Overcoming the rayleigh criterion limit with optical vortices

Quantifying image quality in AOSLO images of photoreceptors

The use of "quality" to describe the usefulness of an image is ubiquitous but is often subject to domain specific constraints. Despite its continued use as an imaging modality, adaptive optics scanning light ophthalmoscopy (AOSLO) lacks a dedicated metric for quantifying the quality of an image of photoreceptors. Here, we present an approach to evaluating image quality that extracts an estimate of the signal to noise ratio. We evaluated its performance in 528 images of photoreceptors from two AOSLOs, two modalities, and healthy or diseased retinas. The algorithm was compared to expert graders' ratings of the images and previously published image quality metrics. We found no significant difference in the SNR and grades across all conditions. The SNR and the grades of the images were moderately correlated. Overall, this algorithm provides an objective measure of image quality that closely relates to expert assessments of quality in both confocal and split-detector AOSLO images of photoreceptors.

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.

Pulsed Optical Vortex Array Generation in a Self-Q-Switched Tm:YALO3 Laser

Optical vortex arrays are characterized by specific orbital angular momentums, and they have important applications in optical trapping and manipulation, optical communications, secure communications, and high-security information processing. Despite widespread research on optical vortex arrays, the 2 μm wavelength range remains underexplored. Pulsed lasers at 2 μm are vital in laser medicine, sensing, communications, and nonlinear optic applications. The need for 2 μm-pulsed structured optical vortices, combining the advantages of this wavelength range and optical vortex arrays, is evident. Therefore, using just three elements in the cavity, we demonstrate a compact self-Q-switched Tm:YALO3 vortex laser by utilizing the self-modulation effect of a laser crystal and a defect spot mirror. By tuning the position of the defect spot and the output coupler, the resonator delivers optical vortex arrays with phase singularities ranging from 1 to 4. The narrowest pulse widths of the TEM00 LG0,-1, two-, three-, and four-vortex arrays are 543, 1266, 1281, 2379, and 1615 ns, respectively. All the vortex arrays in our study have relatively high-power outputs, slope efficiencies, and single-pulse energies. This work paves the way for a 2 μm-pulsed structured light source that has potential applications in optical trapping and manipulation, free-space optical communications, and laser medicine.

Propagation of integral and fractional perfect vortex beams in a gradient-index medium

The analytical expressions for the complex amplitude of integral and fractional perfect vortex (PV) beams propagating in a gradient-index (GRIN) medium are derived. The intensity and phase distributions, propagation trajectories, Poynting vectors, and the effects of topological charge and refractive index at the medium axis on the intensity of both beams in the medium are numerically investigated. It is shown that both beams propagate periodically in the GRIN medium with alternating spot focusing and reconstruction. Unlike the integral PV beam, the fractional PV beam has a dark line in intensity profiles and a line edge dislocation in phase distributions along the positive x-axis. These properties persist during the beam propagation in the GRIN medium. Moreover, the topological charge and the refractive index at the medium axis have little effect on the intensity of the PV beam propagating in the GRIN medium. The results presented in this paper may be useful for the application of integral and fractional PV beams in optical guiding and optical communications.

Enhancing axial localization with wavefront control

Enhancing the ability to resolve axial details is crucial in three-dimensional optical imaging. We provide experimental evidence showcasing the ultimate precision achievable in axial localization using vortex beams. For Laguerre-Gauss (LG) beams, this remarkable limit can be attained with just a single intensity scan. This proof-of-principle demonstrates that microscopy techniques based on LG vortex beams can potentially benefit from the introduced quantum-inspired superresolution protocol.

Tunable parity-time symmetry vortex laser from a phase change material-based microcavity

Traditional light sources cannot emit an electromagnetic (EM) field with an orbital angular momentum (OAM), limiting their applications in modern optics. The recent development of the OAM laser, mainly based on micro- and nanostructures, can satisfy the increasing requirements for on-chip photonics and information capacities. Nevertheless, the photonic structures have fixed parameters that prevent these OAM lasers from being dynamically tuned. Here, we propose tunable vortex lasing from a microring cavity integrated by a phase change material, Ge2Sb2Te5 (GST225). By modulating the complex refractive index to create an exceptional point (EP) to break the degeneracy of whispering gallery modes with opposite orientations, the microlaser working at the EP can impart an artificial angular momentum, thus emitting vortex beams with well-defined OAM. The grating scatter on the edge of the microring can provide efficient vertical radiation. The vortex laser wavelength from the GST225/InGaAsP dual-layered microring cavity can be dynamically tuned by switching the state of GST225 between amorphous and crystalline without changing the microring geometry. We construct an electric-thermal model to show the tuning range of operating wavelengths (EPs) from 1544.5 to 1565.9 nm in ~25 ns. Our study on high-speed tunable PT-symmetry vortex lasers facilitates the next generation of integrated optoelectronic devices for optical computing and communications in both classical and quantum regions.

