High-order optical vortex harmonics generated by relativistic femtosecond laser pulse

Harmonics generated by an intense femtosecond Gaussian laser pulse normally incident on a spiral-shaped thin foil target were studied. By using two-dimensional （2D） particle-in-cell （PIC） simulation, we observed evident odd harmonics signals in the reflection direction and found that the reflected field has a helical structure determined by the target shape. This method provides a new way to generate an intense ultraviolet vortex with high-order topological charge by use of ultrahigh intense laser-driven harmonics.

Design and experimental test of an optical vortex coronagraph

Using an optical vortex coronagraph （OVC） is one of the most promising techniques for di- rectly imaging exoplanets because of its small inner working angle and high throughput. This paper presents the design and laboratory demonstration performance of an OVC based on liquid crystal polymers （LCPs） at 633 nm and 1520 nm. The OVC can deliver good performance in laboratory tests and achieve a contrast of 10-6 at an angular distance of 3A/D, which can be implemented for imaging young giant exoplanets in combination with extreme adaptive optics.

Optical vortex array:generation and applications[Invited]

Optical vortex arrays,with their unique wavefront structures,find extensive applications in fields such as optical communications,trapping,imaging,metrology,and quantum.The methods used to generate these vortex beam arrays are crucial for their applications.In this review,we begin with introducing the fundamental concepts of optical vortex beams.Subsequently,we present three methods for generating them,including diffractive optical elements,metasurfaces,and integrated optical devices.We then explore the applications of optical vortex beam arrays in five different domains.Finally,we conclude with a summary and outlook for the research on optical vortex beam arrays.

Tilted spatiotemporal optical vortex with partial temporal coherence [Invited]

We report the experimental and theoretical investigation of tilted spatiotemporal optical vortices with partial temporal coherence.The theoretical study shows that the instantaneous spatiotemporal optical vortex is widely variable with the statistical orbital angular momentum(OAM)direction.While decreasing temporal coherence results in a larger variability of OAM tilt,the average OAM direction is relatively unchanged.

Optical vortex copier and regenerator in the Fourier domain

The generation and manipulation of optical vortices are of fundamental importance in a variety of promising applications. Here, we develop a nonlinear optical paradigm to implement self-and cross-convolution of optical vortex arrays, demonstrating the features of a vortex copier and regenerator. We use a phase-only spatial light modulator to prepare the 1064 nm invisible fundamental light to carry special optical vortex arrays and use a potassium titanyl phosphate crystal to perform type Ⅱ second-harmonic generation in the Fourier domain to achieve 532 nm visible structured vortices. Based on pure cross-convolution, we succeed in copying arbitrary-order single vortices as well as their superposition states onto a prearranged array of fundamental Gaussian spots. Also, based on the simultaneous effect of self-and cross-convolutions, we can expand the initial vortex lattices to regenerate more vortices carrying various higher topological charges. Our presented method of realizing an optical vortex copier and regenerator could find direct applications in optical manipulation, optical imaging, optical communication, and quantum information processing with structured vortex arrays.

Arbitrary and reconfigurable optical vortex generation:a high-efficiency technique using director-varying liquid crystal fork gratings

A high-efficiency technique for optical vortex(OV) generation is proposed and demonstrated. The technique is based on liquid crystal fork gratings with space-variant azimuthal orientations, which are locally controlled via polarization-sensitive alignment layers. Thanks to the optical rewritability of the alignment agent and the dynamic image generation of the digital micro-mirror device, fork gratings can be instantly and arbitrarily reconfigured.Corresponding optical vortices carrying arbitrary azimuthal and radial indices are demonstrated with a conversion efficiency of 98.5%, exhibiting features of polarization control and electrical switching. The technique may pave a bright road toward OV generation, manipulation, and detection.

Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters

Spatial modes have received substantial attention over the last decades and are used in optical communication applications.In fiber-optic communications,the employed linearly polarized modes and phase vortex modes carrying orbital angular momentum can be synthesized by fiber vector eigenmodes.To improve the transmission capacity and miniaturize the communication system,straightforward fiber vector eigenmode multiplexing and generation of fiber-eigenmode-like polarization vortices(vector vortex modes)using photonic integrated devices are of substantial interest.Here,we propose and demonstrate direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters.By exploiting vector vortex modes(radially and azimuthally polarized beams)generated from silicon microring resonators etched with angular gratings,we report data-carrying fiber vector eigenmode multiplexing transmission through a 2-km large-core fiber,showing low-level mode crosstalk and favorable link performance.These demonstrations may open up added capacity scaling opportunities by directly accessing multiple vector eigenmodes in the fiber and provide compact solutions to replace bulky diffractive optical elements for generating various optical vector beams.

Femtosecond infrared optical vortex lasers based on optical parametric amplification

Infrared femtosecond optical vortices open up many new research fields,such as optical micro–nano manipulation,time-resolved nonlocal spectroscopy in solids,vortex secondary radiation and particle generations.In this article,we demonstrate a femtosecond optical vortex laser system based on a two-stage optical parametric amplifier.In our experiment,1.45µm vortex signal pulses with energy of 190µJ and 1.8µm vortex idler pulses with energy of 158µJ have been obtained,and the pulse durations are 51 and 48 fs,respectively.Both the energy fluctuations of the signal and idler pulses are less than 0.5%(root mean square),and the spectral fluctuations are less than 1.5%within 1 hour.This type of highly stable femtosecond optical vortex laser has a wide range of applications for vortex strong-field physics.

Scintillations of optical vortex in randomly inhomogeneous medium

The comparative numerical and analytical analysis of scintillation indices of the vortex Laguerre–Gaussian beam and the nonvortex doughnut hole and Gaussian beams propagating in the randomly inhomogeneous atmosphere has been performed. It has been found that the dependence of the scintillation index at the axis of the optical vortex on the turbulence intensity at the path has the form of a unit step. It has been shown that the behavior of scintillations in the cross sections of vortex and nonvortex beams differs widely. Despite the scintillation index of vortex beams has been calculated only for the simplest LG10 mode, the obtained results are quite general, because they demonstrate the main properties inherent in scintillations of vortex beams of any type.

New kind of Hermite-Gaussian-like optical vortex generated by cross phase

We propose a new kind of optical vortex called the Hermite-Gaussian-like optical vortex(HGOV)inspired by the cross phase(CP).Theoretically,we investigate how the CP is decoupled from the phase of a cylindrical lens.We also investigate the propagation characteristics of an HGOV,which has a Hermite-Gaussian-like intensity distribution but still retains the orbital angular momentum.F urthermore,we derive the Fresnel diffraction integral of an HGOV and study the purity at infinity.Besides,we show a novel function of the self-measurement of the HGOV.Finally,we show that we can change the relative positions of singularities and the direction of an HGOV precisely,which facilitates applications in optical micro manipulation.

Coherent optical vortex generation with multiple topological charges based on a seeded free electron laser

To generate optical vortex with multiple topological charges,a simple scheme based on the phase mask shaping technique is proposed and applied in a seeded free electron laser.With a tailored phase mask,an extreme-ultraviolet(EUV)vortex with multiple topological charges can be produced.To prove the feasibility of this method,an eight-step phase mask is designed to shape the seed laser.The simulation results demonstrate that 100-MW,fully coherent EUV vortex pulses with topological charge 2 can be generated based on the proposed technique.We have also demonstrated the possibility of generating higher topological charges by using a phase mask with more steps.

