Determination of topological charges of polychromatic optical vortices

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.

Nonlinear post-compression of a hybrid vortex mode in a gas-filled capillary

We demonstrate nonlinear temporal compression of a vortex beam by propagation in a gas-filled capillary. Starting from an ytterbium-based laser delivering 700 μJ 640 fs pulses at a 100 kHz repetition rate, the vortex beam is generated using a spiral phase plate and coupled to a capillary where it excites a set of four modes that have an overlap integral of 97% with a Laguerre-Gauss LG10 mode. Nonlinear propagation of this hybrid, orbital angular momentum (OAM)-carrying mode results in temporal compression down to 74 fs at the output. Beam and pulse characterizations are carried out to determine the spatial profile and temporal duration of compressed pulses. This result in multimode nonlinear optics paves the way towards the generation of OAM-carrying few-cycle pulses, isolated attosecond XUV pulses, and tunable UV pulses through resonant dispersive wave emission.

Broadband optical vortex beam generation using flat-surface nanostructured gradient index vortex phase masks

We developed a new kind of compact flat-surface nanostructured gradient index vortex phase mask, for the effective generation of optical vortex beams in broadband infrared wavelength range. A low-cost nanotechnological material method was employed for this work. The binary structure component consists of 17,557 nano-sized rods made of two lead-bismuth-gallium silicate glasses which were developed in-house. Those small rods are spatially arranged in such a way that, according to effective medium theory, the refractive index of this internal structure is constant in the radial direction and linearly changes following azimuthal angle. Numerical results demonstrated that a nanostructured vortex phase mask with a thickness of 19 μm can convert Gaussian beams into fundamental optical vortices over 290 nm wavelength bandwidth from 1275 to 1565 nm. This has been confirmed in experiments using three diode laser sources operating at 1310, 1550, and 1565 nm. The generation of vortex beams is verified through their uniform doughnut-like intensity distributions, clear astigmatic transformation patterns, and spiral as well as fork-like interferograms. This new flat-surface component can be directly mounted to an optical fiber tip for simplifying vortex generator systems as well as easier manipulation of the generated OVB in three-dimensional space.

1.7 µm sub-200 fs vortex beams generation from a thulium-doped all-fiber laser

The pulsed 1.7 µm vortex beams (VBs) has significant research prospects in the fields of imaging and material processing. We experimentally demonstrate the generation of sub-200 fs pulsed VBs at 1.7 µm based on a home-made mode-selective coupler (MSC). Through dispersion management technology in a thulium-doped fiber laser, the stable linearly polarized VBs pulse directly emitting from the cavity is measured to be 186 fs with central wavelength of 1721.2 nm. By controlling the linear superposition of LP11 modes, cylindrical vector beams (CVBs) can also be obtained. In addition, a variety of bound states pulsed VBs at 1.7 µm can also be observed. Our finding provides an effective way to generate ultrashort pulsed VBs and CVBs at 1.7 µm waveband.

Transmission of an optical vortex beam in antiresonant fibers generated in an all-fiber system

We report an experimental study on transmission of orbital angular momentum mode in antiresonant fibers generated with a dedicated all-fiber optical vortex phase mask. The vortex generator can convert Gaussian beam into vortex beams with topological charge l = 1. Generated vortex beam is directly butt-coupled into the antiresonant fiber and propagates over distance of 150 cm. The stability and sensitivity of the transmitted vortex beam on the external perturbations including bending, axial stress, and twisting is investigated. We demonstrate distortion-free vortex propagation for the axial stress force below 0.677 N, a bend radius greater than 10 cm.

Adjusted EfficientNet for the diagnostic of orbital angular momentum spectrum

Orbital angular momentum (OAM) is one of multiple dimensions of beams. A beam can carry multiple OAM components, and their intensity weights form the OAM spectrum. The OAM spectrum determines complex amplitude distributions of a beam and features unique characteristics. Thus, measuring the OAM spectrum is of great significance, especially for OAM-based applications. Here we employ a deep neural network combined with a phase-only diffraction optical element to measure the OAM spectrum. The diffraction optical element is designed to diffract incident beams into distinct patterns corresponding to OAM distributions. Then, the EfficientNet, a kind of deep neural network, is adjusted to adapt and analyze the diffraction pattern to calculate the OAM spectrum. The favorable experimental results show that our proposal can reconstruct the OAM spectra with high precision and speed, works well for different numbers of OAM channels, and is also robust to Gaussian noise and random zooming. This work opens a new, to the best of our knowledge, ability for OAM spectrum recognition and will find applications in a number of advanced domains including large capacity optical communications, quantum key distribution, optical trapping, rotation detection, and so on.