Twisted moiré photonic crystal enabled optical vortex generation through bound states in the continuum

The twisted stacking of two layered crystals has led to the emerging moiré physics as well as intriguing chiral phenomena such as chiral phonon and photon generation. In this work, we identified and theoretically formulated a non-trivial twist-enabled coupling mechanism in twisted bilayer photonic crystal (TBPC), which connects the bound state in the continuum (BIC) mode to the free space through the twist-enabled channel. Moreover, the radiation from TBPC hosts an optical vortex in the far field with both odd and even topological orders. We quantitatively analyzed the twist-enabled coupling between the BIC mode and other non-local modes in the photonic crystals, giving rise to radiation carrying orbital angular momentum. The optical vortex generation is robust against geometric disturbance, making TBPC a promising platform for well-defined vortex generation. As a result, TBPCs not only provide a new approach to manipulating the angular momentum of photons, but may also enable novel applications in integrated optical information processing and optical tweezers. Our work broadens the field of moiré photonics and paves the way toward the novel application of moiré physics.

Generation of integer and fractional vortex beams based on liquid crystal electronically reconfigurable spiral phase plates

The manufacturing and characterization of a large-size 72-electrode liquid crystal-based reconfigurable spiral phase plate (SPP) is presented. The SPP is addressed by a custom-made driver with 72 independent channels, which allows for the generation of any arbitrary integer or fractional optical vortex beam with topological charges ranging from -24 to +24. The 25 mm diameter device is fabricated using direct laser writing, leading to a fill factor over 99%. The device performance and flexibility exceed previous transparent reconfigurable SPP in terms of size, tuning range, and fill factor. The device and the light path have been simulated using the angular spectrum propagation method, showing excellent correspondence.

Time-resolved plasmon-assisted generation of optical-vortex pulses

The microscopic mechanism of the light-matter interactions that induce orbital angular momentum (OAM) in electromagnetic fields is not thoroughly understood. In this work, we employ Archimedean spiral vortex generators in time-resolved numerical simulations using the Octopus code to observe the behind-the-scenes of OAM generation. We send a perfect circularly-polarized plane-wave light onto plasmonic optical vortex generators and observe the resulting twisted light formation with complete spatio-temporal information. In agreement with previous works, we find that emission from the plasmonic spiral branches shapes the vortex-like structure and governs the OAM generation in the outgoing electromagnetic field. To characterize the generated beam further, we emulate the emission from vortex generators with current emitters preserving the spiral geometry. We subject a point-particle system to the generated field and record the orbital angular momentum transfer between the electromagnetic field and the point particle. Finally, we probe the OAM density locally by studying the induced classical trajectory of point particles, which provides further insight into the spatio-temporal features of the induced OAM.

Switchable optical vortex beam generator based on an all-dielectric metasurface governed by merging bound states in the continuum

The polarization topology around the bound states in continuum (BIC) affects the optical vortex (OV) beam generation. We propose a cross-cross-shaped resonator based on a THz metasurface to realize an OV beam generator in real space by exploiting the inherent winding topology around the BIC. The BIC merging at the point Γ is achieved by tuning the width of the cross resonator, which significantly improves the Q factor and enhances the field localization. Furthermore, the switching between the high-order OV beam generator governed by the merged BIC and the low-order OV beam generator is realized. This extends the application of BIC in modulating orbital angular momentum.

Orbital angular momentum in the near-field of a fork grating

Light beams with Orbital Angular Momentum (OAM) are explored in applications from microscopy to quantum communication, while the Talbot effect revives in applications from atomic systems to x-ray phase contrast interferometry. We evidence the topological charge of an OAM carrying THz beam in the near-field of a binary amplitude fork-grating by means of the Talbot effect, which we show to persist over several fundamental Talbot lengths. We measure and analyze the evolution of the diffracted beam behind the fork grating in Fourier domain to recover the typical donut-shaped power distribution, and we compare experimental data to simulations. We isolate the inherent phase vortex using the Fourier phase retrieval method. To complement the analysis, we assess the OAM diffraction orders of a fork grating in the far-field using a cylindrical lens.

Generation of terahertz spatiotemporal optical vortices with frequency-dependent orbital angular momentum

Optical vortices with longitudinal orbital angular momentum (OAM) as a powerful tool for particle control, imaging and communication have been greatly developed. We introduce a novel property of broadband terahertz (THz) pulse, represented by frequency-dependent OAM orientation in spatiotemporal domain with transverse and longitudinal OAM projection. We illustrate a frequency-dependent broadband THz spatiotemporal optical vortex (STOV) in plasma-based THz emission driven by cylindrical symmetry broken two-color vortex field. We detect the evolution of OAM by time-delayed 2D electro-optic sampling combined with Fourier transform. This THz optical vortices tunability in spatiotemporal domain expands a new way for studying STOV and plasma-based THz radiation.

Nonlocality-mediated spatiotemporal optical vortex generation in nanorod-based epsilon-near-zero metamaterials

Optical vortices have myriad applications in photonics. Very recently, promising concepts of spatiotemporal optical vortex (STOV) pulses based on the phase helicity in the space-time coordinates have attracted much attention owing to their donut shape. We elaborate on the molding of STOV under the transmission of femtosecond pulses through a thin epsilon-near-zero (ENZ) metamaterial slab based on a silver nanorod array in a dielectric host. At the heart of the proposed approach is the interference of the so-called main and additional optical waves enabled by strong optical nonlocality of these ENZ metamaterials, which leads to the appearance of phase singularities in transmission spectra. The cascaded metamaterial structure is proposed for high-order STOV generation.

