Propagation dynamics of an optical vortex imposed on an Airy beam

Topological charges measurement of circular Bessel Gaussian beam with multiple vortex singularities via cross phase

In this paper, we firstly propose a method to measure the topological charges (TCs) of a circular Bessel Gaussian beam with multiple vortex singularities (CBGBMVS) by utilizing cross phase. Based on theory and experiment, the cross phase is utilized to realize the TCs measurement of the CBGBMVS in free space with different situations, such as different singularity number, TCs and singularity location. Especially, the TCs measurement method is also investigated and verified in atmosphere turbulence. Our work provides an effective and convenient way to realize the TCs measurement of multiple singularities embedded in abruptly autofocusing host beams which has plenty of potential application in optical communication.

Caustics of the axially symmetric vortex beams: analysis and engineering

We demonstrate that our theoretical scheme developed in the previous study on the caustics of the abruptly autofocusing vortex beams [Xiao et al., Opt. Express29, 19975 (2021)10.1364/OE.430497] is universal for all the axially symmetric vortex beams. Further analyses based on this method show the complex compositions of the vortex caustics in real space. Fine features of the global caustics are well reproduced, including their deviations from the trajectories of the host beams. Besides, we also show the possibility of tailoring the vortex caustics in paraxial optics based on our theory. The excellent agreements of our theoretical results with both numerical and experimental results confirm the validity of this scheme.

Propagation Characteristics of Circular Airy Vortex Beams in a Uniaxial Crystal along the Optical Axis

Circular airy vortex beams (CAVBs) have attracted much attention due to their “abruptly autofocusing” effect, phase singularity, and their potential applications in optical micromanipulation, communication, etc. In this paper, we numerically investigated the propagation properties of circular airy beams (CABs) imposed with different optical vortices (OVs) along the optical axis of a uniaxial crystal for the first time. Like other common beams, a left-hand circular polarized (LHCP) CAVB, propagating along the optical axis in a uniaxial crystal, can excite a right-hand circular polarized (RHCP) component superimposed with an on-axis vortex of topological charge (TC) number of 2. When the incident beam is an LHCP CAB imposed with an on-axis vortex of TC number of l = 1, both of the two components have an axisymmetric intensity distribution during propagation and form hollow beams near the focal plane because of the phase singularity. The phase pattern shows that the LHCP component carries an on-axis vortex of TC number of l = 1, while the RHCP component carries an on-axis vortex of TC number of l = 3. With a larger TC number (l = 3), the RHCP component has a larger hollow region in the focal plane compared to the LHCP component. We also studied cases of CABs imposed with one and two off-axis OVs. The off-axis OV makes the CAVB’s profile remain asymmetric throughout the propagation. As the propagation distance increases, the off-axis OVs move near the center of the beam and overlap, resulting in a special intensity and phase distribution near the focal plane.

Propagation properties of finite Airy beams on curved surfaces

Airy beams have provided exciting inspiration in the field of optical communication, particle manipulation, and imaging. We investigate the propagation properties of the exponential truncation Airy beams (ETABs) on constant Gaussian curvature surfaces (CGCSs) in this paper. The analytical expression of the electric field of ETABs propagating on the CGCSs is derived. It shows that the equivalent periodical accelerations of the trajectories of ETABs on the curved surface are always larger than the constant one on the flat surface because the CGCSs have a strong focusing ability. For the same reason, the non-diffraction propagation of ETABs is found when the focusing ability of the CGCSs is strong enough. Moreover, we investigate the self-healing length of ETABs on CGCSs and explore that the ability of self-healing is related to the geometry of CGCSs besides the width of the block and the size of the beam. The self-healing length gets larger with the increase of radius of CGCSs and finally consists with that on the flat surface. These propagation characteristics are different from those in the flat space and are useful for the future applications of ETABs in particle manipulation on waveguides, light-sheet fluorescence microscopy, curved nanophotonics, and so on.

Characteristics of an elliptical Airy beam with a circular concentric vortex and its realization

We theoretically and experimentally study the propagation characteristics of elliptical Airy vortex beams (EAVBs) with a circular concentric vortex. It is found that EAVBs inherit the abruptly autofocusing properties of the circular Airy beams (CABs), but EAVBs will have a better autofocusing performance than circular Airy vortex beams (CAVBs) under certain conditions. It is also found that the initial m-order concentric vortex of EAVBs splits into |m| first-order vortices at the autofocusing plane, and the focusing pattern splits into |m|+1 bright spots with the pattern's tilting direction related to the sign of m [m is the topological charge (TC) of the vortex]. These characteristics of EAVBs may have potential applications in TC detection, optical micromanipulation, communications, and other fields.

