Symmetric Airy beams

Accelerating quad Airy beams-based point response for interferenceless coded aperture correlation holography

Interferenceless-coded aperture correlation holography (I-COACH) is a promising single-shot 3D imaging method in which a coded phase mask (CPM) is used to encode 3D information about an object into an intensity distribution. However, conventional CPM encoding methods usually lead to intensity dilution, especially in the recording of point spread holograms (PSHs), resulting in low-resolution reconstruction of I-COACH. Here, we propose accelerating quad Airy beams with four mainlobes as a point response to enable weak diffraction propagation and a sharp maximum intensity in the transverse direction. Moreover, the four mainlobes exhibit lateral acceleration in 3D space, so the PSHs in different axial positions show a unique and concentrated intensity distribution on the image sensor, thereby realizing a high-resolution reconstruction of I-COACH. Compared with conventional CPM encoding methods, the proposed accelerating quad Airy-beam-encoding method has superior performance in improving the resolution of I-COACH reconstruction even in the presence of external interference.

Realization of a circularly transformed Airyprime beam with powerful autofocusing ability

The reported autofocusing ability of a ring Airyprime beam array reaches up to 8632.40, while the strongest autofocusing ability of a circular Airyprime beam (CAPB) is only 1822.49. How can the autofocusing ability of a single beam reach the autofocusing ability of a beam array? To achieve this goal, a circularly transformed Airyprime beam (CTAPB) is introduced by following two steps. First, a circular equation transformation on the two transverse coordinates in the electric field expression of a propagating Airyprime beam is performed. Then, the electric field expression of a propagating Airyprime beam is integrated over the angle. The intensity profile of a CTAPB on the initial plane changes significantly with varying the primary ring radius r0. With increasing r0, therefore, the autofocusing ability of a CTAPB undergoes a process of first increasing and then decreasing, while the focal length always increases. A CTAPB exhibits more powerful autofocusing ability than a CAPB. The maximum autofocusing ability of a CTAPB can reach up to 8634.76, which is 4.74 times that of a CAPB, while the corresponding focal length is 95.11% of a CAPB. A CTAPB on the initial plane can be approximately characterized by a ring Airyprime beam array with sufficient number of Airyprime beams. Due to the better symmetry, a CTAPB has a slightly stronger autofocusing ability than a ring Airyprime beam array and almost the same focal length as a ring Airyprime beam array. The CTAPB is also experimentally generated, and the experimental results indicate that the CTAPB has powerful autofocusing ability. As a replacement of a CAPB and a ring Airyprime beam array, this introduced CTAPB can be applied to the scenes which involve abruptly autofocusing effect.

Hybrid cubic-chessboard metasurfaces for wideband angle-independent diffusive scattering and enhanced stealth

Because of the shortcomings associated with their scattering patterns, both the chessboard and cubic phased metasurfaces show non-perfect diffusion and hence sub-optimal radar cross section reduction (RCSR) properties. This paper presents a novel and powerful hybrid RCSR design approach for diffusive scattering by combining the unique attributes of cubic phase and chessboard phase profiles. The hybrid phase distribution is achieved by simultaneously imposing two distinct phase profiles (chessboard and cubic) on the hybrid metasurface area with the aid of geometric phase theory to further enhance the diffusive scattering and RCSR. It is shown in this paper that through the integration of cubic and chessboard phase profiles, a metasurface with the hybrid phase mask successfully overcomes all the above issues and shortcomings related to the RCSR of both chessboard and cubic metasurfaces. In addition, the proposed design leverages the unique scattering properties offered by these distinct phase profiles to achieve enhanced stealth capabilities over wide frequency ranges and for large incidence angles. Simulation and measurement results show that the designed hybrid metasurfaces using the proposed strategy achieved RCSR and low-level diffused scattering patterns from 12-28 GHz (80%) for normal incidence of a far-field CP radar plane wave. The hybrid metasurface shows a stable angular diffusion and RCSR performance when the azimuthal and elevation incidence angles are in the range of 0° → ± 75° which is wider than other designs in the literature. Therefore, this work can make objects significantly less detectable in complex radar environments when enhanced stealth is required.

