Fractional optical vortex beam induced rotation of particles

Reconfiguration of orbital angular momentum via circularly polarized multi-focal spin-to-orbit conversion

Circularly polarized light (CPL), when tightly focused, can generate longitudinal spin-induced orbital angular momentum (OAM) through spin-to-orbit conversion (STOC). While STOC in single-focal systems is well studied, multi-focal STOC remains underexplored. In this Letter, we proposed a multi-focal STOC strategy that leverages tightly focused CPL to generate longitudinal OAM at each focal point. Our numerical simulations demonstrate that reducing the distance between foci induces nonlinear coupling, transforming independent OAMs into a unified OAM state rather than a linear simple superposition. By increasing the number of foci in a ring-symmetric arrangement, we found that the spin angular momentum (SAM) of CPL can be converted into longitudinal OAM distributed along the entire ring. Optical tweezer experiments using non-birefringent dielectric particles confirm the feasibility of the multi-focal STOC strategy, providing direct evidence of OAM-driven rotation independent of SAM. This study reveals a unique method for STOC in multi-focal ring-symmetric structures and offers insights and methods for precision optical manipulation and optical communication.

Rotating windmill array beam with adjustable wing angle

In this study, we introduce a method for adjusting the wing angles of windmill beams. After varying the phase parameters, the sector strengths with different wing angles were generated, and they exhibited a self-rotating property in free-space propagation. This phase was obtained by performing an elliptical operation on the stretching vortex phase. The angle between the wings of the beam varied with the ellipticity. Accordingly, array windmill beams with adjustable wing angles were designed. Finally, we analyzed the evolution of the wing angle and self-rotating properties of the beam in detail. The experimental results were consistent with those of simulations. This operational method can be applied to optical cropping techniques, and the beam can be used in optical manipulation and imaging applications.

Characterizing the fractional coherence vortices through the area of the intensity cross-correlation function

We have generated the fractional coherence vortices using the speckle patterns obtained from the scattering of the fractional vortex beams. In this study, we found the topological charge of the fractional vortex beam with a resolution of 0.01 using the area of the coherence function of scattered fractional optical vortex beams. We have also provided accuracy for the measurement of topological charges of fractional vortex beams using the studies of the area of the coherence function. Our experimental results are well matched with the theoretical results. These fractional coherence functions can be used to generate a security key for data authentication and data encryption. In addition, fractional vortex beams have multiple OAM modes and can be used to address the explosive growth in free-space optical communication.

Coherent control on the generation and annihilation of a pseudospin-induced optical vortex in a honeycomb photonic lattice

We experimentally investigate the coherently controllable generation and annihilation of a pseudospin-induced optical vortex in an optically induced honeycomb photonic lattice in a Λ-type 85Rb atomic vapor cell. Three Gaussian coupling beams are coupled into the atomic gases to form a hexagonal interference pattern, which can induce a honeycomb photonic lattice under electromagnetically induced transparency. Then, two probe beams interfere with each other to form periodical fringes and cover one set of sublattice in the honeycomb lattice, corresponding to excite the K or K' valleys in momentum space. By properly adjusting the experimental parameters, the generation and annihilation of the induced optical vortex can be effectively controlled. The theoretical simulations based on the Dirac and Schrödinger equations are performed to explore the underlying mechanisms, which will support the observations. The demonstrated properties of such controllable optical vortex may lay the foundation for the design of vortex-based optical devices with multidimensional tunability.

Fractional topological charge measurement through optical correlation

The emerging field of optical vortex beams having fractional topological charges (TCs) is of high interest due to its usefulness in various applications. The efficiency of the result depends on the precise measurement of the orbital angular momentum information tied to the fractional TC. This Letter demonstrates, to our knowledge, a novel and simple technique to measure the fractional TC of optical vortex beams through a hybrid digital-optical correlator with the help of auto-correlation between fork-shaped interference patterns corresponding to integer and fractional TCs. Unlike machine learning-based approaches, the proposed method does not require a complex architecture, which lowers computational cost and enables real-time implementation.

Arbitrary combinations of helical-conical optical beams in free space

Helical-conical optical beams (HCOBs) have attracted considerable interest due to their peculiar optical features. Their characteristic helical light intensity distribution has exerted unprecedented advantages in many fields, but multiple combinations of HCOBs have not been reported due to the limitations of algorithms and light field modulation techniques. We propose and experimentally demonstrate arbitrary combinations of multiple HCOBs in free space to construct hybrid HCOB arrays. The similarity between the experimental results and the numerical simulation results is 94.22%. The initial orientation of the HCOBs is flexibly tuned by the rotation factor β, and the optical pen is used to combine the HCOBs. This approach allows multiple parameters in the array to be precisely tuned, including the type, number, and position of HCOBs, adding more design flexibility. The constructed HCOB arrays have a higher degree of modulation freedom and may find applications in fields where dynamic control is in high demand, including optical tweezers, biological cell sorting, and multiparticle manipulation.

