Photo-excitation and Angular-Momentum Imprint of Gray Excitons in WSe2 Monolayers by Spin-Orbit-Coupled Vector Vortex Beams

A light beam can be spatially structured in the complex amplitude to possess orbital angular momentum (OAM), which introduces an extra degree of freedom alongside the intrinsic spin angular momentum (SAM) associated with circular polarization. Furthermore, superimposing two such twisted light (TL) beams with distinct SAM and OAM produces a vector vortex beam (VVB) in nonseparable states where not only complex amplitude but also polarization is spatially structured and entangled with each other. In addition to the nonseparability, the SAM and OAM in a VVB are intrinsically coupled by the optical spin-orbit interaction and constitute the profound spin-orbit physics in photonics. In this work, we present a comprehensive theoretical investigation, implemented on the first-principles base, of the intriguing light-matter interaction between VVBs and WSe2 monolayers (WSe2-MLs), one of the best-known and promising two-dimensional (2D) materials in optoelectronics dictated by excitons, encompassing bright exciton (BX) as well as various dark excitons (DXs). One of the key findings of our study is that a substantial enhancement of the photoexcitation of gray excitons (GXs), a type of spin-forbidden DX, in a WSe2-ML can be achieved through the utilization of a 3D-structured TL with the optical spin-orbit interaction. Moreover, we show that a spin-orbit-coupled VVB surprisingly allows for the imprinting of the carried optical information onto GXs in 2D materials, which is robust against the decoherence mechanisms in the materials. This suggests a promising method for deciphering the transferred angular momentum from structured light to excitons.

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.

Mirror Symmetry Broken of Sound Vortex Transmission in a Single Passive Metasurface via Phase Coupling

Asymmetric transmission in a passive vortex system is highly desirable, as it enables the development of compact vortex-based devices. However, breaking the mirror symmetry of transmission via a single metasurface poses challenges due to the inherent symmetric transmission properties in reciprocity. Here, we theoretically propose and experimentally demonstrate a novel transmission-reflection phase coupling mechanism to achieve the broken mirror symmetry of sound vortex transmission. This mechanism establishes a special coupling link between transmission and reflection waves, superimposing asymmetric reflection phases on the transmission phases. By utilizing a single passive phase gradient metasurface with asymmetric reflection phase twists, distinct transmission phase twists for mirror-symmetric incident vortices can be achieved within a cylindrical waveguide. This is typically difficult to imple-ment in a reciprocal system. Numerical and experimental results both demonstrate the broken mirror symmetry of vortex transmission and reflection. Our findings offer a new strategy for controlling vortex wave propagation, which may inspire new directional applications and extend to the field of photonics.

Longitudinal evolution of phase vortices generated by rotationally interleaved multi-spiral

Phase vortices exhibit significant applications and hold promising prospects across various scientific fields. However, while extensive attention has been devoted to the two-dimensional transverse plane of these vortices, their longitudinal properties have received comparatively limited exploration. Our study focuses on the longitudinal evolution of phase vortices, encompassing an investigation of variational topological charges and phase distributions. The investigation employs the rotationally interleaved multi-spiral, characterized by multiple identical spirals arranged in an azimuthally symmetric rotation, to modulate phase distributions by the variable spiral radius versus the azimuthal angle. Initially, we analyze the modulation effect theoretically, delving into propagation properties and vortex formations. Subsequently, through numerical simulations of vortices generated by both single and multi-spiral setups, we examine the longitudinal evolution of topological charges and phase distributions. The analyses reveal a step-wise reductant topological charges and a tortuous increasing spatial variations of phase singularities in transmission direction, with the dependency on both propagation distance and number of multi-spiral. The outcomes hold significant potential applications in optical communications and optical tweezers.

Laser Beam Self-Focusing in Silicon at an Absorbed Wavelength by a Vortex Beam in the Same Wavelength

In this research, we present a novel approach to achieving super-resolution in silicon using the plasma dispersion effect (PDE) that temporarily controls the complex refractive index of matter. By employing a laser vortex pump beam, which is absorbed in the silicon, we can shape the complex refractive index as a gradient index (GRIN) lens, enabling the focusing of a laser probe beam within the material. Our study introduces a single beam at a wavelength of 775 nm for both the pump and the probe beams, offering tunable focusing capabilities and the potential to attain higher spatial resolution. These findings hold significant promise for applications in nanoelectronics and integrated circuit failure analysis, paving the way for advanced semiconductor imaging and analysis techniques.