Single-Pulse Measurement of Orbital Angular Momentum Generated by Microring Lasers

Optical beams with helical phase fronts carry orbital angular momentum (OAM). To exploit this property in integrated photonics, micrometer-scale devices that generate beams with well-defined OAM are needed. Consequently, lasers based on microring resonators decorated with azimuthal grating elements have been investigated. However, future development of such devices requires better methods to determine their OAM, as current approaches are challenging to implement and interpret. If a simple and more sensitive technique were available, OAM microring lasers could be better understood and further improved. In particular, despite most devices being pulsed, their OAM output has been assumed to be constant. OAM fluctuations, which are detrimental for applications, need to be quantified. Here, we fabricate quantum-dot microring lasers and demonstrate a simple measurement method that can straightforwardly determine the magnitude and sign of the OAM down to the level of individual laser pulses. We exploit a Fourier microscope with a cylindrical lens and then investigate three types of microring lasers: with circular symmetry, with "blazed" grating elements, and with unidirectional rotational modes. Our results confirm that previous measurement techniques obscured key details about the OAM generation. For example, while time-averaged OAM from our unidirectional laser is very similar to our blazed grating device, single-pulse measurements show that detrimental effects of mode competition are almost entirely suppressed in the former. Nevertheless, even in this case, the OAM output exhibits shot-to-shot fluctuations. Thus, our approach reveals important details in the underlying device operation that can aid in the improvement of micrometer-scale sources with pure OAM output.

High energy switchable pulsed High-order Mode beams in a mode-locking Raman all-fiber laser with high efficiency

High energy pulsed High-order Mode (HOM) beams has great potential in materials processing and particle acceleration. We experimentally demonstrate a high energy mode-locking Raman all-fiber laser with switchable HOM state. A home-made fiber mode-selective coupler (MSC) is used as the mode converter with a wide bandwidth of 60 nm. By combining advantages of MSC and stimulated Raman scattering, 1.1 μJ pulsed HOM beams directly emitting from the all-fiber cavity can be achieved. After controlling the category and phase delay of vector modal superposition, different pulsed HOM beams including cylindrical vector beams (CVBs) (radial and angular) and optical vortex beams (OVBs) are reasonably obtained with high purity (all over 95%), as well as arbitrary switching. Furtherly, the slope efficiency of HOM beams in the mode-locking and continuous wave operations are as much as 20.3% and 31.8%, respectively. It may provide an effective way to achieve high energy pulsed HOM beams.

Broadband decoupled spin and orbital angular momentum detection via programming dual-twist reactive mesogens

The introduction of spin and orbital angular momentum mode division multiplexing to existing wavelength division multiplexing will significantly enlarge the capacity of optical networks. Therefore, components compatible with the above techniques are in high demand. Here, a geometric phase combined a Dammann vortex grating, and a polarization grating is designed and encoded to a dual-twist reactive mesogen. It can generate a couple of vortex channel arrays highly efficiently in broadband. Meanwhile, orthogonal spins are spatially separated, facilitating spin identification. A vortex will recover to a Gaussian beam when it is diffracted to an order with opposite topological charge, which enables the detection of orbital angular momentum. It supplies a parallel and efficient way for decoupled spin and orbital angular momentum detection operating at the entire visible range, and the design may be extended to many other compatible optical communication components.