Controllable self-rotating array beam with an arc-shaped accelerating trajectory

In this study, a modified interfering vortex phase mask (MIVPM) is proposed to generate a new type of self-rotating beam. The MIVPM is based on a conventional and stretched vortex phase for generating a self-rotating beam that rotates continuously with increasing propagation distances. A combined phase mask can produce multi-rotating array beams with controllable sub-region number. The combination method of this phase was analyzed in detail. This study proves that this self-rotating array beam has an effectively enhanced central lobe and reduced side lobe owing to adding a vortex phase mask compared with a conventional self-rotating beam. Furthermore, the propagation dynamics of this beam can be modulated by varying the topological charge and constant a. With an increase in the topological charge, the area crossed by the peak beam intensity along the propagation axis increases. Meanwhile, the novel self-rotating beam is used for optical manipulation under phase gradient force. The proposed self-rotating array beam has potential applications in optical manipulation and spatial localization.

Measurement of the fractional topological charge of an optical vortex beam through interference fringe dislocation

An optical vortex beam carrying fractional topological charge (TC) has become an immerging field of interest due to its unique intensity distribution and fractional phase front in a transverse plane. Potential applications include micro-particle manipulation, optical communication, quantum information processing, optical encryption, and optical imaging. In these applications, it is necessary to know the correct information of the orbital angular momentum, which is related to the fractional TC of the beam. Therefore, the accurate measurement of fractional TC is an important issue. In this study, we demonstrate a simple technique to measure the fractional TC of an optical vortex with a resolution of 0.05 using a spiral interferometer and fork-shaped interference patterns. We further show that the proposed technique provides satisfactory results in cases of low to moderate atmospheric turbulences, which has relevance in free-space optical communications.

Spiral fractional vortex beams

A new type of spatially structured light field carrying orbital angular momentum (OAM) mode with any non-integer topological order, referred to as the spiral fractional vortex beam, is demonstrated using the spiral transformation. Such beams have a spiral intensity distribution and a phase discontinuity in the radial direction, which is completely different from an opening ring of the intensity pattern and an azimuthal phase jump, common features that all previously reported non-integer OAM modes (referred to as the conventional fractional vortex beams) shared. The intriguing properties of a spiral fractional vortex beam are studied both in simulations and experiments in this work. The results show that the spiral intensity distribution will evolve into a focusing annular pattern during its propagation in free space. Furthermore, we propose a novel scheme by superimposing a spiral phase piecewise function on spiral transformation to convert the radial phase jump to the azimuthal phase jump, revealing the connection between the spiral fractional vortex beam and its conventional counterpart, of which OAM modes both share the same non-integer order. Thus this work is expected to inspire opening more paths for leading fractional vortex beams to potential applications in optical information processing and particle manipulation.

Spin-orbit interactions of a circularly polarized vortex beam in paraxial propagation

Spin-orbit interactions (SOIs) of circularly polarized beam and circularly polarized vortex beam during paraxial propagation in a radial gradient-index (GRIN) fiber are analyzed using the generalized Huygens-Fresnel principle and the GRIN fiber's ABCD matrix. SAM is only associated with polarized light helicity and OAM is only associated with topological charge m. SAM and OAM do not crosstalk or convert between each other; SOIs did not occur at the GRIN fiber's focal plane. SOIs of partially coherent circularly polarized beam and partially coherent circularly polarized vortex beam in the GRIN fiber are also studied and show the same characteristics as the perfectly polarized beam.

Role of fractional high harmonics with non-integer OAM on the generation of a helical attosecond pulse train

Extreme-ultraviolet pulses of attosecond duration carrying orbital angular momentum (OAM) can be produced by spectrally filtering vortex high harmonics generated in a gas medium. Here we reveal that fractional high harmonics (FHHs) with non-integer OAM generated by a short duration Laguerre-Gaussian laser beam are origins for the change of helical attosecond pulse train (APT) with azimuthal angle. We show that these harmonics have gap and minimum structures in the annular intensity profile and discontinue phase distribution along azimuthal angle. And each FHH can be expressed as a superposition of OAM modes with integer topological charges. Features of FHH can be identified by coherently combining selected OAM modes. We also uncover that these features are formed after FHH is propagated in gas medium and in vacuum. We finally demonstrate that the generation of FHHs and the dependence of helical APTs on azimuthal angle are changed by varying the macroscopic condition.