Image transmission with a circular Airy array beam

A circular Airy array beam (CAAB) comprising four symmetric circular Airy beams is proposed and demonstrated for image transmission. It is generated by the Fourier transform of the combined phase, which contains the radial cubic phase, the diffractive axicon phase, and the shift function phase. Two adjustable parameters of the combined phase can control the radius and the initial position of each circular Airy beam at the spatial plane. The image can be modulated into the CAAB through overlapping it at the Fourier plane of this beam and recovered by Fourier transform after diffracting a certain distance. It can be observed clearly that the CAAB after being partly blocked by a movable obstacle guarantees the recovery of the image. In comparison with the existing right-angle Airy array beam, the image transmission by the proposed CAAB is less sensitive to the position of the obstacles on the beam path.

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.

Dependence of autofocusing ability of a ring Airyprime beams array on the number of beamlets

A ring Airyprime beams (RAPB) array, which consists of N evenly displaced Airyprime beamlets in the initial plane, is first introduced, to the best of our knowledge, in this Letter. Here, we focus on the effect of the number of beamlets N on the autofocusing ability of the RAPB array. With the given beam parameters, an optimal number of beamlets, which is the minimum number of beamlets to realize the saturated autofocusing ability, is selected. The focal spot size of the RAPB array remains unchanged before the number of beamlets reaches the optimal number of beamlets. More importantly, the saturated autofocusing ability of the RAPB array is stronger than that of the corresponding circular Airyprime beam. The physical mechanism of the saturated autofocusing ability of the RAPB array is interpreted by simulating the Fresnel zone plate lens. The influence of the number of beamlets on the autofocusing ability of the ring Airy beams (RAB) array under the same beam parameters with the RAPB array is also presented for comparison. Our findings are beneficial for the design and application of the ring beams array.

Generation and control of tornado waves by means of ring swallowtail vortex beams

Tornado waves (ToWs), which refer to a light that accelerates and twists over both the radial and the angular directions, have gained a great deal of interest since the concept was introduced by Brimis et al [Opt. Lett.45, 280 (2020)10.1364/OL.45.000280]. In this paper, we superimpose two pairs of ring swallowtail vortex beams (RSVBs) to generate ToWs and we call them tornado swallowtail waves (ToSWs). Each pair consists of RSVBs while carrying orbital angular momentum of opposite helicity and slightly different with the radius of the main ring of RSVBs. The waves spiral forward and reveal intensity maxima, exhibiting a tornado-like intensity profile during propagation. Meanwhile, the angular acceleration of the ToSWs is illustrated via tracing the angular position of the high-intensity main lobes. It is found that ToSWs present very high values of angular acceleration. Compared with typical tornado waves, ToSWs are more diverse and tunable, giving a new degree of freedom to tailor the propagation dynamics due to the flexibility of the swallowtail diffraction catastrophe. In addition, we confirm such waves experimentally and the results match well with the numerical ones. Also, we demonstrate the ability of optical manipulation of ToSWs for the first time in that they allow for particles not only to be trapped but also to be rotated. Finally, we analyze the poynting vectors and power exchange of ToSWs to demonstrate convincingly the physical mechanism.

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.

Shaping autofocusing Airy beams through the modification of Fourier spectrum

A new type of Airy beam arisen from the modification of Fourier spectrum is introduced numerically and experimentally. The autofocusing Airy beam (AAB) exhibits the features of off-axis autofocusing and transverse self-accelerating, producing a needle-like focus in the longitudinal direction and a tiny focal spot at the focusing plane. Furthermore, the focusing properties such as focusing position, focal spot size, focusing intensity and depth of focus can be adjusted by modulating parameters of the AAB. Experimental demonstrations of particle trapping and manipulation with the AAB are also presented. The number of trapped particles can be controlled by changing the focal spot size at the autofocusing plane. Our results offer practical applications in particle manipulation, fluorescent imaging technology, laser spectroscopy and so on.

Experimental visualization of various cross sections through a butterfly caustic

Optical caustics and wavefronts of butterfly beams (BBs) derived by using a catastrophe theory determined by potential functions depending on the state and control variables are reported. Due to the high dimensionality for the control variables, BBs can be manipulated into various optical light structures. It is also demonstrated that these curious beams have relatively simple Fourier spectra that can be described as polynomials, and another way to generate BBs from the Fourier spectrum's perspective is provided. The dynamics for BBs are investigated by potential functions. Our experimental results agree well with the theoretical predictions. In addition to micro-manipulation and machining, these novel, to the best of our knowledge, caustic beams will pave the way for creating waveguide structures since they display high-intensity formations that evolve along curved trajectories.