Properties of the generation and propagation of spatiotemporal optical vortices

Spatiotemporal optical vortex (STOV) light is a new type of vortex light with transverse orbital angular momentum (OAM) which is different from conventional spatial vortex light. Understanding the properties of STOV are meaningful before STOV are applied. We present a theoretical study on the generation and propagation of spatiotemporal vortices step by step based on diffraction theory. The properties of the output pulses with different topological charges generated using 4 f pulse shaper in both the near-field and the far-field are analyzed. Using spiral phase mask, the intensity profiles of the output pulses immediately after the 4 f pulse shaper are of multi-lobe structures. With energies circulating around the phase singularity in the space-time plane, energy coupling occurs between the spatial and temporal domains in the wave packets during propagation, then the intensity profiles evolve into multi-hole shapes, and the holes tend to be merged for higher order STOV. The conservation of OAM in the space-time domain is shown clearly. The profiles of the output pulses in the near-field form donut rectangle shapes using π-step mask, and in the far-field, they split into a multi-lobe structure. The rules of the generation and evolution of STOV are revealed. The results demonstrate the physical properties of the STOV and the generation and propagation processes directly and clearly. It provides a guidance on the application of STOV.

Generation of an asymmetric optical vortex array with tunable singularity distribution

Light beams with multiple phase singularities, namely, optical vortex arrays (OVAs), can be generated via coherent superpositions of symmetric laser modes, e.g., the combination of a circular vortex beam and a Gaussian beam. Further, a non-trivial evolution of the singularity structure can be obtained when the system's symmetry is broken. In this paper, we propose an asymmetric OVA (AOVA) with a highly tunable structure. The AOVA is generated by the coaxial superposition of a vortex beam and an elliptical Gaussian beam in the waist plane. After the interference of the two beams, the original high-order phase singularity residing on the beam axis breaks up into multiple +1 and -1 order vortices. The vortices are located at discrete azimuthal angles and different distances from the beam center. Unlike previous OVAs with annular shapes, the AOVA can present various singularity structures devoid of rotational symmetry, which are decided by the radii of the elliptical Gaussian beam and the topological charge of the vortex beam. Furthermore, we theoretically show that the number, sign, and distribution of local singularities can be modulated by defining two azimuthal discriminant functions. Numerical simulations and visualizations are also carried out. This work provides a new perspective for designs of connected OVAs and may find potential applications, especially in particle manipulation, optical communication, and optical metrology.

Patterned Photoalignment in Thin Films: Physics and Applications

Photoalignment of liquid crystals by using azo dye molecules is a commonly proposed alternative to traditional rubbing alignment methods. Photoalignment mechanism can be well described in terms of rotational diffusion of azo dye molecules exposed by ultraviolet polarized light. A specific feature of the irradiated light is the intensity dependent change of azimuthal anchoring of liquid crystals. While there are various mechanisms of azo dye photoalignment, photo-reorientation occurs when dye molecules orient themselves perpendicular to the polarization of incident light. In this review, we describe both recent achievements in applications of photoaligned liquid crystal cells and its simulation. A variety of display and photonic devices with azo dye aligned nematic and ferroelectric liquid crystals are presented: q-plates, optically rewritable flexible e-paper (monochromatic and color), and Dammann gratings. Some theoretical aspects of the alignment process and display simulation are also considered.

Real-time OAM cross-correlator based on a single-pixel detector HOBBIT system

The creation and detection of spatial modes of light with transient orbital angular momentum (OAM) properties is of critical importance in a number of applications in sensing and light matter interactions. Most methods are limited in their frequency response as a result of their modulation techniques. In this paper, a new method is introduced for the coherent detection of transient properties of OAM using a single pixel detector system for the creation of an OAM spectrogram. This technique is based on the ideas utilized in acousto-optic based optical correlators with log-polar optical elements for the creation and detection of higher order bessel beams integrated in time (HOBBIT) at MHz data rates. Results are provided for beams with time varying OAM, coherent combinations, and transient scattering by phase objects.

Optical-vortex diagnostics via Fraunhofer slit diffraction with controllable wavefront curvature

Far-field slit diffraction of circular optical-vortex (OV) beams is efficient for measurement of the topological charge (TC) magnitude but does not reveal its sign. We show that this is because in the common diffraction schemes the diffraction plane coincides with the incident OV waist plane. Based on the examples of Laguerre-Gaussian incident beams containing a spherical wavefront component, we demonstrate that the far-field diffracted beam profile possesses an asymmetry depending on the incident wavefront curvature and the TC sign. This finding enables simple and efficient ways for the simultaneous diagnostics of the TC magnitude and sign, which can be useful in many OV applications, including OV-assisted metrology and information processing.

