Circular Airy Beams Research Articles

Effect of chirped factors on the abrupt autofocusing ability of a chirped circular Airyprime beam.

Recently, a new type of abruptly autofocusing beam called circular Airyprime beam (CAPB) has been reported. Its abrupt autofocusing ability has been proven to be approximately seven times that of a circular Airy beam under the same conditions. Further improving the abrupt autofocusing ability of the CAPB without changing the beam parameters is a concern in optical research. In this study, we investigated the effect of introducing first- and second-order chirped factors on the abrupt autofocusing ability of the CAPB. When the positive first-order chirped factor was below the saturated chirped value, the abrupt autofocusing ability of the chirped CAPB was stronger and the focus position was smaller compared with those of the conventional CAPB. Regarding the abrupt autofocusing ability, there was an optimal value for the first-order chirped factor. At the optimal value, the abrupt autofocusing ability of the chirped CAPB was the strongest. On the other hand, a positive second-order chirped factor promoted the abrupt autofocusing ability of the CAPB and shortened the focus position. The introduction of such value was more effective than the introduction of a positive first-order chirped factor in promoting abrupt autofocusing of the CAPB. The abrupt autofocusing ability of the CAPB was further improved by combining the optimal first-order chirped factor and a positive second-order chirped factor. Finally, the chirped CAPB was experimentally generated, and the corresponding abrupt autofocusing behaviors were measured, validating the theoretical results. Overall, we provide an approach for improving abruptly autofocusing CAPBs.

Flux trajectory analysis of Airy-type beams.

Airy beams are solutions to the paraxial Helmholtz equation known for exhibiting shape invariance along their self-accelerated propagation in free space. These two properties are associated with the fact that they are not square integrable, that is, they carry infinite energy. To circumvent this drawback, families of so-called finite-energy Airy-type beams have been proposed in the literature and, in some cases, also implemented in the laboratory. Here an analysis of the propagation of this type of structured light beam is presented from a flux trajectory perspective with the purpose of better understanding the mechanisms that make infinite and finite energy beams exhibit different behaviors. As is shown, while the foremost part of the beam can be clearly and unambiguously associated with the well-known accelerating term, the rear part of the beam corresponds to a nearly homogeneous distribution of flow trajectories, particularly for long propagation distances. This is shown to be related to an effective transfer of trajectories between adjacent lobes (gradually, from the fore part of the beam to its rear part), which leads to smearing out the transverse flow along the rear part of the beam. This is in sharp contrast to the situation found in ideal Airy beams, where trajectories belonging to a given lobe of the intensity distribution remain the same all along the propagation. The analysis is supplemented with an also trajectory-based description of Young's experiment performed with finite-energy Airy beams to provide a dynamical understanding of the autofocusing phenomenon observed with circular Airy beams.

Multi-focus autofocusing circular hyperbolic umbilic beams.

We propose and demonstrate a type of multi-focus autofocusing beams, circular hyperbolic umbilic beams (CHUBs), based on the double-active variable caustics in catastrophe theory. The mathematical form is more general compared to circular Airy, Pearcey and swallowtail beams. The CHUBs can generate multi-focus at its optical axis, while the on-axis intensity fluctuates up to two orders of magnitude that of the maximum intensity in the initial plane. Using the concept of topographic prominence, we quantify the autofocusing ability. We construct the criteria for selecting the effective foci, and then explore the influence of related parameters. Our findings suggest that the CHUBs could be a suitable tool for multi-particle manipulation, optical tweezers, optical lattices and related applications.

3D optical trapping by a tightly focused circular airy beam

In this Letter, we report on the experimental investigation of three-dimensional (3D) optical trapping by a tightly focused circular Airy beam (CAB). We compare the trapping strength of the beam for 800 nm polystyrene particles, with two equivalent Gaussian beams of the same envelope (SEGB) and the same spot-size (SSGB). Through video microscopy, we found that SEGB is incapable of forming a 3D trap, and particles are pushed along the beam propagation direction, while SSGB and CAB could form stable 3D traps. Measurements of trap stiffness revealed that although both beams have similar lateral trap stiffnesses, interestingly CAB has a 6.6-fold stronger axial trap, owning to its autofocusing nature. Furthermore, we found that trap stiffness at various trapping depths is nearly constant for CAB, in contrast with the Gaussian beam, implying that CAB is robust against spherical aberration.