Design of a dynamic multi-topological charge graphene orbital angular momentum metalens

Traditional OAM generation devices are bulky and can generally only create OAM with one specific topological charge. Although metasurface-based devices have overcome the volume limitations, no tunable metasurface-based OAM generators have been demonstrated to date. Here, a dynamically tunable multi-topological charge OAM generator based on an ultrathin integrable graphene metalens is demonstrated by simulation using the detour phase technique and spatial multiplexing. Different topological charges can be designed on different focal planes. Stretching the OAM graphene metalens allows the focal plane and the topological values to be changed dynamically. This design method paves an innovative route toward miniaturization and integrating OAM beam-type photonic devices for practical applications.

Multi-Function Reflective Vector Light Fields Generated by All-Dielectric Encoding Metasurface

Traditional optics usually studies the uniform polarization state of light. Compared with uniform vector beams, non-uniform vector beams have more polarization information. Most of the research on generating cylindrical vector beams using metasurfaces focuses on generating transmitted beams using the geometric phase. However, the geometric phase requires the incident light to be circularly polarized, which limits the design freedom. Here, an all-dielectric reflective metasurface is designed to generate different output light according to the different polarization states of the incident light. By combining the two encoding arrangements of the dynamic phase and the geometric phase, the output light is a radial vector beam when the linearly polarized light is incident along the x-direction. Under the incidence of linearly polarized light along the y-direction, the generated output light is an azimuthal vector beam. Under the incidence of left-handed circularly polarized light, the generated output light is a vortex beam with a topological charge of -1. Under the incidence of right-handed circularly polarized light, the generated output light is a vortex beam with a topological charge of +1. The proposed reflective metasurface has potential applications in generating vector beams with high integration.

Generalized Newton's rings with vortex beams

The Newton's rings are interference patterns with concentric rings, and Newton's rings experiment is one of the most famous classic optics experiments. Here, we show that if we use a vortex beam, we can obtain generalized Newton's rings. Unlike traditional Newton's rings, the generalized ones are no longer concentric rings but spiral arms, and fork-shaped dislocations appear in spiral arms. More interesting, we reveal that both the number of spiral arms and the number of fork-shaped dislocations are equal to the value of topological charge of incident vortex beams. Our theoretical results are demonstrated experimentally. This novel interference pattern can be used for measuring the topological charge of vortex beams.

Single-Frame Characterization of Ultrafast Pulses with Spatiotemporal Orbital Angular Momentum

Light that carries spatiotemporal orbital angular momentum (ST-OAM) makes possible new types of optical vortices arising from transverse OAM. ST-OAM pulses exhibit novel properties during propagation, transmission, refraction, diffraction, and nonlinear conversion, attracting growing experimental and theoretical interest and studies. However, one major challenge is the lack of a simple and straightforward method for characterizing ultrafast ST-OAM pulses. Using spatially resolved spectral interferometry, we demonstrate a simple, stationary, single-frame method to quantitatively characterize ultrashort light pulses carrying ST-OAM. Using our method, the presence of an ST-OAM pulse, including its main characteristics such as topological charge numbers and OAM helicity, can be identified easily from the unique and unambiguous features directly seen on the raw data-without any need for a full analysis of the data. After processing and reconstructions, other exquisite features, including pulse dispersion and beam divergence, can also be fully characterized. Our fast characterization method allows high-throughput and quick feedback during the generation and optical alignment processes of ST-OAM pulses. It is straightforward to extend our method to single-shot measurement by using a high-speed camera that matches the pulse repetition rate. This new method can help advance the field of spatially and temporally structured light and its applications in advanced metrologies.

Ultra-intense vortex laser generation from a seed laser illuminated axial line-focused spiral zone plate

Relativistic vortex laser has drawn increasing attention in the laser-plasma community owing to its potential applications in various domains, e.g., generation of energetic charged particles with orbital angular momentum (OAM), high OAM X/γ-ray emission, high harmonics generation, and strong axial magnetic-field production. However, the generation of such relativistic vortex laser is still a challenge to the current laser technology. Using micro-structure targets named axial line-focused spiral zone plate (ALFSZP), we propose a novel scheme for ultra-intense vortex laser generation. In the scheme, a relativistic Gaussian laser pulse irradiates an ALFSZP, and diffracts as it passes through the ALFSZP. Due to the focusing and radial Hilbert transform capabilities of the ALFSZP, the seed laser is converted efficiently to a vortex one which is then well focused in a tunable focal volume. Three-dimensional particle-in-cell simulations indicate that using a seed laser pulse with intensity of 1.3 × 10²⁰ W/cm², the vortex laser intensity achieved is as high as 1.3 × 10²¹ W/cm² with the averaged angular momentum per photon up to 0.73ℏ, promising diverse applications in various fields aforementioned.