Ferroelectric liquid crystal mediated fast switchable orbital angular momentum of light

Orbital angular momentum (OAM) of light has been extensively studied during the past two decades. Till now, it is a formidable challenge to dynamically manipulate OAM in fast switching speed, good beam quality and low power consumption. Here, an alternative strategy is proposed through the combination of the uniformly-aligned ferroelectric liquid crystal (FLC) and the space-variant photo-patterned nematic liquid crystal. Owing to the excellent electro-optical properties of the adopted FLC, the high-performance electrical switching of OAM, especially, its helicity and the superposed state (i.e., the cylindrical vector beam), can be realized in good quality and high efficiency. The symmetric switching time is down to 120 µs even at a very low driving voltage of 1.7 V/µm. This supplies a practical and universal method towards high-frequency manipulation of OAM and other structured beams.

Atomically Thin Nonlinear Transition Metal Dichalcogenide Holograms

Nonlinear holography enables optical beam generation and holographic image reconstruction at new frequencies other than the excitation fundamental frequency, providing pathways toward unprecedented applications in optical information processing and data security. So far, plasmonic metasurfaces with the thickness of tens of nanometers have been mostly adopted for realizing nonlinear holograms with the potential of on-chip integration but suffering from low conversion efficiency and high absorption loss. Here, we report a nonlinear transition metal dichalcogenide (TMD) hologram with high conversion efficiency and atomic thickness made of only single nanopatterned tungsten disulfide (WS₂) monolayer, for producing optical vortex beams and Airy beams as well as reconstructing complex holographic images at the second harmonic (SH) frequency. Our concept of nonlinear TMD holograms paves the way toward not only the understanding of light-matter interactions at the atomic level but the integration of functional TMD-based devices with atomic thickness into the next-generation photonic circuits for optical communication, high-density optical data storage, and information security.

Intensity modulated terahertz vortex wave generation in air plasma by two-color femtosecond laser pulses

We investigate the generation of broadband terahertz (THz) pulses with phase singularity from air plasmas created by fundamental and second harmonic laser pulses. We show that when the second harmonic beam carries a vortex charge, the THz beam acquires a vortex structure as well. A generic feature of this THz vortex is that the intensity is modulated along the azimuthal angle, which can be attributed to the spatially varying relative phase difference between the two pump harmonics. Fully space- and time-resolved numerical simulations reveal that transverse instabilities of the pump further affect the emitted THz field along nonlinear propagation, which may produce additional singularities resulting in a rich vortex structure. The predicted intensity modulation is experimentally demonstrated with a thermal camera, in excellent agreement with simulation results. The presence of phase singularities in the experiment is revealed by astigmatic transformation of the beam using a cylindrical mirror.

Second-harmonic optical vortex conversion from WS2 monolayer

Wavelength, polarization and orbital angular momentum of light are important degrees of freedom for processing and encoding information in optical communication. Over the years, the generation and conversion of orbital angular momentum in nonlinear optical media has found many novel applications in the context of optical communication and quantum information processing. With that hindsight, here orbital angular momentum conversion of optical vortices through second-harmonic generation from only one atomically thin WS₂ monolayer is demonstrated at room temperature. Moreover, it is shown that the valley-contrasting physics associated with the nonlinear optical selection rule in WS₂ monolayer precisely determines the output circular polarization state of the generated second-harmonic vortex. These results pave the way for building future miniaturized valleytronic devices with atomic-scale thickness for many applications such as chiral photon emission, nonlinear beam generation, optoelectronics, and quantum computing.

Theory of diffraction of vortex beams from structured apertures and generation of elegant elliptical vortex Hermite-Gaussian beams

In this work, a comprehensive analytic study of the diffraction of vortex beams from structured apertures is presented. We formulate the near- and far-field diffraction of a vortex beam from an aperture having an arbitrary functionality in the Cartesian coordinates by two general and different approaches. We show that each of the resulting diffraction patterns can be determined by a number of successive derivatives of the 2D Fourier transform of the corresponding hypothetical aperture function or equally can be obtained by a summation of 2D Fourier transforms of the corresponding modified aperture function. We implement both introduced analytic approaches in predicting the diffraction of a vortex beam from an elliptic Gaussian aperture, an elliptic Gaussian phase mask, and a hyperbolic Gaussian phase mask in the near- and far-field regimes. It is shown that the predicted diffraction patterns by both these approaches are exactly the same. It is shown that the diffraction of a vortex beam from an elliptic Gaussian aperture at the far-field regime forms a light beam that belongs to a family of light beams we call elegant elliptical vortex Hermite-Gaussian beams. In addition, the diffractions of a vortex beam from a Fresnel zone plate in general form for the on- and off-axis situations are formulated, and sinusoidal and binary zone plates are investigated in detail. Our general analytic formula can be used for a large variety of apertures including off-center situations and asymmetrical cases.