Mirror and Circular Symmetry of Autofocusing Beams

This article demonstrates the crucial importance of the symmetrization method for the formation of autofocusing beams. It is possible to impart autofocusing properties to rather arbitrary distributions, for example, truncated and inverted classical modes (such as Hermite–Gaussian, Laguerre–Gaussian, and Bessel modes) or shift the fundamental Gaussian beam by inserting mirror or circular symmetry. The most convenient for controlling autofocusing characteristics is the truncated sinus function with a power-law argument dependence. In this case, superlinear chirp beams (with power q > 2) exhibit sudden and more abrupt autofocusing than sublinear chirp beams (with power 1 < q < 2). Comparison of the different beams’ propagation is performed using fractional Fourier transform, which allows obtaining the field distribution in any paraxial region (both in the Fresnel and Fraunhofer diffraction regions). The obtained results expand the capabilities of structured beams in various applications in optics and photonics.

Generation of Talbot-like fields

We present an integral of diffraction based on particular eigenfunctions of the Laplacian in two dimensions. We show how to propagate some fields, in particular a Bessel field, a superposition of Airy beams, both over the square root of the radial coordinate, and show how to construct a field that reproduces itself periodically in propagation, i.e., a field that renders the Talbot effect. Additionally, it is shown that the superposition of Airy beams produces self-focusing.

Propagation dynamics of the odd-Pearcey Gaussian beam in a parabolic potential

In this paper, the propagation properties of the odd-Pearcey Gaussian beam (OPGB) in a parabolic potential are investigated analytically and numerically. Except for the auto-focusing at the focal plane, the OPGB performs a weak off-axis focusing unexpectedly. The focusing distance and the focal intensity can be adjusted by choosing an appropriate parabolic parameter. Also, the Poynting vector of the OPGB is demonstrated. In addition, we investigate the radiation forces of the OPGB and find that the trapping points can be generated during propagation.

Image transmission using Airy array beam

An approach for image transmission based on the Airy array beam is proposed and demonstrated. The Airy array beam is generated by employing the product of a special cubic phase and a shift function at its Fourier plane. The image can be modulated into this Airy array beam by overlapping it at the Fourier plane of this beam. After passing through a certain distance, the image information can be recovered from the modulated Airy array beam by Fourier transform. Compared to the existing Airy array beam, higher integrity and image information quality can be achieved by increasing the width of the obstacle that blocks the propagation of these beams. The capability mentioned above is experimentally verified. Moreover, to research the diffraction of this Airy array beam in the scattering environment, the propagation process of this Airy array beam in a scattering medium is theoretically derived and numerically studied. The corresponding experiment demonstrates that the propagation process matches well with the numerical study and simulation.

Morphologies of caustics and dislocation lines: some clues about their interrelation

According to singular optics, the phase and intensity that characterize structured electromagnetic beams can be understood in terms of concepts that involve subspaces where they or their derivatives exhibit a particular behavior, such as giving rise to extreme values or not being well defined. Caustics are a paradigmatic example of the former, while helical dislocation lines exemplify the latter. In this work the interrelation of the morphology of caustics and the morphology of dislocation lines is theoretically studied. The analysis for highly structured beams requires an efficient methodology that allows the identification of optical vortices, their topological charge, and the helical dislocation lines they belong to. Such a methodology is introduced and applied to paraxial elliptic umbilic beams and nonparaxial Airy symmetric three-dimensional beams. Nonparaxial beams exhibit caustic surfaces that delimit regions with a finite volume and different intensity average. It is shown that in the high intensity region so defined, the dislocation lines play the role of an internal skeleton, i.e., an endoskeleton, of the beam. The exoskeleton created in the low intensity regions shows subtle and interesting features that complement those of the endoskeleton; the caustics that delimit low intensity regions have a strong influence on the morphology of the exoskeleton.