Topological flowers and spider webs in 3D vector fields

Topological structures currently are of special interest in the integration of singular optics and topological photonics. In this article, the topological flowers and spider webs, which got less attention comparing to the lemon-, star- structures of the same category, are investigated in 3D vector fields. We show that by strongly focusing higher-order singular beams, both the spin density (SD) vectors and the polarization states of the transverse fields on the focal plane exhibit flowers and spider webs structures in topology with 2|m - 1| folds/sectors (m is the beam order), and the topological structures of the SD vectors are demonstrated to have a 90°/|m - 1| rotation. On the other hand, the topological theory also needs to be developed according to the rapid growth of topological photonics. Here, by defining a 'relative topological charge', we have observed and analyzed the topological reactions of the loops (composed of SD singularities) rather than the 'point-type' singularities in conventional reactions. More specially, the 'radial index' and 'azimuthal index' are proposed to characterize the topological features of the flowers and spider webs, and have been verified that the 'radial index' is peculiar to 3D vector fields and proportional to 1/|m - 1| in general. Our work provides a way to describe the topological behaviors of groups of singularities and supplies new parameters for measuring the topological patterns in 3D vector fields, which will rich the topological theory and may have applications in topological photonics.

Wavelength-tunable spiral-phase-contrast imaging

Wavelength-tunable spiral-phase-contrast (SPC) imaging was experimentally accomplished in the visible wavelengths spanning a broad bandwidth of ∼200 nm based on a single off-axis spiral phase mirror (OSPM). By the rotation of an OSPM, which was designed with an integer orbital angular momentum (OAM) of l = 1 at a wavelength of 561 nm and incidence angle of 45°, high-quality SPC imaging was obtained at different wavelengths. For the comparison with wavelength-tunable SPC imaging using an OSPM, SPC imaging using a spiral phase plate (manufactured to generate an OAM of l = 1 at 561 nm) was performed at three wavelengths (473, 561, and 660 nm), resulting in clear differences. Theoretically, based on field tracing simulations, high-quality wavelength-tunable SPC imaging could be demonstrated in a very broad bandwidth of ∼400 nm, which is beyond the bandwidth of ∼200 nm obtained experimentally. This technique contribute to developing high-performance wavelength-tunable SPC imaging by simply integrating an OSPM into the current optical imaging technologies.

Dancing vortices in a driven nematic liquid crystal cell: Theory and experiment

The interaction of light beams with helical defects in optical materials generates optical vortices. Understanding and manipulating the dynamics of helical defects allows for the creation of versatile sources of optical vortex beams. Using a magnetic ring on a nematic liquid crystal cell, we trapped helical defects identified as matter vortices. We observe oscillatory rotating and beating matter vortices by applying a low-frequency voltage. Experimentally, we determine the region of parameters where these vortices are observed. The amplitude of oscillatory rotating vortices decays with the inverse of the voltage frequency. We propose an adequate amplitude equation, which allows us to describe the vortex dynamics; theoretical findings have a qualitative agreement with the experimental observations.

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.

Evaluation of Blood Coagulation by Optical Vortex Tracking

Blood coagulation is a complicated dynamic process that maintains the blood's fluid state and prevents uncontrollable bleeding. The real-time monitoring of coagulation dynamics is critical for blood transfusion guidance, emergency management of trauma-induced coagulopathy, perioperative bleeding, and targeted hemostatic therapy. Here, we utilize optical vortex dynamics to detect the blood coagulation dynamic process in a rapid and non-contact manner. To characterize the temporal changes in viscoelastic properties of blood during coagulation, we track the stochastic motion of optical vortices in the time-varying speckles reflected from 100 blood samples with varied coagulation profiles. The mean square displacement (MSD) of the vortices increases nonlinearly with time lag during blood coagulation reminiscent of the particles in viscoelastic fluids. The MSD curves with coagulation time are similar to the tracings of thromboelastography (TEG) during the blood coagulation. The retrieved coagulation parameters, such as reaction time and activated clotting time measured using the optical vortex method, exhibit a close correlation to those parameters acquired from TEG. These results demonstrate the feasibility of the optical vortex method for monitoring blood coagulation at the point of care. Our method is also applicable to measuring the viscoelasticity of complex fluids and turbid soft matters.

Spontaneous Formation of Time-Periodic Vortex Cluster in Nonlinear Fluids of Light

We demonstrate spontaneous formation of a nonlinear vortex cluster state in a microcavity exciton-polariton condensate with time-periodic sign flipping of its topological charges at the GHz scale. When optically pumped with a ring-shaped nonresonant laser, the trapped condensate experiences intricate high-order mode competition and fractures into two distinct trap levels. The resulting mode interference leads to robust condensate density beatings with periodic appearance of orderly arranged phase singularities. Our work opens new perspectives on creating structured free-evolving light, and singular optics in the strong light-matter coupling regime.

Influence of Spatio-Temporal Couplings on Focused Optical Vortices

Ultra-intense laser pulses with helical phases are of interest in laser-driven charged particle acceleration and related experiments with extreme light. However, such optical vortices can be affected by the presence of residual spatial-temporal couplings. Their field distributions after propagating in free-space and in the focal plane of an ideal focusing mirror were assessed through numerical modeling, based on the Gaussian decomposition method for a 25 fs pulse with a Supergaussian spatial profile. The wash-out of the central hole in the doughnut-shaped profile in the focal plane corresponds to the rotation of the phase discontinuity.