Learning-enabled data transmission with up to 32 multiplexed orbital angular momentum channels through a commercial multi-mode fiber

Multiplexing orbital angular momentum (OAM) modes enable high-capacity optical communication. However, the highly similar speckle patterns of adjacent OAM modes produced by strong mode coupling in common fibers prevent the utility of OAM channel demultiplexing. In this paper, we propose a machine learning-supported fractional OAM-multiplexed data transmission system to sort highly scattered data from up to 32 multiplexed OAM channels propagating through a commercial multi-mode fiber parallelly with an accuracy of >99.92%, which is the largest bit number of OAM superstates reported to date (to the best of our knowledge). Here, by learning limited samples, unseen OAM superstates during the training process can be predicted precisely, which reduces the explosive quantity of the dataset. To verify its application, both gray and colored images, encoded by the given system, have been successfully transmitted with error rates of <0.26%. Our work might provide a promising avenue for high-capacity OAM optical communication in scattering environments.

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.

Observation of spatiotemporal optical vortices enabled by symmetry-breaking slanted nanograting

Providing additional degrees of freedom to manipulate light, spatiotemporal optical vortex (STOV) beams carrying transverse orbital angular momentum are of fundamental importance for spatiotemporal control of light-matter interactions. Unfortunately, existing methods to generate STOV are plagued by various limitations such as inefficiency, bulkiness, and complexity. Here, we theoretically propose and experimentally demonstrate a microscale singlet platform composed of a slanted nanograting to generate STOV. Leveraging the intrinsic topological singularity induced by C2 symmetry and z-mirror symmetry breaking of the slanted nanograting, STOV is generated through the Fourier transform of the spiral phase in the momentum-frequency space to the spatiotemporal domain. In experiments, we observe the space-time evolution of STOV carried by femtosecond pulses using a time-resolved interferometry technique and achieve a generation efficiency exceeding 40%. Our work sheds light on a compact and versatile platform for light pulse shaping, and paves the way towards a fully integrated system for spatiotemporal light manipulation.

Vortex electromagnetic wave imaging with orbital angular momentum and waveform degrees of freedom

The vortex electromagnetic wave has shown great prospects of radar applications, due to the orbital angular momentum (OAM) degree of freedom. However, the radiation energy convergence of the OAM beam remains a hard problem to be solved for radar target imaging in realistic scenario. In this paper, an OAM beam generation method is developed exploiting the OAM and waveform degrees of freedom simultaneously, which can collimate the beams with different OAM modes. Furthermore, the echo demodulation and the imaging methods are proposed to reconstruct the target profiles in the range and azimuth domain. Simulation and experimental results both validate that the OAM-based radar imaging can achieve azimuthal super-resolution beyond the diffraction limit of the array aperture. This work can advance the system design of vortex electromagnetic wave radar and its real-world applications.

Paraxial and ray approximations of acoustic vortex beams

A compact analytical solution obtained in the paraxial approximation is used to investigate focused and unfocused vortex beams radiated by a source with a Gaussian amplitude distribution. Comparisons with solutions of the Helmholtz equation are conducted to determine bounds on the parameter space in which the paraxial approximation is accurate. A linear relation is obtained for the dependence of the vortex ring radius on the topological charge, characterized by its orbital number, in the far field of an unfocused beam and in the focal plane of a focused beam. For a focused beam, it is shown that as the orbital number increases, the vortex ring not only increases in radius but also moves out of the focal plane in the direction of the source. For certain parameters, it is demonstrated that with increasing orbital number, the maximum amplitude in a focused beam becomes localized along a spheroidal surface enclosing a shadow zone in the prefocal region. This field structure is described analytically by ray theory developed in the present work, showing that the spheroidal surface in the prefocal region coincides with a simple expression for the coordinates of the caustic surface formed in a focused vortex beam.