Goos-Hänchen and Imbert-Fedorov shifts of off-axis Airy vortex beams

Based on the angular spectrum of high order off-axis Airy vortex beams (AiVBs), Goos-Hänchen (GH) shifts and Imbert-Fedorov (IF) shifts near the Brewster angle are numerically calculated. It is found that both GH and IF shifts increase with the increase of the vortex's topological charge of AiVBs. The influences of the vortex's positions on GH and IF shifts are studied for the case of the topological charge m = 1. The studies of the off-axis vortex show that the influences of the vortex's position on shifts are inversely proportional to the distance between the vortex's position and the origin point.

Propagation properties of the radially polarized Airy vortex beams in a chiral medium

We study the propagation of the radially polarized Airy vortex beams (RPAiVBs) in a chiral medium analytically. The RPAiVBs split into the left circular polarization of the RPAiVBs (LCPRPAiVBs) and the right circular polarization of the RPAiVBs (RCPRPAiVBs). We mainly discuss the effects of the vortex and the chiral parameter on the propagation properties of the RPAiVBs, involving the intensity distributions and the radiation forces. It is shown that with the chiral parameter increasing, the intensity focusing position of the RCPRPAiVBs is further from ${ z} = 0\text{Zr}$z=0Zr, while that of the LCPRPAiVBs is opposite. Besides, the maximum radiation forces of the RCPRPAiVBs are stronger than those of the LCPRPAiVBs. It is significant that we can control the acceleration, the intensity focusing position, and the radiation forces of the RPAiVBs by varying the vortex order and the chiral parameter.

Propagation dynamics of autofocusing circle Pearcey Gaussian vortex beams in a harmonic potential

We introduce the circle Pearcey Gaussian vortex (CPGV) beams in a harmonic potential for the first time and investigate their abruptly autofocusing properties by theoretical analysis and numerical simulations in this paper. By varying the spatial distribution factors, one can effectively control the propagating dynamics of the beams, including the position of the focus, the radius of the focal light spot and the intensity contrast. Meanwhile, the magnitude of topological charges and the position of the vortex can alter the focal pattern and the intensity contrast. Furthermore, the position of the focus can be flexibly controlled in a tiny range by adjusting the scaled parameter of the incident beam properly.

Propagation dynamics of Janus vortex waves

We study the propagation dynamics of Janus vortex wave under the action of a focusing lens based upon the formula of focused circular vortex Airy beams. Two dark foci would be generated under the action of a lens, and thus a perfect light hollow bottle could be formed. By controlling corresponding parameters, we could control the focal position and the relative intensity between the two focal intensities. The off-axis optical vortex (OV) would rotate rapidly in two focal regions, but keep still in the lens focus region. The angular displacement of OV in each focusing process is nearly π/2. (Note that the angular displacement for an off-axis OV in single focusing process of Gaussian beam is nearly π.) Two same OVs would repel to each other, but two opposite OVs would attract each other and annihilate at first focus plane in Janus vortex waves.

Generation of Airy vortex beam arrays using computer-generated holography

We report on the generation of diverse arrays of Airy vortex beams (AiVBs) with normal or deformed structures by employing computer-generated holography. The intensity distributions and evolution of the arrays containing four AiVBs with different topological charges are theoretically and experimentally studied. The generated AiVBs are converged due to the self-bending characteristic independent of the sign and topological charges of the AiVBs. The experimental and numerical results agree well with each other. These novel arrays are expected to be used for multiple capture or manipulation of particles at the same time but at different positions, providing powerful theoretical and experimental bases for improving the efficiency of optical manipulation.

Auto-transition of vortex- to vector-Airy beams via liquid crystal q-Airy-plates

We propose the auto-transition of vortex-Airy to vector-Airy beams realized via a liquid crystal q-Airy-plate, whose director distribution is the integration of a q-plate and a polarization Airy mask. The polarization, phase, intensity distributions of the vortex-vector-Airy beams (VVABs) during the transition process and individual trajectories of the vortex beam, vector beam and Airy beam components are both theoretically and experimentally investigated. Interesting findings show that the pair of vortex components firstly experience transverse deflection with a smaller acceleration than the Airy components and then automatically evolve into a vector component propagating in a straight path. The polarization mode of the VVABs can be easily switched by tuning the incident polarization direction. Meanwhile, the Airy component still maintains its intrinsic self-accelerating and self-healing properties. The asymmetric intensity distribution and variation of VVABs are revealed, and the energy flows are simulated to better illustrate the interaction of the Airy, vortex and vector components. This work provides an approach for the manipulation of the spatially structured light beams, which may inspire their potential applications in optics, photonics and multidisciplinary fields.