Source coherence-induced control of spatiotemporal coherency vortices

A novel method to achieve the coherence control of spatiotemporal coherency vortices of spatially and temporally partially coherent pulsed vortex (STPCPV) beams is proposed. The influence of spatial and temporal coherence of the source on the phase distributions and the positions of spatiotemporal coherency vortices of the STPCPV beams propagating through fused silica is investigated in detail, for the first time to our knowledge. It is found that the coherence width and the coherence time of the incident beam can be regarded as a perfect tool for controlling the phase distribution and position of a spatiotemporal coherency vortex. The results obtained in this paper will benefit a number of applications relating to light-matter interaction, quantum entanglement, quantum imaging, optical trapping and spatiotemporal spin-orbit angular momentum coupling.

Experimental observation and manipulation of optical tornado waves

We report experimental realization and manipulation of optical tornado waves (ToWs). By controlling the self-focusing length, total angular momentum, and foci deviation of ToWs, the propagation properties of optical ToWs, especially their angular velocity, can be manipulated. Controlling the accumulated rotation angle of the main intensity lobes of ToWs from 0° through 1100° is experimentally demonstrated, and their angular velocity is predicted to be the highest around the foci overlap situation. Our experimental results are in good agreement with numerical results.

Orientation-selective sub-Rayleigh imaging with spatial coherence lattices

The Rayleigh resolution criterion sets the minimum separation for two-point objects to be distinguishable in a classical optical imaging system. We demonstrate that the sub-Rayleigh resolution can be achieved in a telecentric imaging system with the help of a partially coherent illumination whose spatial coherence has lattice-like distribution. We show that the orientation-selective sub-Rayleigh imaging can be realized by controlling the spatial distribution of the coherence lattice into different symmetries. We carry out a proof-of-principle experiment to demonstrate the orientation-selective sub-Rayleigh imaging for a 1951 USAF resolution target. Our results indicate a flexible orientation-selective high-resolution imaging with spatial coherence engineering of the partially coherent light.

Observation of Magnetic Helicoidal Dichroism with Extreme Ultraviolet Light Vortices

We report on the experimental evidence of magnetic helicoidal dichroism, observed in the interaction of an extreme ultraviolet vortex beam carrying orbital angular momentum with a magnetic vortex. Numerical simulations based on classical electromagnetic theory show that this dichroism is based on the interference of light modes with different orbital angular momenta, which are populated after the interaction between light and the magnetic topology. This observation gives insight into the interplay between orbital angular momentum and magnetism and sets the framework for the development of new analytical tools to investigate ultrafast magnetization dynamics.

Wavelength-Tunable Vortex Beam Emitter Based on Silicon Micro-Ring with PN Depletion Diode

Herein we propose a design of a wavelength-tunable integrated vortex beam emitter based on the silicon-on-insulator platform. The emitter is implemented using a PN-depletion diode inside a microring resonator with the emitting hole grating that was used to produce a vortex beam. The resonance wavelengths can be shifted due to the refractive index change associated with the free plasma dispersion effect. Obtained numerical modeling results confirm the efficiency of the proposed approach, providing a resonance wavelength shift while maintaining the required topological charge of the emitted vortex beam. It is known that optical vortices got a lot of attention due to extensive telecommunication and biochemical applications, but also, they have revealed some beneficial use cases in sensors. Flexibility in spectral tuning demonstrated by the proposed device can significantly improve the accuracy of sensors based on fiber Bragg gratings. Moreover, we demonstrate that the proposed device can provide a displacement of the resonance by the value of the free spectral range of the ring resonator, which means the possibility to implement an ultra-fast orbital angular momentum (de)multiplexing or modulation.

Suspended Metasurface for Broadband High-Efficiency Vortex Beam Generation

Electromagnetic (EM) waves carrying orbital angular momentum (OAM) exhibit phase vortex and amplitude singularity. Broadband OAM generation with high efficiency is highly desired with suggested applications such as broadband imaging and communications. In this paper, suspended metasurface structure achieving low-Q factor is proposed to realize broadband phase control and excellent reflection efficiency. Broadband vortex beam generation with OAM order of 1 and 2 are realized using the proposed suspended structure. Furthermore, by analyzing different metasurface aperture phase distribution schemes, the efficiency of the OAM generator is maximally achieved. The designs are validated by simulation and measurement. The proposed OAM generators work across 4–10 GHz with efficiency higher than 82%. This design provides a route to broadband metasurface realization and high efficiency OAM generation.