Calculation of fractional orbital angular momentum of superpositions of optical vortices by intensity moments

Two simple and high-efficiency techniques for measuring the orbital angular momentum (OAM) of paraxial laser beams are proposed and studied numerically and experimentally. One technique relies on measuring the intensity in the Fresnel zone, followed by calculating the intensity that is numerically averaged over angle at discrete radii and deriving squared modules of the light field expansion coefficients via solving a linear set of equations. With the other technique, two intensity distributions are measured in the Fourier plane of a pair of cylindrical lenses positioned perpendicularly, before calculating the first-order moments of the measured intensities. The experimental error grows almost linearly from ~1% for small fractional OAM (up to 4) to ~10% for large fractional OAM (up to 34).

Vortex astigmatic Fourier-invariant Gaussian beams

We find a two-parameter family of astigmatic elliptical Gaussian (AEG) optical vortices, which are free space modes up to scale and rotation. We calculate total normalized orbital angular momentum of AEG vortices, which can be an integer, fractional and zero, and which is equal to the algebraic sum of two terms reflecting the contribution of the vortex and astigmatic components of the light field. In any transverse plane, such a beam has an isolated n-fold degenerate intensity null on the optical axis (an optical vortex) embedded into an elliptical Gaussian beam. In addition to the quadratic elliptical phase, a beam has the phase of a cylindrical lens rotated by an angle of 45 degrees with respect to the principal axes of the ellipse of the Gaussian beam intensity distribution. The degenerated central intensity null in these beams does not split it into n spatially separated intensity nulls, as is usually assumed for elliptical astigmatic beams.

Nonlinear generation of Airy vortex beam

Recently, hybrid beams have sparked considerable interest because of their properties coming from different kinds of beams at the same time. Here, we experimentally demonstrate Airy vortex beam generation in the nonlinear frequency conversion process when the fundamental wave with its phase modulated by a spatial light modulator is incident into a homogeneous nonlinear medium. In our experiments, second harmonic Airy circle vortex beams and Airy ellipse vortex beams were generated and the topological charge was also measured. The parabolic trajectory of those Airy vortex beams can be easily adjusted by altering the fundamental wave phase. This study provides a simple way to generate second harmonic Airy vortex beams, which may broaden its future use in optical manipulation and light-sheet microscopy.

Formation of optical vortices with all-glass nanostructured gradient index masks

We report the development of microscopic size gradient index vortex masks using the modified stack-and-draw technique. The vortex mask has a form of flat surface all-glass plate. Its functionality is determined by an internal nanostructure composed of two types of soft glass nanorods. The generation of optical vortices with charges 1 and 2 is demonstrated.

Examining second-harmonic generation of high-order Laguerre-Gaussian modes through a single cylindrical lens

We experimentally investigate the second-harmonic generation of a high-order Laguerre-Gaussian (LG) mode under the quasi-phase-matching (QPM) configuration. First, we introduce a simple method to observe the azimuthal (l) and radial (p) indices of the high-order LG modes. Based on the astigmatic transformation technique, l and p are revealed in the number of dark stripes of the converted pattern in the focal plane. Then, using this efficient method of measurement, we demonstrate in experiments a second-harmonic LG mode with its radial and azimuthal indices being twice those of the inputted fundamental wave through QPM in a periodically poled KTP crystal. Our results provide a feasible way to obtain simultaneously the LG modes with larger radial and azimuthal indices.

Helicity-dependent forked vortex lens based on photo-patterned liquid crystals

A liquid crystal forked vortex lens integrated with Pancharatnam-Berry phase is proposed and demonstrated via a dynamic photo-patterning technique. The forked vortex lens can generate two optical vortices with opposite spin and orbital angular momentum, which are spatially separated to two focal points with one optical vortex focused and the other defocused. It exhibits distinctive helicity-dependency and ultra-high diffraction efficiency up to 95%. The topological charges of generated optical vortices are detected via astigmatic transformation. This work supplies an easy fabrication and low power consumption strategy for generating and separating (de-)focused optical vortices simultaneously.