Self-healing property of the self-rotating beam

In this study, we demonstrate the self-healing of self-rotating beams with asymmetric intensity profiles. The proposed self-rotating beam exhibits an asymmetric intensity profile and self-healing properties in free-space propagation. In addition, the rotation direction and beam intensity profile of the self-rotating beam can be adjusted using the parameters a and b in the phase function. The effects of the position and size of the obstruction on the self-healing property of a self-rotating beam were studied both experimentally and numerically. The simulation and experimental results demonstrate that a self-rotating beam can overcome a block of obstacles and regenerate itself after a characteristic distance. Transverse energy flows were used to explain the self-healing properties. Moreover, the beam rotates during propagation, which can be used to capture and manipulate microscopic particles in a three-dimensional space. It is expected that these rotating beams with self-healing properties will be useful in penetrating obstacles for optical trapping, transportation, and optical therapy.

Dynamics of Fractional Vortex Beams at Fraunhofer Diffraction Zone

Fractional vortex beams (FVBs) possess unique topological properties that are manifested in the vortex distribution. However, there are still discrepancies in the value of the vortex strength of FVBs at the far field. In this work we present a complete picture of the behavior of the phase singularities of non-integer (commonly known as fractional) beams in the Fraunhofer diffraction region and demonstrate a very good correspondence between experiments and simulations. As shown in the text, the original beam waist ω0 was found to be a key factor relating to the beam profile topology. This variable was measured in the process of calibrating the experiment. Finally, an experimental method to obtain the non-integer topological charge is proposed. This method only requires an analysis of the intensity, knowledge of the transition behaviors, and the beam waist.

Supercontinuum Induced by Filamentation of Bessel-Gaussian and Laguerre-Gaussian Beams in Water

In this paper, we study the characteristics of the supercontinuum (SC) induced by the filamentation of two typical vortex beams (i.e., Laguerre-Gaussian (LG) and Bessel-Gaussian (BG) beams) in water. By moving the cuvette filled with water along the laser propagation path, we measure the SC induced by the filamentation of the two vortex beams at different positions in water. The results show that the degree of spectral broadening induced by the filamentation of LG beams hardly changes with the change of position, while for BG beams, the spectral broadening induced by filamentation is weak on both sides and strong in the middle. The value of topological charge (TC) affects the length of the filament formed by BG beams; however, its effect on the spectral broadening induced by the filamentation of LG and BG beams is negligible.

Direct experimental evidence for free-space fractional optical vortex transmutation

The emergence of vortex transmutation has opened new ways for vorticity modulation of optical vortices. Although several approaches have been proposed to realize vortex transmutation, fractional optical vortex (FOV) transmutation remains elusive owing to a lack of effective generation and detection methods. Here we report quantitative experimental evidence for a free-space FOV transmutation rule. The key idea is to combine the advantages of a single optical element, termed as fractional spiral polygonal lenses (FSPLs), with a deep learning approach. The desired wavefront is simultaneously generated and manipulated at the focal plane of the FSPL, and the fractional output vorticity is measured by analyzing a single far-field diffraction pattern. Especially, a deep learning scheme using a Bayesian optimization method is developed for output vorticity prediction with a data recovery rate up to 98.2%. The average error of recognized fractional orbital angular momentum modes is as small as 0.02. We clearly observe the intriguing phenomenon that the central vorticity of FOV is changed following a modulo-n transmutation rule in free space. Our results have important implications for fundamental understanding of FOV systems in free space, and offer a technological foundation for potential applications such as quantum information processing and particle manipulation and transportation.

Spin-orbit periodic conversion in a gradient-index fiber

The characteristics of the cylindrical vector beam (CVB) and the cylindrical vector vortex beam (CVVB) in a radial gradient-index (GRIN) fiber are analyzed on the basis of the generalized Huygens-Fresnel principle. The CVB and CVVB exhibit periodic and stable transmission characteristics in the radial GRIN fiber. In the beam with a vortex phase (CVVB), the polarization changes and the spin angular momentum (SAM) is detected at the focal plane of the radial GRIN fiber. A spin-orbit periodic conversion is observed in the radial GRIN fibers. Finally, the SAM expression of partially coherent light is deduced and verified via a simulation.

Spoon-like Beams Generated with Exponential Phases

In this paper, we report a new kind of beam, named “spoon-like” beams, generated with the exponential phase. The intensity distributions and transverse energy flow of the spoon-like beam at the focal plane are analyzed theoretically and experimentally. The results demonstrate that the size of the spoon-like beam becomes enlarged with the increasing power exponent n, and the length of the spoon-like intensity trajectory becomes shorter with the increasing parameter p. Furthermore, there is an intensity gradient along the spoon-like trajectory of the beam, which introduces the intensity-gradient force exerted onto microparticles. The experiment on optical tweezers demonstrates that the focused beams can create spoon-like traps for the two-dimensional manipulation of particles.