Symmetric Pearcey Gaussian beams

In this Letter, a new, to the best of our knowledge, type of autofocusing and symmetric beam arisen from two quartic spectral phases is introduced in theory and experiment. The symmetric Pearcey Gaussian beam (SPGB), formed with a Gaussian term and two multiplying Pearcey integrals, processes a focusing intensity approximately 1.32 times stronger than the intensity of the symmetric Airy beam. Its four off-axis main lobes split into four bending trajectories symmetrically after focusing. The rectangular intensity distribution and the focal length of the SPGB can be adjusted by two kinds of distribution factors. Additionally, the vortex-guiding property of the beam is demonstrated by embedding an off-axis vortex into the SPGB, which can be applied in particle guiding.

Airy beam propagation: autofocusing, quasi-adiffractional propagation, and self-healing

We study the propagation of superpositions of Airy beams and show that, by adequately choosing the parameters in the superposition, effects as opposite as autofocusing and quasi-adiffractional propagation may be obtained. We also give a simple analytical expression for free propagation of any initial field, based on so-called number states (eigenstates of the quantum harmonic oscillator), that allows us to study their self-healing properties.

Generation of Complex Transverse Energy Flow Distributions with Autofocusing Optical Vortex Beams

Optical vortex (OV) beams are widely used for the generation of light fields with transverse energy flow inducing orbital motion of the nano- and microparticles in the transverse plane. Here, we present some new modifications of OV beams with autofocusing properties for shaping complex transverse energy flow distributions varying in space. The angular component of the complex amplitude of these beams is defined by the superpositions of OV beams with different topological charges. The proposed approach provides a convenient method to control the three-dimensional structure of the generated autofocusing OV beams. The control of the transverse distribution of an autofocusing beam provides a wide variety of generated fields with both rotating and periodic properties, which can be used in the field of laser manipulation and laser material processing. Thus, the obtained numerical results predict different types of motion of the trapped particles for the designed OV autofocusing beams. The experimental results agree with modeling results and demonstrate the principal possibility to shape such laser beams using spatial light modulators.

Swallowtail-type diffraction catastrophe beams

We demonstrate a universal approach for generating high-order diffraction catastrophe beams, specifically for Swallowtail-type beams (abbreviated as Swallowtail beams), using diffraction catastrophe theory that was defined by potential functions depending on the control and state parameters. The three-dimensional curved caustic surfaces of these Swallowtail catastrophe beams are derived by the potential functions. Such beams are generated by mapping the cross sections of the high-order control parameter space to the corresponding transverse plane. Owing to the flexibility of the high-order diffraction catastrophe, these Swallowtail beams can be tuned to a diverse range of optical light structures. Owing to the similarity in their frequency spectra, we found that the Swallowtail beams change into low-order Pearcey beams under given conditions during propagation. Our experimental results are in close agreement with our simulated results. Such fantastic catastrophe beams that can propagate along curved trajectories are likely to give rise to new applications in micromachining and optical manipulation, furthermore, these diverse caustic beams will pave the way for the tailoring of arbitrarily accelerating caustic beams.

Symmetric accelerating beam generation via all-dielectric metasurfaces

Traditionally, symmetric accelerating beam (SAB) generation requires bulky optical components, which hinder the miniaturization of optical systems. Recently, metasurfaces, which are composed of sub-wavelength features, have provided a captivating boulevard for the realization of ultra-thin and flat optical devices. Therefore, for the first time, we design and simulate all-dielectric metasurfaces based on an optical caustic approach to generate highly efficient SABs by tailoring the phase of an incident wave. The designed metasurface utilizes spatial distribution of optimized Nb₂O₅ nano-rods on SiO₂ substrate to perform the phase modulation. In contrast with conventional accelerating beams, the generated SABs can follow any predefined propagation trajectory with unique features, such as symmetric intensity profile, autofocusing, and thin needle-like structure in their intensity profile. In addition to this, these beams have also shown the ability to avoid obstacles, placed in the direction of propagation of main lobes. We believe that these beams can be useful in applications, including Raman spectroscopy and fluorescent imaging, and multiparticle manipulation.

Multioptical bottles from second-order chirped symmetric Airy vortex beams

In this Letter, we introduce a new, to the best of our knowledge, structure of multioptical bottles formed by second-order chirped symmetric Airy vortex beams (CSAVBs). The numbers and the locations of the optical bottles embedded in the CSAVBs depend on the numbers and the locations of the vortices. Besides, the lengths and the sizes of the optical bottles could be adjusted by changing the chirp parameter and the topological charges of the vortices, respectively. We believe that our results can diversify the optical tweezers system for multiparticle manipulation.