Multiple generations of high-order orbital angular momentum modes through cascaded third-harmonic generation in a 2D nonlinear photonic crystal

We experimentally demonstrate multiple generations of high-order orbital angular momentum (OAM) modes through third-harmonic generation in a 2D nonlinear photonic crystal. Such third-harmonic generation process is achieved by cascading second-harmonic generation and sum-frequency generation using the non-collinear quasi-phase-matching technique. This technique allows multiple OAM modes with different colors to be simultaneously generated. Moreover, the OAM conservation law guarantees that the topological charge is tripled in the cascaded third-harmonic generation process. Our method is effective for obtaining multiple high-order OAM modes for optical imaging, manipulation, and communications.

Astigmatic transforms of an optical vortex for measurement of its topological charge

We obtain analytical expressions for the complex amplitudes of optical vortices deformed by astigmatic transforms, i.e., passed either through a cylindrical lens or through an inclined spherical lens. We also obtain similar analytical expressions describing propagation of an optical vortex generated when a Gaussian beam illuminates an inclined spiral phase plate (SPP) or when an elliptic Gaussian beam illuminates a SPP (not inclined). All these optical vortices with a topological charge (TC) n are described by the n-th order Hermite polynomial with a complex argument. It is shown that the argument is real only on a straight line in the transverse plane of the laser beam. There are n intensity nulls on this line. The treated here astigmatic transforms are used to determine the integer TC of optical vortices. We conduct a comparative experimental study of different astigmatic transforms and we show that the transform with a cylindrical lens is the best for determining the TC. Unlike other similar works, in this study we achieve transformation of n-degenerate intensity null of an optical vortex with the TC n=100 into n isolated first-order intensity nulls.

Highly intense monocycle terahertz vortex generation by utilizing a Tsurupica spiral phase plate

Optical vortex, possessing an annular intensity profile and an orbital angular momentum (characterized by an integer termed a topological charge) associated with a helical wavefront, has attracted great attention for diverse applications due to its unique properties. In particular for terahertz (THz) frequency range, several approaches for THz vortex generation, including molded phase plates consisting of metal slit antennas, achromatic polarization elements and binary-diffractive optical elements, have been recently proposed, however, they are typically designed for a specific frequency. Here, we demonstrate highly intense broadband monocycle vortex generation near 0.6 THz by utilizing a polymeric Tsurupica spiral phase plate in combination with tilted-pulse-front optical rectification in a prism-cut LiNbO₃ crystal. A maximum peak power of 2.3 MW was obtained for THz vortex output with an expected topological charge of 1.15. Furthermore, we applied the highly intense THz vortex beam for studying unique nonlinear behaviors in bilayer graphene towards the development of nonlinear super-resolution THz microscopy and imaging system.

Quantitative measurement of the orbital angular momentum of light with a single, stationary lens

We show that the average orbital angular momentum (OAM) of twisted light can be measured simply and robustly with a single stationary cylindrical lens and a camera. Theoretical motivation is provided, along with self-consistent optical modeling and experimental results. In contrast to qualitative interference techniques for measuring OAM, we quantitatively measure non-integer average OAM in mode superpositions.

Integrated and reconfigurable optical paths based on stacking optical functional films

A strategy for integrated and reconfigurable optical paths based on stacking optical functional films is proposed. It is demonstrated by stacking two liquid crystal polymer q-plates and one quarter-wave plate for vector vortex beams generation. The topological charge and polarization order of generated vector vortex beams can be controlled independently by stacking and reordering different optical films with repeated adhesive ability. It supplies a low-cost, light-weight and versatile technique for reducing the volume of free-space optical system and has a great potential in optical researches and applications.

Conical third-harmonic generation of optical vortex through ultrashort laser filamentation in air

We experimentally generate third-harmonic (TH) vortex beams in air by the filamentation of femtosecond pulses produced in a lab-built Ti:sapphire chirped pulse amplifier. The generated TH beam profile is shown to evolve with increasing pump energy. At a sufficiently high pump energy, we observe a conical TH emission of the fundamental vortex and confirm that the conical radiation follows the conservation law for orbital angular momentum. We further investigate the far-field angularly resolved spectra of the TH wave to analyze the conical emission angle. We theoretically verify that the formation of the conical TH vortex results from the phase-matching between the fundamental and TH waves during the filamentation process.