Direct generation of ultrafast vortex beam from a Tm:CaYAlO4 oscillator featuring pattern matching of a folded-cavity resonator

Optical vortices, beams with spiral wavefronts and screw phase dislocations have been explored in applications in optical manipulation, quantum optics, and the next generation of optical communications. In traditional methods, optical vortices are generated using space light modulators or spiral phase plates, which would sharply decrease the integration of optical systems. Different from previous transverse mode conversion outside the cavity, here we experimentally demonstrate a direct generation of ultrafast vortex beam from a Tm:CaYAlO₄ oscillator by pattern matching of a six-mirror-folded-cavity resonator. By accurately adjusted the angle of the end mirror and the distance L between the M4 and the SESAMs to control the beam diameter of laser incidence on the gain medium in the sagittal and tangential planes, a stable 2 µm ultrafast vortex laser emission of annular Laguerre-Gaussian (LG) mode was obtained with a maximum output power of 327 mW and pulse duration of 2.1 ps. A simple YAG crystal plate was used as handedness selector and a homemade Mach-Zehnder (MZ) interferometer has verified the vortical property of the LG₀₁ mode. By furtherly controlling the cavity mode pattern matching, other stable transverse-mode operations for TEM₀₀, high-order Hermite-Gaussian (HG) transverse mode and doughnut-shaped beams were successfully realized. This work provides a flexible and reliable way to generate mid-infrared ultrafast vortex beams and is of special significance for applications in the areas of molecular spectroscopy and organic material processing amongst others.

Quantum Hypothesis Testing for Exoplanet Detection

Detecting the faint emission of a secondary source in the proximity of the much brighter one has been the most severe obstacle for using direct imaging in searching for exoplanets. Using quantum state discrimination and quantum imaging techniques, we show that one can significantly reduce the probability of error for detecting the presence of a weak secondary source, especially when the two sources have small angular separations. If the weak source has intensity ε≪1 relative to the bright source, we find that the error exponent can be improved by a factor of 1/ε. We also find linear-optical measurements that are optimal in this regime. Our result serves as a complementary method in the toolbox of optical imaging, with applications ranging from astronomy to microscopy.

Generation of spatiotemporal optical vortices with partial temporal coherence

Recently, a spatiotemporal optical vortex (STOV) with a transverse orbital angular momentum (OAM) has been generated from coherent ultrafast pulses using mode-locked lasers. In contrast, we demonstrate theoretically and experimentally that a STOV can be generated from a light source with partial temporal coherence with fluctuating temporal structures. By eliminating the need of mode-locked laser sources, the partially coherent STOV will serve as a convenient and cost-effective transverse OAM source.

Method for evaluating spectral resolution based on a single-lens spectrometer

Spectral resolution is a key parameter of a spectrometer. Typically, the Rayleigh criterion is used to evaluate spectral resolution; however, it is not applicable to a single-lens-based spectrometer, as its principle is different from that using a prism or grating. Therefore, this work proposes that a method resolution is a key parameter to evaluate spectral resolution by exploiting the concept of focus depth. Accordingly, the spectral resolution is determined using three factors, namely, aperture factor F of the lens, pixel size p of the charge-coupled device, and the derivative of the rate of change of focal length with respect to wavelength f^'(λ). The proposed method is verified by simulations with the following lens parameters: a diameter of 50.8 mm, focal length of 200 mm at 587.6 nm, and F=3.94. The calculated and simulated spectral resolution values are, respectively, 1.7 nm and 1.2 nm at 480 nm. Based on an analysis of the influences of F, p, and f^'(λ) on the spectral resolution, increasing f^'(λ) or decreasing both F and p might improve the spectral resolution. Finally, the proposed method is validated via experiments for lenses with different F values as well as materials, and we determine their spectral resolutions; these results are observed to be similar to the calculated values.

Recent Advances in Generation and Detection of Orbital Angular Momentum Optical Beams-A Review

Herein, we have discussed three major methods which have been generally employed for the generation of optical beams with orbital angular momentum (OAM). These methods include the practice of diffractive optics elements (DOEs), metasurfaces (MSs), and photonic integrated circuits (PICs) for the production of in-plane and out-of-plane OAM. This topic has been significantly evolved as a result; these three methods have been further implemented efficiently by different novel approaches which are discussed as well. Furthermore, development in the OAM detection techniques has also been presented. We have tried our best to bring novel and up-to-date information to the readers on this interesting and widely investigated topic.

Efficient vortex beam generation using gradient refractive-index microphase plates

Vortex beams were theoretically demonstrated by patterning a fiber facet with $N$-segment microphase plates. By changing the aluminum oxynitride material composition of each segment, gradient refractive-index phase plates (GRPs) were designed and introduced a ${{2}}\pi l$ azimuthal optical phase difference. The gradient index profile was able to convert a fiber Gaussian mode to a Laguerre-Gaussian mode with varieties of topological charge $l$. A three-dimensional finite-difference time-domain method was applied to calculate the near-field optical phase maps and the far-field beam profiles projected from the micro-GRPs. A uniform vortex beam with a symmetrical doughnut shape was obtained by optimizing the GRPs' radii and the number of segments. The micro-GRPs enabled flat optical components for efficient vortex beam generation.