Annular arrayed-Airy beams carrying vortex arrays

We propose and experimentally demonstrate annular arrayed-Airy beams (AAABs) carrying vortex arrays by combining multiple beams. The propagation dynamics and abrupt autofocusing property are studied. The focal intensity can be greatly increased by two orders of magnitude by increasing vortex array number. Furthermore, the autofocusing property is also enhanced significantly. This tightly autofocusing property would be advantageous for the generation of high intensity laser, optical manipulation, medical treatments, and nonlinear effects.

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.

Controlling abruptly autofocusing vortex beams to mitigate crosstalk and vortex splitting in free-space optical communication

Orbital angular momentum (OAM) mode crosstalk induced by atmospheric turbulence is a challenging phenomenon commonly occurring in OAM-based free-space optical (FSO) communication. Recent advances have facilitated new practicable methods using abruptly autofocusing light beams for weakening the turbulence effect on the FSO link. In this work, we show that a circular phase-locked Airy vortex beam array (AVBA) with sufficient elements has the inherent ability to form an abruptly autofocusing light beam carrying OAM, and its focusing properties can be controlled on demand by adjusting the topological charge values and locations of these vortices embedded in the array elements. The performance of a tailored Airy vortex beam array (TAVBA) through atmospheric turbulence is numerically studied. In a comparison with the ring Airy vortex beam (RAVB), the results indicate that TAVBA can be a superior light source for effectively reducing the intermodal crosstalk and vortex splitting, thus leading to improvement in the FSO system performance.

Interplay between topological phase and self-acceleration in a vortex symmetric Airy beam

Photons in an optical vortex usually carry orbital angular momentum, which boosts the application of the micro-rotation of absorbing particles and quantum information encoding. Such photons propagate along a straight line in free space or follow a curved trace once guided by an optical fiber. Teleportation of an optical vortex using a beam with non-diffraction and self-healing is quite challenging. We demonstrate the manipulation of the propagation trace of an optical vortex with a symmetric Airy beam (SAB) and found that the SAB experiences self-rotation with the implementation of a topological phase structure of coaxial vortex. Slight misalignment of the vortex and the SAB enables the guiding of the vortex into one of the self-accelerating channels. Multiple off-axis vortices embedded in SAB are also demonstrated to follow the trajectory of the major lobe for the SAB beam. The Poynting vector for the beams proves the direction of the energy flow corresponding to the intensity distribution. Hence, we anticipate that the proposed vortex symmetric Airy beam (VSAB) will provide new possibilities for optical manipulation and optical communication.

Suppression of collapse for two-dimensional Airy beam in nonlocal nonlinear media

Dynamics and collapse of two-dimensional Airy beams are investigated numerically in nonlocal nonlinear media with split step Fourier transform method. In particular, the stability and self-healing properties of the Airy beams depend crucially on the location and topological charge of the vortex when the beams carry angular momentum. The propagation of abruptly autofocusing Airy beams is also demonstrated in local and nonlocal media. In strongly self-focusing regime, with the help of nonlocality, stationary propagation of two-dimensional Airy beams can be obtained, which always collapse in local nonlinear media.

Measurement of Airy-vortex beam topological charges based on a pixelated micropolarizer array

In this paper, we numerically studied the intensity patterns and screw phases of an embedded optical vortex in an Airy beam generated by a 3/2 phase pattern imposed on a spatial light modulator. It is found that the optical vortex and the Airy beam's main lobe approach each other during propagation, which means the energy of the Airy beam's intensity peaks can be taken advantage of by the imposed vortices. Based on a pixelated micropolarizer array in the interference path, we succeeded in measuring the integer topological charges up to -10 according to the phase jump. In addition, fractional topological charges were also obtained in the experiment. Both of the experimental results are acquired in a high-precision and robust way. This work will promote potential application of Airy-vortex beams in fields such as optical manipulation, laser processing, and photon entanglement.

Unveiling the propagation dynamics of self-accelerating vector beams

We study theoretically and experimentally the varying polarization states and intensity patterns of self-accelerating vector beams. It is shown that as these beams propagate, the main intensity lobe and the polarization singularity gradually drift apart. Furthermore, the propagation dynamics can be manipulated by controlling the beams’ acceleration coefficients. We also demonstrate the self-healing dynamics of these accelerating vector beams for which sections of the vector beam are being blocked by an opaque or polarizing obstacle. Our results indicate that the self-healing process is almost insensitive for the obstacles’ polarization direction. Moreover, the spatial polarization structure also shows self- healing properties, and it is reconstructed as the beam propagates further beyond the perturbation plane. These results open various possibilities for generating, shaping and manipulating the intensity patterns and space variant polarization states of accelerating vector beams.