Precise measurement of trapping and manipulation properties of focused fractional vortex beams

Fractional vortex beams (FVBs) were believed to be hard to rotate microparticles at a half-integer topological charge due to the unique radial opening (low-intensity gap) in their intensity ring. However, recent research discovered more symmetric intensity structures with less intensity inhomogeneity of practical FVBs at the focal plane. Here, we experimentally demonstrated the manipulation of trapped microparticles and precisely measured their rotation periods at the focal plane of practical FVBs by using a high-speed camera. We verified that the measured orbital angular momentum (OAM) derived from the collective microparticle rotation is roughly proportional to the fractional OAM of practical FVBs. Furthermore, we also experimentally obtained the trapped microparticles' power spectra under the illumination of FVBs, from which we achieved the average trap stiffness to evaluate the two-dimensional trapping strength of the practical focused FVB intensity ring. Our results provide a new insight and an efficient tool on finely trapping and rotating microparticles and bio-cells by using fractional vortex beams.

Experimental generation of the polycyclic tornado circular swallowtail beam with self-healing and auto-focusing

In this paper, the polycyclic tornado circular swallowtail beam (PTCSB) with autofocusing and self-healing properties is generated numerically and experimentally and their properties are investigated. Compared with the circular swallowtail beam (CSB), the optical distribution of the PTCSB presents a tornado pattern during the propagation. The number of spiral stripes, as well as the orientation of the rotation, can be adjusted by the number and the sign of the topological charge. The Poynting vectors and the orbital angular momentum are employed to investigate the physical mechanism of beam-rotating. In addition, we also introduce a sector-shaped opaque obstacle to investigate the self-healing property of the PTCSB, passing through it with different center angles and discuss the influence of the scaling factor along the propagation direction. Our results may expand the potential applications in the optical spanner and material processing.

Review on fractional vortex beam

As an indispensable complement to an integer vortex beam, the fractional vortex beam has unique physical properties such as radially notched intensity distribution, complex phase structure consisting of alternating charge vortex chains, and more sophisticated orbital angular momentum modulation dimension. In recent years, we have noticed that the fractional vortex beam was widely used for complex micro-particle manipulation in optical tweezers, improving communication capacity, controllable edge enhancement of image and quantum entanglement. Moreover, this has stimulated extensive research interest, including the deep digging of the phenomenon and physics based on different advanced beam sources and has led to a new research boom in micro/nano-optical devices. Here, we review the recent advances leading to theoretical models, propagation, generation, measurement, and applications of fractional vortex beams and consider the possible directions and challenges in the future.

Superposition of two fractional optical vortices and the orbital angular momentum measurement by a deep-learning method

We propose a single diffractive optical element called the composite fractional spiral zone plates to generate superimposed fractional optical vortices. Such an element is composed of two fractional spiral zone plates (FSZPs) through logical AND operation, and the produced beam carries superimposed fractional orbital angular momentum (OAM) states. By controlling the topological charge of the superimposed FSZPs, denoted by l₁ and l₂, one can flexibly obtain the desired superimposed fractional OAM modes of the generated beam. Especially, a deep-learning model with a densely connected convolutional neural network architecture is utilized to accurately predict the superimposed fractional OAM states of SFOVs. The average recovery rate of the superimposed fractional OAM states based on the training model is over 99%, and the average error is as small as 0.02. This work may pave the way for wide-ranging applications such as smart OAM communication, particle transmission, and even quantum entanglement.

Measure the arbitrary topological charge of perfect optical vortex beams by using the dynamic angular double slits

Perfect optical vortex beams (POV) have attracted considerable attention in many novel applications because they have the advantage of a radial profile that is independent of the topological charge (TC). Nowadays, there are few effective methods to measure both the integer and the fractional TCs of the POV. In this paper, we achieve the precise measurement of arbitrary TCs through the approach of dynamic angular double slits (ADS), which performs the transformation from the POV to the interference intensity patterns at the angular bisector direction of the ADS. The information of the TC can be obtained from the periodically changing interference pattern. The deviation is less than 2% by comparing the theoretical values with the fitting results, therefore the detection method is effective and reasonable.

Angular momentum separation in focused fractional vector beams for optical manipulation

The generation, propagation, and applications of different types of integer vector beams have been extensively investigated. However, little attention focuses on the photophysical and photomechanical properties of the fractional vector beam (FVB). Herein, we theoretically and experimentally investigate the spin angular momentum (SAM) separation and propagation characteristics of weakly focused FVBs. It is demonstrated that such a beam carrying no SAM leads to both the transverse separation of SAM and the special intensity patterns in the focal region. Furthermore, we study the intensity, SAM, and orbital angular momentum (OAM) distributions of the tightly focused FVBs. It is shown that both three-dimensional SAM and OAM are spatially separated in the focal region of tightly focused FVBs. We investigate the optical forces, spin torques, and orbital torques on a dielectric Rayleigh particle produced by the focused FVBs. The results reveal that asymmetrical spinning and orbiting motions of optically trapped particles can be realized by manipulating FVBs.