Toward high-energy few-cycle optical vortices with minimized topological charge dispersion

A simple approach to generate high-energy few-cycle optical vortices with minimized topological charge dispersion is introduced. By means of numerical simulations, it is shown that, by leveraging the intrinsic properties of optical parametric chirped pulse amplification (OPCPA), clean transfer of topological charge from a high-energy narrowband pump pulse to a broadband idler is feasible under certain particular conditions, enabling the generation of high-energy few-cycle vortex pulses with extremely low topological charge dispersion.

Spin Unlocked Vortex Beam Generation on Nonlinear Chiroptical Metasurfaces

Optical vortices with spin and orbital angular momentum (SAM and OAM) states offer multiple degrees of freedom for manipulating optical fields and thus enable great potentials in optical information processing. Recently, the optical metasurface has become an important platform for vortex beam generation and steering. However, the strong spin-orbit interaction on such metasurfaces usually leads to spin locked OAM generation, which limits the complete control of the angular momentum state of light. Here, we propose to solve this constraint using geometric phase controlled nonlinear chiroptical metasurfaces. The metasurface consists of two types of plasmonic meta-atoms which have opposite handedness and exhibit a strong spin-dependent circular dichroism effect. By encoding specific phase singularities and phase gradients to different channels, we experimentally demonstrate the spin unlocked second harmonic beam steering. The proposed nonlinear chiroptical metasurfaces may have important applications in developing multifunctional nonlinear optical devices.

Conditional convolutional GAN-based adaptive demodulator for OAM-SK-FSO communication

The perturbation of atmosphere turbulence is a significant challenge in orbital angular momentum shift keying-based free space optical communication (OAM-SK-FSO). In this study, we propose an adaptive optical demodulation system based on deep learning techniques. A conditional convolutional GAN (ccGAN) network is applied to recover the distorted intensity pattern and assign it to its specified class. Compared to existing methods based on convolutional neural networks (CNNs), our network demonstrates powerful capability in recovering the distorted light beam, resulting in a higher recognition accuracy rate under the same conditions. The average recognition accuracy rates are 0.9928, 0.9795 and 0.9490 when the atmospheric refractive index structure constant $C_n^2$ is set at 3 × 10-13, 4.45 × 10-13, 6 × 10-13m-2/3, respectively. The ccGAN network provides a promising potential tool for free space optical communication.

Ultrafast all-optical second harmonic wavefront shaping

Optical communication can be revolutionized by encoding data into the orbital angular momentum of light beams. However, state-of-the-art approaches for dynamic control of complex optical wavefronts are mainly based on liquid crystal spatial light modulators or miniaturized mirrors, which suffer from intrinsically slow (µs-ms) response times. Here, we experimentally realize a hybrid meta-optical system that enables complex control of the wavefront of light with pulse-duration limited dynamics. Specifically, by combining ultrafast polarization switching in a WSe2 monolayer with a dielectric metasurface, we demonstrate second harmonic beam deflection and structuring of orbital angular momentum on the femtosecond timescale. Our results pave the way to robust encoding of information for free space optical links, while reaching response times compatible with real-world telecom applications.

Metasurface-Controlled Holographic Microcavities

Optical microcavities confine light to wavelength-scale volumes and are a key component for manipulating and enhancing the interaction of light, vacuum states, and matter. Current microcavities are constrained to a small number of spatial mode profiles. Imaging cavities can accommodate complicated modes but require an externally preshaped input. Here, we experimentally demonstrate a visible-wavelength, metasurface-based holographic microcavity that overcomes these limitations. The micrometer-scale metasurface cavity fulfills the round-trip condition for a designed mode with a complex-shaped intensity profile and thus selectively enhances light that couples to this mode, achieving a spectral bandwidth of 0.8 nm. By imaging the intracavity mode, we show that the holographic mode changes quickly with the cavity length and that the cavity displays the desired spatial mode profile only close to the design cavity length. When a metasurface is placed on a distributed Bragg reflector and steep phase gradients are realized, the correct choice of the reflector's top layer material can boost metasurface performance considerably. The applied forward-design method can be readily transferred to other spectral regimes and mode profiles.