Propagation properties of Airy-Gaussian vortex beams through the gradient-index medium

Propagation of Airy-Gaussian vortex (AiGV) beams through the gradient-index medium is investigated analytically and numerically with the transfer matrix method. Deriving the analytic expression of the AiGV beams based on the Huygens diffraction integral formula, we obtain the propagate path, intensity and phase distributions, and the Poynting vector of the first- and second-order AiGV beams, which propagate through the paraxial ABCD system. The ballistic trajectory is no longer conventional parabolic but trigonometric shapes in the gradient-index medium. Especially, the AiGV beams represent the singular behavior at the propagation path and the light intensity distribution. The phase distribution and the Poynting vector exhibit in reverse when the AiGV beams through the singularity. As the order increases, the main lobe of the AiGV beams is gradually overlapped by the vortex core. Further, the sidelobe weakens when the AiGV beams propagate nearly to the singularity. Additionally, the figure of the Poynting vector of the AiGV beams proves the direction of energy flow corresponding to the intensity distribution. The vortex of the second-order AiGV beams is larger, and the propagation velocity is faster than that of the first order.

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.

Propagation of sharply autofocused ring Airy Gaussian vortex beams

Controlling the focal length and the intensity of the optical focus in the media is an important task. Here we investigate the propagation properties of the sharply autofocused ring Airy Gaussian vortex beams numerically and some numerical experiments are performed. We introduce the distribution factor b into the initial beams, and discuss the influences for the beams. With controlling the factor b, the beams that tend to a ring Airy vortex beam with the smaller value, or a hollow Gaussian vortex beam with the larger one. By a choice of initial launch condition, we find that the number of topological charge of the incident beams, as well as its size, greatly affect the focal intensity and the focal length of the autofocused ring Airy Gaussian vortex beams. Furthermore, we show that the off-axis autofocused ring Airy Gaussian beams with vortex pairs can be implemented.

Generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases

We propose a novel method for the generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases. In our scheme, the Airy beam is generated by the dynamic phase with a spatial light modulator, and the vortex phase or the vector polarization is modulated by the geometric phase with a dielectric metasurface. The modulation of the geometric phase provides an extra degree of freedom to manipulate the phase and the polarization of Airy beams. This scheme can be extended to generate any other types of optical beams with desirable phase and polarization.

Improved nonparaxial accelerating beams due to additional off-axis spiral phases

An accelerating beam with a Gaussian transverse profile can preserve its shape while propagating along a quarter of a circle. When an off-axis spiral phase is imposed, however, the beam will have an additional acceleration perpendicular to the circle. A two-dimensional accelerating beam is constructed and is found to accelerate along both the x and the y directions, but its transverse intensity profile cannot be maintained well due to the interaction of accelerations along different directions. The intensity profile can be improved by imposing two off-axis spiral phases onto the input beam.

Nonlinear dynamics of Airy-vortex 3D wave packets: emission of vortex light waves

The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Because of the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and nonzero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse.

Beam wander of an Airy beam with a spiral phase

Beam wander of an Airy beam with a spiral phase in turbulence is investigated. Using the Wigner distribution function, analytical expressions for the second-order moments and second central moments of an Airy beam with a spiral phase in turbulence are derived. A general expression of the beam wander for an Airy beam with a spiral phase is obtained. Based on the derived formula, various factors that impact on the beam wander are illustrated numerically. The results show that increasing the topological charge and the characteristic scale, or decreasing the exponential truncation factor, can be used to decrease the beam wander.

Dynamics of three-Airy beams carrying optical vortices

We study numerically and demonstrate experimentally a novel type of singular optical beams formed by the phase imprinting of an optical vortex into the structure of the three-Airy beams. In contrast to a vortex-free product of three Airy beams, in this type of singular-Airy beam, the vortex in the beam axis causes a twist in the beam transverse intensity profile with propagation. Such a new type of singular beams appears especially attractive for applications in optical micromanipulation.

Optical vortex arrays from smectic liquid crystals

We demonstrate large-area, closely-packed optical vortex arrays using self-assembled defects in smectic liquid crystals. Self-assembled smectic liquid crystals in a three-dimensional torus structure are called focal conic domains. Each FCD, having a micro-scale feature size, produces an optical vortex with consistent topological charge of 2. The spiral profile in the interferometry confirms the formation of an optical vortex, which is predicted by Jones matrix calculations.