Generation of regular optical vortex arrays using double gratings

In order to generate high quality regular optical vortex array(OVA),we present an experimental method for generating OVA using phase only liquid crystal spatial light modulator(LC-SLM)assisted two gratings.In the scheme,holograms of two grating are displayed on the screen of two LC-SLMs respectively;the diffraction optical fields are captured by a CCD camera.The simulated and experimental results show that the regular OVA can be generated by using double diffraction gratings.The generated OVAs have a constant topological charge of±1.The method can provide a useful pathway to produce regular OVA for some applications in optical communication,particle trapping and optical metrology.

High-harmonic-generation-inspired preparation of optical vortex arrays with arbitrary-order topological charges

In the process of high-harmonic generation with a Laguerre-Gaussian （LG） mode, it was well established that the topological charge could be of an N-fold increase due to angular momentum conservation. Here, by mimicking the effect of high-harmonic generation, we devise a simple algorithm to generate optical vortex arrays carrying arbitrary topological charges with a single phase-only spatial light modulator. By initially preparing a coaxial superposition of suitable low-order LG modes, we demonstrate experimentally that the topological charges of the embedded vortices can be multiplied and transformed into arbitrarily high orders on demand, while the array structure remains unchanged. Our algorithm offers a concise way to efficiently manipulate the structured light beams and holds promise in optical micromanipulation and remote sensing.

Multi-channel generation of vortex beams with controllable polarization states and orbital angular momentum

Optical vortices with tunable polarization states and topological charges are widely investigated in various physical systems and practical devices for high-capacity optical communication.However,this kind of structured light beams is usually generated using several polarization and spatial phase devices,which decreases the configurability of optical systems.Here,we have designed a kind of polarized optical multi-vortices generator based on the Stokes-Mueller formalism and cross-phase modulation.In our scheme,multi-channel generation of polarized vortex beams can be realized through a single optical element and a single-input Gaussian beam.The polarization states and orbital angular momentum of the generated light beams are all-optically controllable.Furthermore,the proposed polarized optical multi-vortices generator has also been demonstrated experimentally through one-step holographic recording in an azobenzene liquid-crystalline film and the experimental results agree with theoretical analysis.

Performance analysis of single-focus phase singularity based on elliptical reflective annulus quadrangle-element coded spiral zone plates

Optical vortices generated by the conventional vortex lens are usually disturbed by the undesired higher-order foci,which may lead to additional artifacts and thus degrade the contrast sensitivity. In this work, we propose an efficient methodology to combine the merit of elliptical reflective zone plates(ERZPs) and the advantage of spiral zone plates(SZPs) in establishing a specific single optical element, termed elliptical reflective annulus quadrangle-element coded spiral zone plates(ERAQSZPs) to generate single-focus phase singularity. Differing from the abrupt reflectance of the ERZPs, a series of randomly distributed nanometer apertures are adopted to realize the sinusoidal reflectance. Typically, according to our physical design, the ERAQSZPs are fabricated on a bulk substrate;therefore, the new idea can significantly reduce the difficulty in the fabrication process. Based on the Kirchhoff diffraction theory and convolution theorem, the focusing performance of ERAQSZPs is calculated. The results reveal that apart from the capability of generating optical vortices,ERAQSZPs can also integrate the function of focusing, energy selection, higher-order foci elimination, as well as high spectral resolution together. In addition, the focusing properties can be further improved by appropriately adjusting the parameters, such as zone number and the size of the consisted primitives. These findings are expected to direct a new direction toward improving the performance of optical capture, x-ray fluorescence spectra, and forbidden transition.

Composite optical vortices in noncollinear Laguerre–Gaussian beams and their propagation in free space

Taking two Laguerre-Gaussian beams with topological charge 1 = ±1 as an example, this paper studies the composite optical vortices formed by two noncollinear Laguerre-Gaussian beams with different phases, amplitudes, waist widths, off-axis distances, and their propagation in free space. It is shown by detailed numerical illustrative examples that the number and location of composite vortices at the waist plane are variable by varying the relative phase β, amplitude ratio η, waist width ratio ξ, or off-axis distance ratio μ. The net topological charge lnet is not always equal to the sum lsum of charges of the two component beams. The motion, creation and annihilation of composite vortices take place in the free-space propagation, and the net charge during the propagation remains unchanged and equals to the net charge at the waist plane.