Auto-focusing and self-healing of symmetric odd-Pearcey Gauss beams

In this study, a new, to the best of our knowledge, form of odd-Pearcey Gauss beams with peculiar characteristics is presented. Compared with the Pearcey beam, the odd-Pearcey Gauss beam is symmetrical about the origin. At the initial stages, the odd-Pearcey Gauss beam propagates with a main central lobe and some residual spots that autofocus to the center, and then splits into two off-axis parabolic lobes after the autofocus finishes. Furthermore, we also introduce the soft well function to investigate the propagation profiles of the odd-Pearcey Gauss beams passing through it with different calibers and discuss the influence of the Gaussian waist width towards the focal distance and the propagation form of the odd-Pearcey Gauss beam. We also enumerate some potential and possible applications based on its peculiar characteristics.

Radially polarized symmetric Airy beam

In this Letter, we introduce a new kind of radially polarized beam called the radially polarized symmetric Airy beam (RPSAB). Compared to the linearly polarized symmetric Airy beam (SAB), the hollow focus spot of RPSAB enables it to trap a microparticle whose refractive index is lower than that of the surrounding medium, and the focus intensity of RPSAB is nearly three times higher than that of SAB under the same conditions. Also, we present the on-axis and off-axis radially polarized symmetric Airy vortex beam (RPSAVB). In the on-axis case, we find the maximum intensity of RPSAVB is about two times higher than that of RPSAB. For the off-axis case, we prove that slight misalignment of the vortex and RPSAB enables guiding the vortex into one of the self-accelerating channels, the same as the symmetric Airy vortex beam. Our results may expand the applications of RPSAB in laser cutting, metal processing, nanofocusing, and three-dimensional trapping of metallic Rayleigh particles.

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 of Cosh-Airy and Cos-Airy Beams in Parabolic Potential

The analytical expressions of one-dimensional cosh-Airy and cos-Airy beams in the parabolic potential are derived in the general and the phase transition points. The expression in the phase transition point shows a symmetric Gaussian intensity profile and is independent of any Airy features, which is completely different from that in the general point. The intensity, the center of gravity, and the effective beam size of the cosh-Airy and cos-Airy beams in the parabolic potential are periodic and have the same period. The effects of the transverse displacement, the cosh factor, and the cosine factor on these periodic behaviors are also investigated. The direction of self-acceleration reverses every half-period. The phase transition point is also the inversion point of the intensity distribution, which indicates that the intensity distributions before and after the phase transition point are mirror symmetrical. The periodic behaviors of the normalized intensity, the center of gravity, and the effective beam size of the cosh-Airy and cos-Airy beams in the parabolic potential are attractive and well displayed. The results obtained here may have potential applications in particle manipulation, signal processing, and so on.

High-intensity and low-divergence THz laser with 1D autofocusing symmetric Airy beams

Single-mode THz quantum-cascade lasers (QCLs) have been realized using a wide variety of techniques to obtain a combination of large power output, good beam quality with single-lobed beams, and low far-field divergence. Beam shaping using external components has not been previously exploited due to limited commercial availability of THz optical components and also the accompanying large loss from most THz optical materials. Here, we demonstrate that excellent beam characteristics could be obtained for a THz QCL by integration of a surface-emitting distributed-feedback (DFB) QCL with a simple lens within the vacuum chamber of a cryocooler. Plano-convex lenses are made from inexpensive plastic balls and integrated in proximity with a 3.4 THz DFB QCL. With appropriately chosen lens parameters, dual-lobed Airy beams are generated that autofocus into a high-intensity single-lobed beam with large focusing efficiency. A simple and general method to generate one-dimensional autofocusing Airy beams is thus demonstrated that is applicable at any wavelength. THz laser beams with high peak intensity (57 mW/mm² in a spot-size of 1 mm²) or low-divergence (1.4^∘×1.8^∘ for a beam with 118 mW peak power) are realized at 62 K in a compact electrically operated Stirling cooler. A high brightness of 5.4×10⁶ Wsr ^-1m ^-2 is estimated for the focused beams by measuring the beam propagation ratios (M ² parameters).