Generation of arbitrarily structured optical vortex arrays based on the epicycle model

Optical vortex arrays (OVAs) are complex light fields with versatile structures that have been widely studied in large-capacity optical communications, optical tweezers, and optical measurements. However, generating OVAs with arbitrary structures without explicit analytical expressions remains a challenge. To address this issue, we propose an alternative scheme for customizing OVAs with arbitrary structures using an epicycle model and vortex localization techniques. This method can accurately generate an OVA with an arbitrary structure by pre-designing the positions of each vortex. The influence of the number and coordinates of the locating points on customized OVAs is discussed. Finally, the structures of the OVA and each vortex are individually shaped into specifically formed fractal shapes by combining cross-phase techniques. This unique OVA will open up novel potential applications, such as the complex manipulation of multiparticle systems and optical communication based on optical angular momentum.

Manipulation of optical orbit-induced localized spin angular momentum using the periodic edge dislocation

Orbit-induced localized spin angular momentum (OILS) has recently garnered significant attention. This paper introduces periodic edge dislocation (PED) into the tight focusing system. The study delves into the tight focusing characteristics of the radially polarized vortex plane beam with PED, demonstrating that PED serves as a straightforward and effective means of manipulating OILS, especially when both the orbital angular momentum and the polarization of the incident beam are fixed. Our findings indicate that the longitudinal OILS reaches its maximum when the difference between the period of PED and the vortex topological charge is equal to 1. Conversely, when the difference is 0, the transverse OILS reaches its maximum, while the longitudinal OILS reaches its minimum. Similar patterns are also observed in linearly polarized vortex beams. This research proposes a simple and practical way to control OILS, contributing to our understanding of optical orbit-spin coupling.

Fast measurement of coherence-orbital angular momentum matrices of random light beams using off-axis holography and coordinate transformation

We propose an effective protocol to measure the coherence-orbital angular momentum (COAM) matrix of an arbitrary partially coherent beam. The method is based on an off-axis holography scheme and the Cartesian-polar coordinate transformation, which enables to simultaneously deal with all the COAM matrix elements of interest. The working principle is presented and discussed in detail. A proof-of-principle experiment is carried out to reconstruct the COAM matrices of partially coherent beams with spatially uniform and non-uniform coherence states. We find an excellent agreement between the experimental results and the theoretical predictions. In addition, we show that the OAM spectrum of a partially coherent beam can also be directly acquired from the measured COAM matrix.

HoloTile light engine: new digital holographic modalities and applications

HoloTile is a patented computer generated holography approach with the aim of reducing the speckle noise caused by the overlap of the non-trivial physical extent of the point spread function in Fourier holographic systems from adjacent frequency components. By combining tiling of phase-only of rapidly generated sub-holograms with a PSF-shaping phase profile, each frequency component-or output 'pixel'- in the Fourier domain is shaped to a desired non-overlapping profile. In this paper, we show the high-resolution, speckle-reduced reconstructions that can be achieved with HoloTile, as well as present new HoloTile modalities, including an expanded list of PSF options with new key properties. In addition, we discuss numerous applications for which HoloTile, its rapid hologram generation, and the new PSF options may be an ideal fit, including optical trapping and manipulation of particles, volumetric additive printing, information transfer and quantum communication.

Non-orthogonal optical multiplexing empowered by deep learning

Orthogonality among channels is a canonical basis for optical multiplexing featured with division multiplexing, which substantially reduce the complexity of signal post-processing in demultiplexing. However, it inevitably imposes an upper limit of capacity for multiplexing. Herein, we report on non-orthogonal optical multiplexing over a multimode fiber (MMF) leveraged by a deep neural network, termed speckle light field retrieval network (SLRnet), where it can learn the complicated mapping relation between multiple non-orthogonal input light field encoded with information and their corresponding single intensity output. As a proof-of-principle experimental demonstration, it is shown that the SLRnet can effectively solve the ill-posed problem of non-orthogonal optical multiplexing over an MMF, where multiple non-orthogonal input signals mediated by the same polarization, wavelength and spatial position can be explicitly retrieved utilizing a single-shot speckle output with fidelity as high as ~ 98%. Our results resemble an important step for harnessing non-orthogonal channels for high capacity optical multiplexing.