Microparticle sorting with a virtual optical chip

We proposed an automatic sorting method based on a virtual optical chip, which was formed by a complex-amplitude beam shaping system. The automatic sorting of different micro-particles was realized by the optical forces of the intensity and phase gradients of the reconstructed optical beam. The method was verified with theoretical analysis and experimental results. Compared with the traditional optical sorting methods, the proposed one does not need high-precision mechanical and/or microfluidic devices. The optical chip is flexible in structure and efficient in optical sorting and can be used in the fields of medical detection and material sensing.

Focusing and propagation properties of Bessel-Gaussian beam with a power-order mixing helical-conical phase wavefront

Based on the vector diffraction theory, this paper investigates the focusing and propagation characteristics of a Bessel-Gaussian beam with a power-order mixing helical-conical wavefront. It discusses the focused light intensity, optical gradient force distribution, and propagation characteristics under different parameters in detail. The results show that the topological charge number L can finely adjust the opening of the spiral-like curve at the focal plane. The power order n can adjust the energy distribution in the focus area. By increasing the eccentricity parameters K, the position of the maximum intensity spot will move along with the y coordinate axis. When the beam parameter β increases, the number of intensity peaks on the focal plane increases. As the propagation distance z increases, the pattern of intensity distribution will change from an ellipse to "doughnut-like." Then a circular dark core will appear in the center of the light, and the propagation mode will gradually become an optical trap. Some optical gradient force distributions also are investigated to illuminate the applications of these alterable focal patterns.

Ultrathin freestanding terahertz vector beam generators with free phase modulation

Simultaneous control of phase and polarization offers a large degree of freedom to tailor the beam properties, for instance, enabling generation of structured beams such as vector beams and vector vortex beams. Here, we propose an ultrathin freestanding metasurface operating at the terahertz frequency for efficient generation of vector vortex beam with an arbitrarily defined topological charge from linearly polarized excitation. The metasurface is composed of bilayer metallic patterns separated by a thin quartz slab, with one layer determining the transmission polarization and the other controlling the transmission phase. The tightly cascaded two layers form a Fabry-Perot cavity to maximize the efficiency of the polarization and phase control. Two metasurfaces for generation of radially polarized vector beam with uniform phase and vortex phase are fabricated and tested at 0.14 THz. The experimental results successfully demonstrate the generation of high-quality vector beams with the desired phase. In the experiment, the ultrathin and freestanding properties allow the metasurface to be easily combined with other components, which shows great potential for the development of various compact terahertz systems.

Two-dimensional Talbot effect of the optical vortices and their spatial evolution

We report on the experimental and theoretical study of the near-field diffraction of optical vortices (OVs) at a two-dimensional diffraction grating. The Talbot effect for the optical vortices in the visible range is experimentally observed and the respective Talbot carpets for the optical vortices are experimentally obtained for the first time. It is shown that the spatial configuration of the light field behind the grating represents a complex three-dimensional lattice of beamlet-like optical vortices. A unit cell of the OV lattice is reconstructed using the experimental data and the spatial evolution of the beamlet intensity and phase singularities of the optical vortices is demonstrated. In addition, the self-healing effect for the optical vortices, which consists in flattening of the central dip in the annular intensity distribution, i.e., restoring the image of the object plane predicted earlier is observed. The calculated results agree well with the experimental ones. The results obtained can be used to create and optimize the 3D OV lattices for a wide range of application areas.

Ultrafast control of fractional orbital angular momentum of microlaser emissions

On-chip integrated laser sources of structured light carrying fractional orbital angular momentum (FOAM) are highly desirable for the forefront development of optical communication and quantum information-processing technologies. While integrated vortex beam generators have been previously demonstrated in different optical settings, ultrafast control and sweep of FOAM light with low-power control, suitable for high-speed optical communication and computing, remains challenging. Here we demonstrate fast control of the FOAM from a vortex semiconductor microlaser based on fast transient mixing of integer laser vorticities induced by a control pulse. A continuous FOAM sweep between charge 0 and charge +2 is demonstrated in a 100 ps time window, with the ultimate speed limit being established by the carrier recombination time in the gain medium. Our results provide a new route to generating vortex microlasers carrying FOAM that are switchable at GHz frequencies by an ultrafast control pulse.

Tailoring diffraction of light carrying orbital angular momenta

A unified approach to controlling the diffraction of light carrying orbital angular momenta (OAM) is developed and experimentally verified in this Letter. This approach allows one to specify not only the number of diffraction maxima, their spatial frequencies, and the intensity distribution between them, but also the OAM in each maximum. It is verified that the approach can be used for structuring both single and multiple beams carrying OAMs. Simulations reveal phase singularities in structured beams. In addition, the approach makes it possible to shape the light in regular and irregular two-dimensional arrays with addressing the OAMs at each site. This approach offers new opportunities for singular optics.