Generation of elliptical airy vortex beams based on all-dielectric metasurface

Elliptical airy vortex beams (EAVBs) can spontaneously form easily identifiable topological charge focal spots. They are used for topological charge detection of vortex beams because they have the abruptly autofocusing properties of circular airy vortex beams and exhibit unique propagation characteristics. We study the use of the dynamic phase and Pancharatnam–Berry phase principles for generation and modulation of EAVBs by designing complex-amplitude metasurface and phase-only metasurface, at an operating wavelength of 1500 nm. It is found that the focusing pattern of EAVBs in the autofocusing plane splits into |m|+1 tilted bright spots from the original ring, and the tilted direction is related to the sign of the topological charge number m. Due to the advantages of ultra-thin, ultra-light, and small size of the metasurface, our designed metasurface device has potential applications in improving the channel capacity based on orbital angular momentum communication, information coding, and particle capture compared to spatial light modulation systems that generate EAVBs.

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 dynamics of abruptly autofocusing circular Airyprime beam with an optical vortex

Circular Airyprime beam (CAPB) is a new kind of abruptly autofocusing beam introduced recently [Opt. Express, 30, 3804 (2022)], which possesses much stronger autofocusing ability than that of circular Airy beam under the same conditions. In this paper, we investigate the free-space propagation dynamics of such kind of beam embedded with an optical vortex (OV), named circular Airyprime vortex beam (CAPVB) hereafter. The effects of the topological charge and the singularity position of the OV on the abruptly autofocusing ability and the focus position of the CAPVB are examined. Our results reveal that the abruptly autofocusing ability of the CAPVB decreases significantly as the topological charge or the radial position of the OV’s singularity increases, whereas its autofocusing ability keeps invariant against the azimuthal angle of the OV’s singularity if the radial position of the singularity is fixed. In addition, the focus position of the CAPVB elongates with the increase of the topological charge, while this position only has a little changes as the radial position varies. Further, we carry out an experiment for the generation of the CAPVB and demonstrate the autofocusing behaviors experimentally. The experimental results are well consistent with the theoretical results. Although the abruptly autofocusing ability of the CAPVB is weaker than that of the CAPB, the most peculiar properties of the CAPVB is that this beam could produce various special focus intensity patterns by manipulating the topological charge and the singularity position of the OV, and carries the orbital angular momentum, which has promising applications in many fields.

Two dimensional large-scale optical manipulation of microparticles by circular Airy beams with spherical and oblique wavefronts

We experimentally demonstrate that spherical-and-oblique-phase-attached circular Airy beams (SOPA-CAB) can be used to realize the two dimensional large-scale optical manipulation of microparticles. The spherical and oblique phases are attached to CAB based on fourier-space generation method with the assistance of a spatial light modulator (SLM). By changing the hologram coded on the SLM through programming, the autofocusing focus of the SOPA-CAB goes further longitudinally compared with CAB and shifts freely on the focal plane, such that it can drive microparticles to move around on the plane within a maximum diameter of 108 microns.

Circular Airy beam with an arbitrary conical angle beyond the paraxial approximation

An arbitrary conical angle is introduced to the circular Airy beam (CAB) beyond the paraxial approximation, with the possibility to demonstrate its obvious tunability for the propagation properties of the CAB. The expressions are worked out to describe the electric field based on the angular spectrum representation, where a closed-form approximation of the angular spectrum is derived by using the stationary phase method. It is found that the nonparaxiality becomes obvious for large conical angles. In particular, the field intensity at the focal point can be enhanced about 10 times with respect to the conventional CAB by simply tailoring the conical angle. Meanwhile, the longitudinal component of the field is enhanced and gradually plays a leading role as the conical angle is increased. Moreover, the longitudinal gradient of the field intensity is also enlarged for large conical angles, suggesting a stable optical trapping for microparticles, which may find many applications in optical manipulations.

Guiding the optical vortex along predesigned parabolic trajectories from circular symmetric Airy-like beams.

In this paper, by phase-modulating an optical wavefront on circular symmetric Airy vortex beams, we present the circular symmetric Airy-like vortex beams propagating along predesigned parabolic trajectories. Our result shows that we can realize the propagation of an optical vortex with a closed ring lobe along an accelerating parabolic trajectory within a certain propagation distance by using this kind of phase-modulated circular symmetric Airy beam. The vortex that is superimposed on the beams is able to reproduce after being blocked. Additionally, a single twisted dark channel or multiple tornado dark channels with orbital angular momentum rotating along the predesigned parabolic trajectories can also be formed when we impose the off-axis optical vortex on this kind of beam, which has potential in applications of light capturing.

Abruptly autofocusing of generalized circular Airy derivative beams.