Polarization-independent electrically tunable/switchable Airy beam based on polymer-stabilized blue phase liquid crystal

Because of their non-diffraction and freely acceleration during propagation, finite energy Airy beams are interesting for application such as optical manipulation, plasma channel generation and optical vortex generation. Especially interesting are tunable/switchable Airy beams, in which the Airy beam tuning by electric field, temperature or optical intensity can be realized. Here we experimentally demonstrate polarization-independent, electrically tunable/switchable Airy beam based on polymer-stabilized blue phase liquid crystals with wide working temperature range and fast response time through a structure called vertical field driven mode.

Dynamic control of collapse in a vortex Airy beam

Here we study systematically the self-focusing dynamics and collapse of vortex Airy optical beams in a Kerr medium. The collapse is suppressed compared to a non-vortex Airy beam in a Kerr medium due to the existence of vortex fields. The locations of collapse depend sensitively on the initial power, vortex order, and modulation parameters. The collapse may occur in a position where the initial field is nearly zero, while no collapse appears in the region where the initial field is mainly distributed. Compared with a non-vortex Airy beam, the collapse of a vortex Airy beam can occur at a position away from the area of the initial field distribution. Our study shows the possibility of controlling and manipulating the collapse, especially the precise position of collapse, by purposely choosing appropriate initial power, vortex order or modulation parameters of a vortex Airy beam.

Propagation of an Airy beam with a spiral phase

The propagation of an Airy beam with a spiral phase is studied. The centroid position and spread of the beam are investigated analytically for different topological charges. Study shows that the centroid position of the Airy beam with a spiral phase keeps moving during propagation. The motion with positive topological charge is in the direction opposite to that with negative topological charge. The speed of the motion of the centroid position is proportional to the topological charge and the normalized distance. From the variation of the second moment of the beam, we can also see that the beam spread is speeded up by the spiral phase during propagation. The speed of the beam spread is proportional to the square of the topological charge.

Propagation dynamics of abruptly autofocusing Airy beams with optical vortices

We investigated the propagation dynamics of the Circular Airy Beams (CAB) with optical vortices (OVs) by numerical calculation. Comparing to the common CAB, the maximum intensity of CAB with vortices can be increased greatly at the focal plane and its focal intensity profile is doughnut-shaped when an on-axis vortex is imposed. The case for an off-axis OV and multiple OVs have been investigated as well. We demonstrate that two opposite OVs will annihilate exactly at the focal plane, with the focal intensity is highly increased.

Airy-related beam generated from flat-topped Gaussian beams

A new kind of Airy-related beam has been obtained from Airy transform for flat-topped Gaussian beams. It is proved in this paper that this beam also possesses an "Airy" profile, quasi-diffraction-free character and transverse accelerating character as the Airy beam generated from the fundamental Gaussian beams. The propagation dynamics of this beam can be modulated by varying N, i.e., the beam order of the flat-topped Gaussian beam.

Abruptly autofocusing vortex beams

We generate abruptly autofocusing beams that produce vortices at the focus. We give explicit equations for the phase-only Fourier masks that generate these beams including explanations for controlling the focal distance and numerical aperture. We show experimental results for the focal distance, the vortex pattern and show that the diameter of the focused beam can be made smaller than the size of a comparable Airy beam from a lens. Finally we show how to move the focus spot in three dimensions by encoding additional optical elements onto the phase pattern.

Propagation properties of an optical vortex carried by an Airy beam: experimental implementation

In this Letter, we experimentally studied the propagation dynamics of Airy beams (AiBs) carrying phase singularity or an optical vortex (OV). A 3/2 phase mask encoded with phase singularity was used to generate AiBs and OVs enjoying precise position alignment and compact optical configuration simultaneously. Experimental results showed that the OV deflection velocity was faster than that of the main lobe of the AiB, agreeing with the analytical prediction. Numerical simulation results are also in agreement with the experimental results. Furthermore, OVs with larger topological charges were also studied experimentally with the same approach.

Symmetry breaking of optical vortices: birth and annihilation of singularities in the evanescent field

The interaction of optical vortices (or phase singularities, or screw dislocations) with ordinary matter is treated with a simple approach. Using the total internal reflection phenomenon and the superposition of four plane waves incident on a material with a refractive index lower than the original propagating medium, we are able to show the birth and annihilation of optical vortices in an evanescent field with curved topological features. Until now, this phenomenon has been explored only in free space propagation. By a suitable tuning process involving the incident angles and the amplitudes of the incident plane waves, it is possible to create unusual topological features of optical vortices in the vicinity of the material. We believe that this work can open new aspects of curved optical vortex manipulation in near-field optics.