Coupled orbital angular momentum conversions in a quasi-periodically poled LiTaO₃ crystal

We experimentally demonstrate the orbital angular momentum (OAM) conversion by the coupled nonlinear optical processes in a quasi-periodically poled LiTaO3 crystal. In such a crystal, third-harmonic generation (THG) is realized by the coupled second-harmonic generation (SHG) and sum-frequency generation (SFG) processes, i.e., SHG is dependent on SFG and vice versa. The OAMs of the interacting waves are proved to be conserved in such coupled nonlinear optical processes. As we increase the input OAM in the experiment, the conversion efficiency decreases because of the reduced fundamental power density. Our results provide better understanding for the OAM conversions, which can be used to efficiently produce an optical OAM state at a short wavelength.

Measurement of acceleration and orbital angular momentum of Airy beam and Airy-vortex beam by astigmatic transformation

Special beams, including the Airy beam and the vortex-embedded Airy beam, draw much attention due to their unique features and promising applications. Therefore, it is necessary to devise a straightforward method for measuring these peculiar features of the beams with ease. Hence we present the astigmatic transformation of Airy and Airy-vortex beam. The "acceleration" coefficient of the Airy beam is directly determined from a single image by fitting the astigmatically transformed beam to an analytic expression. In addition, the orbital angular momentum of optical vortex in Airy-vortex beam is measured directly using a single image.

Evolution of phase singularities of vortex beams propagating in atmospheric turbulence

Optical vortex beams propagating through atmospheric turbulence are studied by numerical modeling, and the phase singularities of the vortices existing in the turbulence-distorted beams are calculated. It is found that the algebraic sum of topological charges (TCs) of all the phase singularities existing in test aperture is approximately equal to the TC of the input vortex beam. This property provides us a possible approach for determining the TC of the vortex beam propagating through the atmospheric turbulence, which could have potential application in optical communication using optical vortices.

Unveiling the orbital angular momentum and acceleration of electron beams

New forms of electron beams have been intensively investigated recently, including vortex beams carrying orbital angular momentum, as well as Airy beams propagating along a parabolic trajectory. Their traits may be harnessed for applications in materials science, electron microscopy, and interferometry, and so it is important to measure their properties with ease. Here, we show how one may immediately quantify these beams' parameters without need for additional fabrication or nonstandard microscopic tools. Our experimental results are backed by numerical simulations and analytic derivation.

Dipole azimuthons and vortex charge flipping in nematic liquid crystals

We demonstrate self-trapped laser beams carrying phase singularities in nematic liquid crystals. We experimentally observe the astigmatic transformation of vortex beams into spiraling dipole azimuthons accompanied by power-dependent charge-flipping of the on-axis phase singularity. The latter topological reactions involve triplets of vortex lines and resemble pitchfork bifurcations.

Efficient beam converter for the generation of high-power femtosecond vortices

We describe an optical beam converter for an efficient transformation of Gaussian femtosecond laser beams to single- or double-charge vortex beams. The device achieves a conversion efficiency of 75% for single- and 50% for double-charge vortex beams and can operate with high-energy broad bandwidth pulses. We also show that the topological charge of a femtosecond vortex beam can be determined by analyzing its intensity distribution in the focal area of a cylindrical lens.

Spatially engineered polarization states and optical vortices in uniaxial crystals

We describe how the propagation of light through uniaxial crystals can be used as a versatile tool towards the spatial engineering of polarization and phase, thereby providing an all-optical technique for vectorial and scalar singular beam shaping in optics. Besides the prominent role played by the linear birefringence, the influence of circular birefringence (the optical activity) is discussed as well and both the monochromatic and polychromatic singular beam shaping strategies are addressed. Under cylindrically symmetric light-matter interaction, the radially, azimuthally, and spirally polarized eigen-modes for the light field are revealed to be of a fundamental interest to describe the physical mechanisms at work when dealing with scalar and vectorial optical singularities. In addition, we also report on nontrivial effects arising from cylindrical symmetry breaking, e.g. tilting the incident beam with respect to the crystal optical axis.