In this paper, we introduce a novel kind of abrupt autofocusing beams namely the generalized circular Airy derivative beams (CADBs) as an extension of circular Airy beam (CAB). The propagation dynamics of the CADBs is examined theoretically. Our results show that the CADBs exhibit stronger autofocusing ability than the CAB under the same condition. The physical mechanism of the abruptly autofocusing of the CADBs is interpreted by mimicking the Fresnel zone plate lens. Here, the abruptly autofocusing ability is described by a ratio K = Ifm/I0m where Ifm and I0m correspond to the maximum intensities in the focal and the source planes, respectively. As an example, the K-value of the circular Airyprime beam (CAPB, the first-order Airy derivative beam) is about 7 times of that of the CAB. In addition, the CAPB have narrower FWHM (full width at half maxima) in the focus position than the CAB, and the focal spot size of the CAPB is smaller than that of the CAB. Furthermore, we establish an optical system involving a phase-only spatial light modulator to generate the CAPB and measure its autofocusing characteristics experimentally. The measured K-value is about 9.4 percentage error between theory and experiment owing to the imperfection generation of the CAPB. The proposed generalized CADBs will find applications in biomedical treatment, optical manipulation and so on.

The tailoring effect of two symmetrically distributed vortices on circular Airy beam

We investigate the tailoring effect of the point vortices on the foci of the circular Airy vortex beam (CAVB). Two optical vortices (OVs) with same or opposite topological charges (TCs) are symmetrically loaded on the beam. It is found that the loading distance between these two OVs (denoted as dv) can significantly tailor the auto-focusing behaviour of the beam. For two OVs with same TCs, as dv increases from 0 to infinite, the intensity pattern at the focal plane changes from a ring to a bright spot. For opposite OVs, when dv is near 0 or very large, there is a bright foci. But within a certain range, two foci are generated at the focal plane. Good agreements have been achieved between simulations and experiments. We qualitatively explain the tailoring phenomena from the perspective of the inward energy flow of the main ring of CAVB and the interaction between two OVs. The tailoring effect of dv of the two OVs on the focal pattern may have potential applications in micromanipulation, communication and other fields.

Propagation properties of circularly symmetric Airy beam modulated by spectral asymmetric envelope

An asymmetric envelope function for modulating the spectrum of circular Airy beam is proposed in this work. The propagation properties of the modified circular Airy beam are investigated in both theory and experiment. The three parameters of the asymmetric hyperbolic secant function can be used to adjust the ratio of the high frequency components to the low frequency components in Fourier space, and thus tuning the propagation properties of this modified circular Airy beam. The results demonstrate that the focal position is affected mainly by the high frequency components. The maximum focal intensity will not be enhanced continuously by increasing the proportion of the high frequency components. It depends on the ratio of the high frequency components to the low frequency components when the center frequency is determined. Therefore, using an asymmetric envelope in Fourier space is much more reasonable than using the high pass filtering or symmetric Gaussian envelope. The FWHM decreases significantly with the increase of center frequency. When the parameters are chosen appropriately, the size of focal spot will be reduced significantly, the maximum focal intensity, especially the abruptly autofocusing property will be enhanced greatly and the focal position can remain almost the same as the focal position of the common circular Airy beam. The maximum focal intensity of the proposed beam is 3.4 times that of the common circular Airy beam and the abruptly autofocusing property of the proposed beam is much better than that of the beam using the symmetric Gaussian envelope. The phase-only encoding method in Fourier space is used to generate the proposed beam in experiment. The experimental results are in reasonable agreement with the simulation results. It indicates that the modified beam can be generated conveniently by using the same method as that used to generate the common circular Airy beam.

Propagation dynamics of the circular Airy Gaussian vortex beams with different polarization in the parabolic potential

A new kind of open-end optical bottle formed by launching the circular Airy Gaussian vortex beams (CAGVBs) in the parabolic potential is demonstrated. Compared to the circular Airy beams, the CAGVBs in the parabolic potential still maintain abruptly auto-focusing property, but their focus spot is hollow. The focal intensity and the focal position can be adjusted by choosing different scaling factor, topological charge and potential depth. What's more, a closed-end or open-end optical bottle can be obtained by imposing two off-axis optical vortices rotating in the opposite or the same direction on the circular Airy Gaussian beams, respectively. Besides, when imposing one vortex in the radially and azimuthally polarized circular Airy Gaussian beams (RPCAGBs and APCAGBs), the topological charge of the vortices of the RPCAGBs and APCAGBs will affect the open state of RPCAGBs and APCAGBs.

The abruptly auto-braiding property of the Bessel beam superimposed with circular Airy beam

We propose and investigate a novel laser beam based on the superposition of circular Airy beam and l-order Bessel beam, which can abruptly braid during the freely propagation. This abruptly auto-braiding beam (AABB) combines the spiral structure and ring shape in one laser beam. The propagation characteristics of AABB is studied, including the effect of the propagation angle and topological charge on the transmission. Depending on the parameters, this beam exhibits the strong spiral characteristic within a certain distance. AABB generated in the experiment has a good agreement with the simulation.