Diffractometry-based vortex beams fractional topological charge measurement

In this Letter, we investigate the Fresnel diffraction of vortex beams from a phase plate and propose a novel (to the best of our knowledge) method to determine the fractional part of the topological charge of vortex beams. When a vortex beam with a fractional topological charge illuminates the edge region of a transparent plate, the visibility of the diffraction pattern on two sides of the beam is different. Rotation of the phase plate changes the visibility on the left and right sides of the beam, periodically. By measuring three consecutive angles of the minimum visibilities, the fractional part of the topological charge is obtained. The proposed method is verified experimentally and is shown to be independent of the phase plate and vortex beam parameters. The precision of the method is obtained better than 0.01.

Spectral control of the orbital angular momentum of a laser beam based on 3D properties of spiral phase plates fabricated for an infrared wavelength

This paper examines the spectral properties of a spiral phase plate (SPP) generating orbital angular momentum (OAM) beams. A simple method is proposed for calculating the resulting OAM by measuring only two maximum expansion coefficients. A comparative numerical simulation of the proposed and traditional methods is performed. An SPP is fabricated for generation of an OAM with integer values at infrared and visible wavelengths. Qualitative experimental studies of the changes in a generated OAM with a change in the operating wavelength are performed using the spatial filtering method. The experimental results are found to agree with the results of numerical simulation. Beams with integer and fractional OAM values are obtained experimentally by changing the wavelength.

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.

Effect of hydrodynamic inter-particle interaction on the orbital motion of dielectric nanoparticles driven by an optical vortex

We experimentally and theoretically characterize dielectric nano- and microparticle orbital motion induced by an optical vortex of the Laguerre-Gaussian beam. The key to stable orbiting of dielectric nanoparticles is hydrodynamic inter-particle interaction and microscale confinement of slit-like fluidic channels. As the number of particles in the orbit increases, the hydrodynamic inter-particle interaction accelerates orbital motion to overcome the inherent thermal fluctuation. The microscale confinement in the beam propagation direction helps to increase the number of trapped particles by reducing their probability of escape from the optical trap. The diameter of the orbit increases as the azimuthal mode of the optical vortex increases, but the orbital speed is shown to be insensitive to the azimuthal mode, provided that the number density of the particles in the orbit is same. We use experiments, simulation, and theory to quantify and compare the contributions of thermal fluctuation such as diffusion coefficients, optical forces, and hydrodynamic inter-particle interaction, and show that the hydrodynamic effect is significant for circumferential motion. The optical vortex beam with hydrodynamic inter-particle interaction and microscale confinement will contribute to biosciences and nanotechnology by aiding in developing new methods of manipulating dielectric and nanoscale biological samples in optical trapping communities.

Focus properties of cosh-Gaussian beams with the power-exponent-phase vortex

Vector diffraction theory is used to investigate the focusing properties of cosh-Gaussian beams with the power-exponent-phase vortex. The effects of the decentered parameter, the power order, and the topological charge on the normalized intensity distribution are examined. Results show that intensity distribution in the focal region can be altered significantly by the topological charge, the power order, and the decentered parameter. The pattern of the optical intensity slowly enlarges with the increase of topological charge. The strongest intensity part of the annulus rotates by the changing topological charge. As the power order increases, the intensity distribution is more concentrated. As the decentered parameter increases, there occur multiple relatively strong intensity peaks, and the entire focus pattern extends outward. Some optical gradient force distributions are investigated to illuminate the applications of these alterable foci patterns.

Second-harmonic generation of asymmetric Bessel-Gaussian beams carrying orbital angular momentum

Nonlinear processes of laser beams carrying orbital angular momentum (OAM) offer a means to generate new wavelengths and to manipulate OAM charge numbers. We demonstrate the second-harmonic generation (SHG) of asymmetric Bessel-Gaussian (BG) beams carrying OAM of both integer and fractional charge numbers. Experimental results show a good one-to-one correspondence of the charge numbers and compliance with the OAM conservation law. The SHG conversion process and efficiency with different combined charge numbers are also discussed.

Fractional vortex ultrashort pulsed beams with modulating vortex strength

In most papers about the fractional vortex continuous beams (FVCBs), the relationship between the total vortex strength S_α and the propagation distance is not analyzed since the vortex structure is not stable in the near field. In this paper, we theoretically study the fractional vortex ultrashort pulsed beams (FVUPBs) possessing non-integer topological charges α at arbitrary plane and find that the vortex structure is propagation-distance-dependent. Both the intensity and phase distributions are calculated to analyze the vortex structure. To evaluate the propagation properties of FVUPBs, we focus on the total vortex strength (TVS) of FVUPBs to investigate the number of vortex, and demonstrate that the birth of a vortex is at α = m + ɛ, where m is an integer, ɛ is a changing fraction depending on the pulse durations, peak wavelengths and propagation distances. Furthermore, we discover that the FVUPBs carry decreasing TVS along the propagation axis in free space. This special vortex structure for FVUPBs appears due to the mixture weight of vortex pulsed beam with different integer topological charges (TCs) n. However, the total orbital angular momentum is invariant during propagation. The above phenomenon presented in our paper are totally particular and intriguing compared with the FVCBs.