Abruptly autofocusing beams from phase perturbations having forced symmetry

A controllable manipulation of the energy distribution of caustic beams possessing rectangular symmetry is presented. The beams are designed from the spectral phase by adding a linear and/or quadratic perturbation having forced symmetry. This approach breaks the overall caustic structure into branches, allowing a fully controllable displacement of each branch. The caustic breaking leads to peculiar propagation configurations for rectangular beams. Among them, we highlight the abruptly autofocusing beam, which until now was exclusively associated to caustic beams with circular symmetry. Thereby, the abruptly autofocusing effect can be yielded for one-dimensional light sheets, contrary to what happens for circularly symmetric beams. The theoretical predictions are supported by experiments. Besides, the focus width of such rectangular beams can be reduced beyond the standard diffraction limit.

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.

Generation of spirally accelerating optical beams

We developed a generalized spectral phase superposition approach for generating accelerating optical beams along arbitrary trajectories. Such beams can be customized by predefining an appropriate superimposed phase pattern that consists of multiple sub-phases. We generated a spirally accelerating beam in a three-dimensional space and developed an algorithm to improve the uniformity of the intensity along the trajectory by introducing phase-shift factors. We also experimentally verified our numerical simulations. The proposed approach breaks the conventional convex trajectory restrictions. These various accelerating beams would pave the way for optically moving particles along a desired trajectory. The generation of such arbitrary accelerating beams is likely to give rise to new applications in flexible optical manipulation, wave front control, and optical transportation and guidance of particles.

Polarization transitions in the focus of radial-variant vector circular Airy beams

We propose a new kind of light beam with both autofocusing ability and radial-variant distribution of polarization states, named radial-variant vector circular Airy beam (RVCAB). The polarization transitions in the focus of RVCABs are simulated based on vectorial angular spectrum formalism and theoretically explained by Stokes parameters. Our results reveal the dependence of the pure polarization state near the focus on the distribution of polarization states in the initial plane, which may lead to manipulation of the polarization state near the focus via controlling the distribution of polarization states in the initial plane.

Propagation trajectory measurement and autofocusing generation of Airy beams using digital propagation

We present a method of measuring the propagation trajectory of Airy beams using digital propagation based on the theory of angular spectrum. The dependence of the transverse displacement of Airy beams on artificial propagation distance in phase masks is investigated with no motion of imaging apparatus. The parabolic propagation trajectory is experimentally verified, which is consistent with theoretical predictions. On this basis, we generate autofocusing beams by combining multiple Airy beams and digital propagation. Results show that this technique can provide accurate and easy measurement of the self-accelerating characteristic in a fixed plane, as well as flexible manipulation without translating the target.

Propagation characteristics of partially coherent circular Airy beams

The abruptly autofocusing properties of partially coherent circular Airy beam (CAB) with different spatial coherent length are theoretically investigated in this paper. It is found that, as spatial coherent length decreases, the size of the focal spot would increase and the focal intensity would decrease. But the abruptly autofocusing property for partially coherent CAB is still quite obvious, when comparing with the common partially coherent Gaussian beam under the same conditions; and its autofocusing position is less easily influenced by coherence. The influences of initial radius r₀ and decaying parameter a on the autofocusing property have also been investigated in the end.

Nonsymmetric curved beams within a symmetric caustic skeleton

Nonsymmetric curved beams having a symmetric caustic skeleton are presented. They arise from a finite jump in the symmetric spectral phase that breaks the symmetry of the beam intensity without altering its associated caustic curve. These nonsymmetric beams can be represented as a superposition of two caustic beams whose wave fields have well-defined even and odd symmetries with weight coefficients dependent on the phase jump. In this approach, the phase jump acts as a measure of the beam asymmetry degree that can be easily controlled in experiments. This scheme is a promising step towards optical cryptography and quantum optics applications.