Vortex phase-induced properties of a partially coherent radially polarized circular Airy beam

In this paper, partially coherent radially polarized vortex circular Airy beams (PCRPVCABs) are theoretically and experimentally studied for the first time. Comparing with partially coherent radially polarized circular Airy beam, the autofocusing ability of PCRPVCAB can be controlled or even enhanced by the topological charge of the vortex phase. Besides, we show a unique distribution of the degree of polarization, vortex-phase induced polarization transition, and the phenomenon of beam spot rotation after the PCRPVCAB passing through a polarizer. Our results make the PCRPVCAB a good candidate for optical micro-manipulation, free-space communications, formation of disordered optical lattices, etc.

Dual autofocusing circular Airy beams with different initial launch angles

Dual autofocusing circular Airy beams (CAB) are proposed by introducing two different initial launch angles into the phase of light fields. Appropriate values of two launch angle parameters are chosen to enhance dual focusing property and reduce the interference effect. The relation between this dual autofocusing property and corresponding parameters are investigated. Our theoretical results show that, launch angle and initial radius of this beam have much influence on dual focal positions; decaying parameter and angle range parameter could only influence the focal intensities or relative intensity. Finally, dual autofocusing CAB is generated and the dual focusing property is demonstrated in experiment.

Bessel-modulated autofocusing beams for optimal trapping implementation

Abruptly autofocusing beams were proposed and tested for a variety of applications such as optical manipulation, yet their trapping performance associated with the optical forces and trap stiffness remains largely unexplored. In this work, we design and demonstrate specially modulated autofocusing beams. We theoretically and experimentally show improved properties of such beams and their trapping capabilities as compared to their unmodulated counterparts. In particular, an autofocusing beam tailored with a Bessel function exhibits a shorter focal length and a much stronger peak intensity than that of an unmodulated circular Airy beam. Moreover, we perform optical tweezer experiments using both the modulated and unmodulated autofocusing beams to trap microbeads and red blood cells for direct comparison, and find that the Bessel-modulated beam displays an enhanced trapping capability, thanks to a stronger optical trapping force due to its peculiar intensity landscape. Compared with the conventional circular Airy beams, optical tweezers based on our modulated autofocusing beams exhibit a superior performance, which may lead to new photonic tools for optical trapping and manipulation.

Dynamical power flow and trapping-force properties of two-dimensional Airy-beam superpositions

Abruptly autofocusing beams have attracted more and more attention because of their potential applications in optical manipulation. Here, we not only experimentally and theoretically investigate dynamical propagation properties of two-dimensional (2D) Airy--beam superpositions in free space and disordered media, but also study their stability, dynamical power flow, and trapping force properties from a different point. 2D Airy-beam superpositions have superior stability and can easily control their autofocusing propagations and trapping forces through a changing number of superimposing beams, truncated factor, scale factor, initial position, and the angle between two wings of 2D Airy beams. Based on the analysis of the evolution of power flow and trapping force, it is demonstrated that 2D Airy-beam superpositions repeat many autofocusing propagations, leading to a series of focuses and stable trapping positions to appear in propagation. Compared to traditional autofocusing beams, i.e., circular Airy beams and one-dimensional Airy-beam superpositions, 2D Airy-beam superpositions can show a better optical trapping performance in theory. Moreover, we used 2D Airy-beam superpositions as an optical tweezer to trap particles in the experiment and quantitatively analyzed trapping force properties such as trap stiffness via the power spectra method. The experimental results further demonstrate that 2D Airy-beam superposition can show better optical trapping ability than the circular Airy beam. Our work provides a systematic understanding of the propagation and trapping properties of 2D Airy-beam superpositions in theory and experiment. It is helpful for the further applications of autofocusing beams on the optical tweezer, especially in biomedical research.

Dual-plane multiple-trapping by tightly focused petal-like circular Airy beam in an aqueous medium

Superposition of two circular Airy vortex beams (CAVB), with opposite sign topological charges (l), produces a new type of petal beam called petal-like circular Airy beam (PCAB) with a transverse field distribution in the form of azimuthally modulated concentric rings that follow Airy function over the radial distance on a transverse plane. In this paper, tight focusing of a truncated PCAB and its application in optical trapping is numerically investigated. It is shown that by adjusting the topological charge, l, and the aperture radius of the focusing objective lens, R, four different trapping configurations can be achieved: a single transverse trap at a single axial position, a multi-trap geometry at a single axial position, two single transverse traps at two positions along the axial direction, and two multi-trap geometries at two different axial positions. It is also shown that the number of trapped particles in the multi-trap configurations is 2l per focal plane, while the number of axial trap positions is determined by the truncation aperture size, R. Moreover, trap stiffnesses and corresponding potential energies for the trapping configurations are presented and discussed. Finally, for a special case of large R and l, it is shown that the focused beam may both guide and traps the particles.