Focus shaping of partially coherent radially polarized vortex beam with tunable topological charge

In this paper, we have introduced a new class of partially coherent vector vortex beams, named radially polarized multi-Gaussian Schell-model (MGSM) vortex beam, carrying the vortex phase with tunable topological charges (i.e., both integral and fractional values) as a natural extension of the radially polarized MGSM beam. The tight focusing properties of the radially polarized MGSM vortex beam passing through a high numerical aperture (NA) objective lens are investigated numerically based on the vectorial diffraction theory. Numerical results show that the focal intensity distributions of the radially polarized MGSM vortex beam can be shaped by regulating the structure of the correlation functions and the topological charge of vortex phase. In contrast with the integral vortex beam, the most intriguing property of the fractional vortex beam is that the focal intensity distribution at the focal plane can be nonuniformity and asymmetry, while such unique characteristics will vanish when the spatial coherence length is sufficiently small. Furthermore, some focal fields with novel structure, such as a focal spot with nonuniform asymmetric or an anomalous asymmetric hollow focal field, can be formed by choosing suitable fractional values of topological charge and spatial coherence length. Our results will be useful for optical trapping, especially for trapping of irregular particles or manipulation of absorbing particles.

Interparticle-Interaction-Mediated Anomalous Acceleration of Nanoparticles under Light-Field with Coupled Orbital and Spin Angular Momentum

Spin-orbit interaction is a crucial issue in the field of nanoscale physics and chemistry. Here, we theoretically demonstrate that the spin angular momentum (SAM) can accelerate and decelerate the orbital motion of nanoparticles (NPs) via light-induced interparticle interactions by a circularly polarized optical vortex. The Laguerre-Gaussian beam as a conventional optical vortex with orbital angular momentum (OAM) induces the orbital and spinning motion of a trapped object depending on the spatial configuration. On the contrary, it is not clear whether circularly polarized light induces the orbital motion for the particles trapped off-axis. The present study reveals that the interparticle light-induced force due to the SAM enhances or weakens the orbital torque and modulates rotational dynamics depending on the number of NPs, where the rotation speed of NPs in the optical field with both positive SAM and OAM can be 4 times faster than that in the optical field with negative SAM and positive OAM. The obtained results will not only clarify the principle for the control of NPs based on OAM-SAM coupling via light-matter interaction but also contribute to the unconventional laser processing technique for nanostructures with various chiral symmetries.

Gouy phase-assisted topological transformation of vortex beams from fractional fork holograms

The topological transformation of optical vortex beams from fractional fork holograms induced by the modulation of controlled Gouy phase (GP) is demonstrated. The GP change is tuned by varying the wavefront curvature of the input beam on the plane of the fractional phase generating optic. The locus of the point of singularity traces a semi-circle about the beam axis for maximum possible change of the associated GP. The morphology parameters describing the anisotropic vortex phases of generated optical vortices are tuned in the experiment by varying the input wavefront curvature. Through the transformation of the transverse Poynting vector of the fractional vortex beams, control of the extrinsic orbital angular momentum is demonstrated for the first time, to the best of our knowledge. This could enable better manipulation of an optically trapped micro-particle and be used in optically driven micro-machines.

Vortex strength and beam propagation factor of fractional vortex beams

Fractional vortex beams (FVBs) with non-integer topological charges attract much attention due to unique features of propagations, but different viewpoints still exist on the change of their total vortex strength. Here we have experimentally demonstrated the distribution and number of vortices contained in FVBs at the Fraunhofer diffraction region. We have verified that the jumps of total vortex strength for FVBs happen only when non-integer topological charge is before and after (but very close to) any even integer number that originates from two different mechanisms for generation and movement of vortices on focal plane. Meanwhile, we have also measured the beam propagation factor (BPF) of such FVBs and have found that their BPF values almost increase linearly in the x component (along the initial edge dislocation) and oscillate increasingly in the y component (vertical to the initial edge dislocation). Our experimental results are in good agreement with numerical results.

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

Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

Topological charge measurement of vortex beams by phase-shifting digital hologram technology

We propose a direct measurement method that is applicable to both integral and fractional vortex beams. In this approach, the phase distribution of the vortex beam is visualized via the phase-shifting digital holography technique. The least square method is initiatively employed to improve the measurement precision. The maximal error of the experimental results is below 4.8%.