Modulational Instability of Optical Vortices in Engineered Saturable Media

Propagation of light beams in turbid media such as underwater environments,fog,clouds,or biological tissues finds increasingly important applications in science and technology,including bio-imaging,underwater communication,and free-space communication technologies.While many of these applications traditionally relied on conventional,linearly polarized Gaussian beams,light possesses many degrees of freedom that are still largely unexplored,such as spin angular momentum(SAM)and orbital angular momentum(OAM).Here,we present nonlinear light-matter interactions of such complex light beams with"rotational"degrees of freedom in engineered nonlinear colloidal media.By making use of both variational and perturbative approach,we consider non-cylindrical optical vortices,elliptical optical vortices,and higher-order Bessel beams integrated in time(HOBBIT)to predict the dynamics and stability of the evolution of these beams.These results may find applications in many scenarios involving light transmission in strongly scattering environments.

Vectorial spin-orbital Hall effect of light upon tight focusing and its experimental observation in azopolymer films

Hall effect of light is a result of symmetry breaking in spin and/or orbital angular momentum(OAM)possessing optical system and is caused by e.g.refractive index gradient/interface between media or focusing of a spatially asymmetrical beam,similar to the electric field breaking the symmetry in spin Hall effect for electrons.The angular momentum(AM)conservation law in the ensuing asymmetric system dictates redistribution of spin and orbital angular momentum,and is manifested in spin-orbit,orbit-orbit,and orbit-spin conversions and reorganization,i.e.spin-orbit and orbit-orbit interaction.This AM restructuring in turn requires shifts of the barycenter of the electric field of light.In the present study we show,both analytically and by numerical simulation,how different electric field components are displaced upon tight focusing of an asymmetric light beam having OAM and spin.The relation between field components shifts and the AM components shifts/redistribution is presented too.Moreover,we experimentally demonstrate,for the first time,to the best of our knowledge,the spin-orbit Hall effect of light upon tight focusing in free space.This is achieved using azopolymers as a media detecting longitudinal or z component of the electrical field of light.These findings elucidate the Hall effect of light and may broaden the spectrum of its applications.

Optical spiral vortex from azimuthally increasing/decreasing exponential phase gradients

A new type of power-exponent-phase vortex-like beams with both quadratic and cubic azimuthal phase gradients is investigated in this work.The intensity and orbital angular momentum(OAM)density distributions are noticeably different when the phase gradient increases or decreases along the azimuth angle,while the orthogonality and total OAM remain constant.The characteristics of the optical field undergo a significant change when the phase shifts from linear to nonlinear,with the variation of the power index having little impact on the beam characteristics under nonlinear phase conditions.These characteristics provide new ideas for applications such as particle manipulation,optical communications,and OAM encryption.

Single-shot phase retrieval for randomly fluctuated and obstructed vortex beams

Vortex beams with orbital angular momentum play a crucial role in increasing the information capacity in optical communications.The magnitude of orbital angular momentum determines the ability of information encoding.In practice,a vortex beam can encounter random objects or turbulence during free-space propagation,resulting in information damage.Therefore,accurately measuring the orbital angular momentum of a randomly fluctuated and obstructed vortex beam is a considerable challenge.Herein,we propose a single-shot method for the phase retrieval of a randomly fluctuated and obstructed vortex beam by combining the phase-shift theorem and self-reference holography.Experimental results reveal that the sign and magnitude of the initial orbital angular momentum can be simultaneously determined based on their quantitative relation with the number of coherence singularities on the observation plane,thus addressing the effects of random occlusion and atmospheric turbulence.The proposed method considerably improved the accurate decoding of orbital angular momentum information in nonideal freespace optical communications.