Twin curvilinear vortex beams

We report on a novel curvilinear optical vortex beam named twin curvilinear vortex beams (TCVBs) with intensity and phase distribution along a pair of two- or three-dimensional curves, both of which share the same shape and the same topological charge. The TCVBs also possess the character of perfect optical vortex, namely having a size independent of topological charge. We theoretically demonstrate that a TCVB rather than a single-curve vortex beam can be created by the Fourier transform of a cylindrically polarized beam. The behavior of TCVBs generated through our method is investigated by simulation and experiment, including interference experiments for identifying the vortex property of the TCVBs. The TCVBs may find applications in optical tweezers, such as trapping low refractive index particles in the dark region between two curves and driving them moving along the curvilinear trajectory.

A New Type of Shape-Invariant Beams with Structured Coherence: Laguerre-Christoffel-Darboux Beams

A new class of sources presenting structured coherence properties is introduced and analyzed. They are obtained as the incoherent superposition of coherent Laguerre-Gaussian modes with suitable coefficients. This ensures that the shape of the intensity profile and the spatial coherence features of the propagated beams are invariant during paraxial approximation. A simple analytical expression is obtained for the cross-spectral density of the sources of this class, regardless of the number of superposed modes. Properties of these sources are analyzed and described by several examples.

Non-diffracting states at exceptional points

We propose to use exceptional points (EPs) to construct diffraction-free beam propagation and localized power oscillation in lattices. We specifically consider two systems to utilize EPs for diffraction-free beam propagation, one in synthetic gauge lattices and the other in unidirectionally coupled resonators where each resonator individually is capable of creating orbital angular momentum (OAM) beams. In the second system, we introduce the concept of robust and tunable OAM beam propagation in discrete lattices. We show that one can create robust OAM beams in an arbitrary number of sites of a photonic lattice. Furthermore, we report power oscillation at the EP of a non-Hermitian lattice. Our research widens the study and application of EPs in different photonic systems including OAM beams and their associated dynamics in discrete lattices.

Angular-multiplexed multichannel optical vortex arrays generators based on geometric metasurface

Recently, metasurface-based multichannel optical vortex arrays have attracted considerable interests due to its promising applications in high-dimensional information storage and high-secure information encryption. In addition to the well-known wavelength and polarization multiplexing technologies, the diffraction angle of light is an alternative typical physical dimension for multichannel optical vortex arrays. In this paper, based on angular multiplexing, we propose and demonstrate multichannel optical vortex arrays by using ultrathin geometric metasurface. For a circularly polarized incident light, the desired optical vortex arrays are successfully constructed in different diffraction regions. Moreover, the diffraction angle of the optical vortex array can be regulated by changing the illumination angle of incident light. Capitalizing on this advantage, the angular-multiplexed recombination of optical vortex array is further investigated. The combination of the diffraction angle of light and optical vortex array may have significant potential in applications of optical display, free-space optical communication, and optical manipulation.

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Ultra-thin angular-multiplexed multichannel vortex array generators are demonstrated

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Geometric phase is employed to realize the desired phase profiles

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Generation of various multichannel vortex arrays and recombination of vortex array

Topological transitions in an oscillatory driven liquid crystal cell

Matter under different equilibrium conditions of pressure and temperature exhibits different states such as solid, liquid, gas, and plasma. Exotic states of matter, such as Bose-Einstein condensates, superfluidity, chiral magnets, superconductivity, and liquid crystalline blue phases are observed in thermodynamic equilibrium. Rather than being a result of an aggregation of matter, their emergence is due to a change of a topological state of the system. These topological states can persist out of thermodynamics equilibrium. Here we investigate topological states of matter in a system with injection and dissipation of energy by means of oscillatory forcing. In an experiment involving a liquid crystal cell under the influence of a low-frequency oscillatory electric field, we observe a transition from a non-vortex state to a state in which vortices persist, topological transition. Depending on the period and the type of the forcing, the vortices self-organise, forming square lattices, glassy states, and disordered vortex structures. The bifurcation diagram is characterised experimentally. A continuous topological transition is observed for the sawtooth and square forcings. The scenario changes dramatically for sinusoidal forcing where the topological transition is discontinuous, which is accompanied by serial transitions between square and glassy vortex lattices. Based on a stochastic amplitude equation, we recognise the origin of the transition as the balance between stochastic creation and deterministic annihilation of vortices. Numerical simulations show topological transitions and the emergence of square vortex lattice. Our results show that the matter maintained out of equilibrium by means of the temporal modulation of parameters can exhibit exotic states.

Super-resolution optical classifier with high photon efficiency

We propose and demonstrate a photon-efficient optical classifier to overcome the Rayleigh limit in spatial resolution. It utilizes mode-selective sum-frequency generation and single-pixel photon detection to resolve closely spaced incoherent sources based on photon counting statistics. Super-resolving and photon efficient, this technique can find applications in microscopy, light detection and ranging, and astrophysics.

Ultrashort Vortex Pulses with Controlled Spectral Gouy Rotation

Recently, the spatio-spectral propagation dynamic of ultrashort-pulsed vortex beams was demonstrated by 2D mapping of spectral moments. The rotation of characteristic anomalies, so-called “spectral eyes”, was explained by wavelength-dependent Gouy phase shift. Controlling of this spectral rotation is essential for specific applications, e.g., communication and processing. Here, we report on advanced concepts for spectral rotational control and related first-proof-of-principle experiments. The speed of rotation of spectral eyes during propagation is shown to be essentially determined by angular and spectral parameters. The performance of fixed diffractive optical elements (DOE) and programmable liquid-crystal-on silicon spatial light modulators (LCoS-SLMs) that act as spiral phase gratings (SPG) or spiral phase plates (SPP) is compared. The approach is extended to radially chirped SPGs inducing axially variable angular velocity. The generation of time-dependent orbital angular momentum (self-torque) by superimposing multiple vortex pulses is proposed.