Conventional volume holography for unconventional Airy beam shapes

Utilizing multiplexed volume holography, a single optical element, enabling to shape structural variants of non-diffracting Airy wavefronts, from one-dimensional Airy mode to unconventional Airy modes such as vortex Airy and quad Airy modes, has been experimentally realized. Here, beam shaped angularly multiplexed volume holographic gratings (AMVHGs) are recorded in PQ: PMMA photopolymer, where five different spatial wavefronts of Airy beams have been sequentially recorded, for simultaneous reconstruction of different Airy modes, by a conventional Gaussian beam. Spatial and spectral mode selective properties of AMVHGs are demonstrated by narrow-band as well as by broadband light source. In addition, through wavelength degeneracy property, the maximum sensitivity wavelength of blue (488 nm) is used for recording in PQ: PMMA, but the AMVHGs are operated at a broad wavelength band of interest, all the way to longer wavelength in near infrared (850 nm). The K-sphere representation is used to explain the spectral properties of AMVHGs.

Elliptical Airy beam

We found a new type of noncircular symmetrical Airy beam called an elliptical Airy beam (EAB). Using a simple single-pixel checkerboard hologram method, we achieved the EAB in an experiment. We observed its unique property of double focusing and the ability of the energy to flow towards the endpoints of the long axis during propagation. These particular properties will have some potential applications.

Abruptly autofocusing property of circular Airy vortex beams with different initial launch angles

Controlling the trajectory of circular Airy beams (CABs) by negative launch angles would greatly reduce their abruptly autofocusing property. By numerically simulating the propagation of a circular Airy vortex beam with different initial launch angles, we demonstrate in this paper that a larger topological charge of optical vortex (OV) is quite helpful to enhance the abruptly autofocusing property under different launch angles (especially for negative launch angles), without affecting the focal position and trajectory. Two opposite OVs would attract each other and partially overlap in the focal plane of CAB under different launch angles, causing even stronger autofocusing. As the distance between two OVs increases, the focal intensity contrast would decrease, especially for a beam with positive launch angles, whose autofocusing property decreases much more quickly with the distance.

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.

Propagation dynamics of partially coherent crescent-like optical beams in free space and turbulent atmosphere

We introduce theoretically and realize experimentally a class of random, wide-sense stationary optical beams with uniform correlations which, on propagation in free space, produce a crescent-like intensity distribution with the maximum at an off-axis position. The crescent's position of maximum intensity accelerates transversally at intermediate distances, and then exhibits a constant lateral shift further from the axis in the far zone of the source. We also show that on propagation in the isotropic turbulent atmosphere, the crescent beam shifts away from the axis as well, but slower than in free space, with rate depending on the strength of turbulence. These results are of importance for optical systems operating through long-range turbulent channels in which a beam must have a range-dependent tilt, e.g. on travelling around an obstacle.

Caustic beams from unusual powers of the spectral phase

Caustic optical beams arising from a spectral phase whose power lies in an unusual range of values less than two are presented. Unlike what happens for conventional phase powers greater than two, it is feasible to generate caustic structures having properties that do not follow the established sorting. For instance, an asymptotic cusp caustic beam having a cusp point at infinity is demonstrated. For the sake of completeness, the caustic beam properties are analyzed within the whole real range of the phase power. Accurate behavior rules between the symmetries of the beam spectral phase and its intensity distribution are found. These findings strengthen the fundamentals and engineering on caustic beams in diverse optical and physical branches.

Multifocus autofocusing Airy beam

We propose a multifocus autofocusing Airy beam (MAAB) by modifying the frequency spectrum of a symmetric Airy beam (SAB) with a Gaussian band elimination filter. Unlike the original SAB, there are four off-axis foci at the autofocusing plane of the MAAB. The MAAB has a better abruptly autofocusing property than the original SAB. In addition, with the increase of the normalized intensity at the first peak, the focal position (second peak) of the MAAB remains almost the same, whereas the position of the first peak shifts along the propagation direction gradually. These unique characteristics of MAAB have been demonstrated by experiment and indicate potential applications in various fields.

Propagation dynamics of generalized and symmetric Airy beams

We present theoretically and experimentally generalized and symmetric Airy beams, where the two sidelobes are not mutually perpendicular, by introducing two rotary angle factors. The symmetric Airy beam is induced by a binary phase pattern. We demonstrate that the intensity distributions of generalized Airy beams are apparently different from those of normal Airy beams. Moreover, they can propagate along arbitrary trajectories. Numerical results show that the generalized and symmetric Airy beams still have the ability of self-healing and nondiffraction. The experimental results are in complete accord with numerical results. Some possible applications are also discussed, and these interesting properties will also likely have potential applications.