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.

Multiplication of orbital angular momentum via multi-plane light conversion

The multiplication of orbital angular momentum (OAM) modes using optical coordinate transformation is useful for OAM optical networks, but the scalability of this scheme is limited by the ray model. Here, we propose an alternative scheme for the scalable multiplication of OAM modes based on modified multi-plane light conversion (MPLC) that can extend azimuthal and radial indices of OAM modes supported by the multipliers and unlock a new degree of freedom for radial high-order OAM states that has been restricted in the zero order. The multiplication for 20 OAM modes with radial index p = 0 and 10 OAM modes with radial index p = 1 is performed in simulation and experiment. The 3-dB optical bandwidth corresponding to the purity of OAM modes covers the entire C-band experimentally. This novel, to the best of our knowledge, approach to manipulating OAM states provides valuable insights and flexible strategies for high-capacity OAM optical communication and high-dimensional optical quantum information processing.

Gallium nitride-based geometric and propagation metasurfaces for vortex beam emissions

This work experimentally demonstrates the highly-efficient geometric and propagation metasurfaces for vortex beam emissions. These metasurfaces are respectively composed of high-aspect-ratio fin-like and cylindrical gallium nitride (GaN) meta-atoms. Remarkably, the optimized configuration of the fin-like GaN meta-atoms achieves a cross-polarization transmission efficiency of up to 99 %. Similarly, the cylindrical GaN meta-atoms exhibit an average co-polarization transmission efficiency of 97 %. Both metasurfaces, designed for vortex beam emission, exhibit annular intensity converging capabilities at distinct wavelengths in the visible. Notably, the geometric metasurface shows achromatic annular intensity distributions over a continuous wavelength range up to 100 nm, in sharp contrast to the propagation metasurface, which is subject to inherent wavelength dispersion limitations.

1D speckle-learned structured light recognition

In this Letter, we introduce a novel, to the best of our knowledge, structured light recognition technique based on the 1D speckle information to reduce the computational cost. Compared to the 2D speckle-based recognition [J. Opt. Soc. Am. A39, 759 (2022)10.1364/JOSAA.446352], the proposed 1D speckle-based method utilizes only a 1D array (1×n pixels) of the structured light speckle pattern image (n × n pixels). This drastically reduces the computational cost, since the required data is reduced by a factor of 1/n. A custom-designed 1D convolutional neural network (1D-CNN) with only 2.4 k learnable parameters is trained and tested on 1D structured light speckle arrays for fast and accurate recognition. A comparative study is carried out between 2D speckle-based and 1D speckle-based array recognition techniques comparing the data size, training time, and accuracy. For a proof-of-concept for the 1D speckle-based structured light recognition, we have established a 3-bit free-space communication channel by employing structured light-shift keying. The trained 1D CNN has successfully decoded the encoded 3-bit gray image with an accuracy of 94%. Additionally, our technique demonstrates robust performance under noise variation showcasing its deployment in practical cost-effective real-world applications.

Fundamental probing limit on the high-order orbital angular momentum of light

The orbital angular momentum (OAM) of light, possessing an infinite-dimensional degree of freedom, holds significant potential to enhance the capacity of optical communication and information processing in both classical and quantum regimes. Despite various methods developed to accurately measure OAM modes, the probing limit of the highest-order OAM remains an open question. Here, we report an accurate recognition of superhigh-order OAM using a convolutional neural network approach with an improved ResNeXt architecture, based on conjugated interference patterns. A type of hybrid beam carrying double OAM modes is utilized to provide more controllable degrees of freedom for greater recognition of the OAM modes. Our contribution advances the OAM recognition limit from manual counting to machine learning. Results demonstrate that, within our optical system, the maximum recognizable OAM modes exceed l = ±690 with an accuracy surpassing 99.93%, the highest achieved by spatial light modulator to date. Enlarging the active area of the CCD sensor extends the number of recognizable OAM modes to 1300, constrained only by the CCD resolution limit. Additionally, we explore the identification of fractional high-order OAM modes with a resolution of 0.1 from l = ±600.0 to l = ±600.9, achieving a high accuracy of 97.86%.