Vortex 4.0 on chip

The orbital angular momentum (OAM) of light has promising applications, ranging from information multiplexing andhigh-speed optical communication to computation. Dynamically tunable and switchable vortex microlasers combinedwith direct photocurrent detection of the topological charges of OAM states have paved unexplored routes for thedevelopment and integration of fourth-generation (4.0) vortex technology, potentially on chip.

Kerr-nonlinearity-modulated dressed vortex four-wave mixing from photonic band gap

Considering the fact that the orbital angular momentum of light can be transferred through light-matter interactions, we experimentally induced a dressed vortex four-wave mixing (FWM) with the interaction between a vortex probe beam and an inverted Y-type four-level atomic system with a photonic band gap. Further, the Kerr-nonlinearity-modulated propagation behaviors of the probe and the dressed FWM vortices are investigated, including the spatial shift, splitting, and incompleteness of the vortex shape. Strikingly, the propagation behaviors of the vortex beams can be influenced by the interaction between the nonlinear phase and the spiral phase. This study would promote the development of optical computing and information processing science related to the interactions between optical vortices and samples.

Composite spiral multi-value zone plates

We present composite spiral multi-value phase zone plates that are achieved by sectioning a spiral multi-value phase zone plate into several radial regions. Each region is composed of specially structured Fresnel zones with optimized phase values and an embedded basic topological charge. In numerical studies, it is shown that the proposed element is capable of producing equal intensity arrays of petal-like modes as well as dark optical ring lattice structures along the optical axis in multiple focal planes of the diffractive element. Additionally, it is demonstrated that the generated petal-like modes can be rotated in a controllable manner by implementing an angular frequency shift between the two composited spiral multi-value phase zone plates. We also illustrate that the rotation angle is independent of the diffraction order. Experimental results are included to verify the theoretical outcomes, where the phase pattern of the composite spiral multi-value zone plate is encoded onto a spatial light modulator.

Topographic synthesis of arbitrary surfaces with vortex Jinc functions

When a circular aperture is uniformly illuminated, it is possible to observe in the far field an image of a bright circle surrounded by faint rings known as the Airy pattern or Airy disk. This pattern is described by the first-order Bessel function of the first type divided by its argument expressed in circular coordinates. We introduce the higher-order Bessel functions with a vortex azimuthal factor to propose a family of functions to generalize the function defining the Airy pattern. These functions, which we call vortex Jinc functions, happen to form an orthogonal set. We use this property to investigate their usefulness in fitting various surfaces in a circular domain, with applications in precision optical manufacturing, wavefront optics, and visual optics, among others. We compare them with other well-known sets of orthogonal functions, and our findings show that they are suitable for these tasks and can pose an advantage when dealing with surfaces that concentrate a considerable amount of their information near the center of a circular domain, making them suitable applications in visual optics or analysis of aberrations of optical systems, for instance, to analyze the point spread function.

Partially coherent radially polarized fractional vortex beam

A new kind of partially coherent vector beam, named a partially coherent radially polarized fractional vortex (PCRPFV) beam, is introduced as a natural extension of the recently introduced scalar partially coherent fractional vortex beams [Zeng et al., Opt. Express26, 26830 (2018)10.1364/OE.26.026830]. Realizability conditions and propagation formulas for a PCRPFV beam are derived. Statistical properties of a focused PCRPFV beam, such as average intensity, degree of polarization, state of polarization and cross-spectral density matrix, are illustrated in detail and compared with that of a partially coherent radially polarized integer vortex beam and a scalar partially coherent fractional vortex beam. It is found that the statistical properties of a PCRPFV beam are qualitatively different from these simpler beam classes and are strongly determined by the vortex phase (i.e., fractional topological charge) and initial coherence width. We demonstrate experimental generation of PCRPFV beams and confirm their behavior. Our results will be useful for the rotating and trapping of particles, the detection of phase objects, and polarization lidar systems.

Generation of stable orbital angular momentum beams with an all-polarization-maintaining fiber structure

In this paper, we propose a stable orbital angular momentum (OAM) mode fiber laser with an all-polarization-maintaining fiber (PMF) structure based on a combination of two linearly polarized modes. The mode intensity ratio between the two linearly polarized modes can be adjusted by adopting a double-pump structure. A pair of polarization-maintaining long-period fiber gratings (PM-LPFGs) are used as a mode converter. The number of topological charges of the OAM mode beam can be tuned between +1 and -1 by stretching the fiber. By adopting an all-PMF structure, we can build an OAM mode fiber laser without a polarization controller and that is resistant to environmental disturbances. The purity of the OAM mode was approximately 93.6%. This stable and compact OAM mode fiber laser can be used as a laser source in practical applications and scientific research.