Tunable near-infrared optical vortex parametric laser with versatile orbital angular momentum states

We demonstrate a tunable vortex laser with versatile orbital angular momentum (OAM) states based on a singly resonant optical parametric oscillator formed of a noncritical phase-matching LiB₃O₅ crystal. The selective generation of a signal (idler) output with three OAMs, including an upconverted (negative) OAM, is achieved simply by appropriate shortening (or extending) of the cavity. The compact cavity configuration also allows for the generation of the signal (idler) output with various OAMs by simply tuning the signal wavelength. The vortex output is tuned within the wavelength region of 0.74 to 1.84 μm with a maximum pulse energy of 2.16 mJ from a pump energy of 9.3 mJ.

Partially coherent fractional vortex beam

We introduce a new kind of partially coherent vortex (PCV) beam with fractional topological charge named partially coherent fractional vortex (PCFV) beam and derive the propagation formula for such beam passing through a stigmatic ABCD optical system with the help of the convolution method. We calculate numerically the propagation properties of a PCFV beam focused by a thin lens, and we find that the PCFV beam exhibits unique propagation properties. The opening gap of the intensity pattern and the rotation of the beam spot disappear gradually and the cross-spectral density (CSD) distribution becomes more symmetric and more recognizable with the decrease of the spatial coherence width, being qualitatively different from those of the PCV beam with integral topological charge. Furthermore, we carry out experimental generation of a PCFV beam with controllable spatial coherence, and measure its focusing properties. Our experimental results are consistent with the theoretical predictions.

Conservation of orbital angular momentum for high harmonic generation of fractional vortex beams

This work demonstrates conservation of average orbital angular momentum for high harmonic generation of fractional vortex beams. High harmonics are generated in reflected light beams in a three-dimensional particle-in-cell simulation. The average orbital angular momentum of the beam is calculated when a relativistic linearly polarized fractional vortex beam impinges on a solid foil. The harmonic generation progress can be well explained by using the vortex oscillating mirror model. Both simulation and theoretical analysis show that the average orbital momentum of the nth harmonic is n times that of the fundamental frequency beam. This provides evidence that the average orbital angular momentum obeys momentum conservation during the harmonic generation of fractional vortex beams.

Close-packed optical vortex lattices with controllable structures

As a spatial structured light field, the optical vortex (OV) has attracted extensive attention in recent years. In practice, the OV lattice (OVL) is an optimal candidate for applications of orbital angular momentum (OAM)-based optical communications, microparticle manipulation, and micro/nanofabrication. However, traditional methods for producing OVLs meet a significant challenge: the OVL structures cannot be adjusted freely and form a close-packed arrangement, simultaneously. To overcome these difficulties, we propose an alternative scheme to produce close-packed OVLs (CPOVLs) with controllable structures. By borrowing the concept of the close-packed lattice from solid-state physics, CPOVLs with versatile structures are produced by using logical operations of expanding OV primitive cells combined with the technique of phase mask generation. Then, the existence of OAM states in the CPOVLs is verified. Furthermore, the energy flow and OAM distribution of the CPOVLs are visualized and analyzed. From a light field physics viewpoint, this work increases the adjustment dimensions and extends the fundamental understanding of the OVL, which will introduce novel applications.

Integrated design of pi/2 converter and its experimental performance

Transverse modes of light have been widely exploited in both classical and quantum optics in recent years. Among the devices to manipulate the transverse modes of light, a π/2 converter is a fundamental and important one that analogs to the quarter-wave plate in the polarization degree of freedom. While a π/2 converter is typically achieved by a pair of well-adjusted cylindrical lenses, it suffers from complexity in its installation and adjustment, which strongly limits its practical applications. In this paper an integrated design of a π/2 converter is reported. We compute the necessary parameters for manufacturing according to refractive theory of a cylindrical surface. Based on the change of refractive indices, we simulate the response of Gouy phase versus wavelengths. We also implement an experiment to verify the conversion between Laguerre-Gaussian modes and Hermite-Gaussian modes by using our compact π/2 converter to confirm its simple adjustment and reliable performance in practice.

Fractal spiral zone plates

We present diffractive optical elements with an extended depth of focus, namely, fractal spiral zone plates (FSZPs), which combine a fractal structure and spiral zone plates (SZPs) to generate a sequence of coaxial vortices in the focal volume along the propagation direction. The axial irradiance of the FSZPs is examined both experimentally and in a simulation and is compared with that of SZPs and that of fractal zone plates. The focusing properties of the FSZPs with different parameters are investigated, and a potential application to edge-enhancement images is also shown.

Microscopic Engine Powered by Critical Demixing

We experimentally demonstrate a microscopic engine powered by the local reversible demixing of a critical mixture. We show that, when an absorbing microsphere is optically trapped by a focused laser beam in a subcritical mixture, it is set into rotation around the optical axis of the beam because of the emergence of diffusiophoretic propulsion. This behavior can be controlled by adjusting the optical power, the temperature, and the criticality of the mixture.

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.