3D-printed diffractive elements induced accelerating terahertz Airy beam

We first demonstrate the accelerating terahertz (THz) Airy beam with a 0.3-THz continuous wave. Two diffractive elements are designed and 3D-printed to form the generation system, which cannot only imprint the desired complex phase pattern but also perform the required Fourier transform (FT). We both numerically and experimentally demonstrate the propagation dynamics of the accelerating THz Airy beam and investigate its self-healing property during propagation in the free space. Our observations are in good agreement with the numerical simulations. Such an accelerating THz Airy beam could be able to develop novel THz imaging systems and robust THz communication links.

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.

Intensity-symmetric accelerating caustic beams

We construct and generate symmetric accelerating caustic beams (ACBs) by using 3/2-order phase-only masks with elliptical contour based on optical caustics and diffraction theory. The symmetric ACBs are a type of bimodal accelerating caustic beam with two quasi-constant intensity peaks, very similar to the combination of two face-to-face Airy-like beams judging by appearance. Their fundamental optical morphology and force properties of particles in ACBs are subsequently provided. The unique optical properties of ACBs can be exploited for practical uses, such as accelerating electrons and clearing micrometer-sized particles as a laser micrometer-sized "water pump" instead of a laser micrometer-sized "snowblower" of accelerating Airy beams.

Trapping two types of particles by modified circular Airy beams

The radiation force of modified circular Airy beams (MCAB) exerted on both a high-refractive-index particle and a low-refractive-index particle are analyzed in this paper. Our results show that the two kinds of particles can be simultaneously stably trapped by MCAB at different positions. Compared with the common circular Airy beams (CAB) with the same parameters, trapping forces on the two kinds of particles are greatly increased because of the enhanced abruptly autofocusing property and the appearance of hollow region in MCAB. The trapping forces can be modulated by varying parameters of MCAB, and it is important to choose appropriate parameters to trap particles in practice.

Propagation characteristics of the modified circular Airy beam

We have proposed a kind of modified circular Airy beam (MCAB) based upon a modification of the Fourier spectrum of circular Airy beams (CAB) in this paper. Unlike most abruptly autofocusing beams, the position of peak intensity of MCAB can be moved to any rings behind. Two apodization parameters are introduced to describe the propagation characteristics of MCAB. It is found that the focal position, focal trajectory and the size of focal spot do not change with the apodization parameters; but the abruptly autofocusing property will be greatly enhanced if appropriately apodization parameters are chosen. Comparing with the common CAB and the previous blocked CAB, the MCAB shows better abruptly autofocusing property. It may have more applications in various fields.

Intensity-symmetric Airy beams

Theoretical, numerical, and experimental research on a novel family of Airy beams in rectangular coordinates having a symmetric transverse pattern of light intensity is presented. The intensity-symmetric Airy beams include both the symmetric Airy beam whose field amplitude is an even function of the transverse coordinates and the antisymmetric Airy beam whose field amplitude is an odd function of such coordinates. The theoretical foundations are based on the relationship of the symmetries of the spectral phase with the cosine and sine Fourier transforms. These beams are analyzed in a propagation range also including the region preceding the Fourier plane. These beams exhibit autofocusing, collapse, self-bending, and reversal propagation. Moreover, the intensity distribution is strongly asymmetric with respect to the Fourier plane. All these peculiar features were not reported for other classes of paraxial beams in a rectangular frame. The experimental generation of intensity-symmetric Airy beams is demonstrated supporting the theoretical predictions. Possible applications in planar waveguide writing and optical trapping are also discussed.

On the general properties of symmetric incomplete Airy beams

We study the general properties of a class of Airy beams symmetric under reflection of the transverse coordinates. Following a recent proposal, their angular spectra depend on the absolute value of the third power of the transverse components of the wave vector. The proposed beams are shown to be described by symmetric superpositions of incomplete Airy special functions. Their angular spectra do not correspond to any of those described by standard catastrophe optics. However, the morphologies of the symmetric beams are similar to some of those already classified within that scheme, differing mainly on the scaling exponents. Finally, the structural stability of three-dimensional symmetric incomplete Airy beams is experimentally probed.