Specular and vortical Airy beams

A new kind of truncated Airy beams is investigated and discussed. These beams are a superposition of shifted and truncated Airy functions and its specular counterparts, where zeroes or extremal points of the Airy function are chosen as a truncation point. The specular Airy beams are smooth at the truncation point and produce a diffraction pattern similar to Hermite-Gaussian modes. Under propagation in Fresnel zone, specular Airy beams demonstrate a symmetrical acceleration in opposite sides and the beam divergence is proportional to the traveled distance squared. The astigmatic mode converter transforms a two-dimensional specular Airy beam into a quasi-annular field with a nonzero orbital angular momentum. Vortical Airy beams based on truncated Airy functions are also discussed. These beams are similar to Laguerre-Gaussian modes, while their annular structure is changed during propagation.     

Airy beams beyond the paraxial approximation

The behavior of the vectorial Airy beams beyond the paraxial approximation is investigated. Indeed, closed-form (even though non exact) expressions for the electric components of the fields generated by the same boundary conditions, which should pertain to the scalar Airy beams, are obtained on the basis of the vectorial Rayleigh-Sommerfeld diffraction integrals under suitable approximations. Such expressions may accompany more complete approaches, like that in Opt. Expr. 17, 22432 (2009), where a fully numerical analysis of the propagation of exponentially smoothed Airy beams has been presented, faithfully reproducing the conditions of their experimental demonstration as reported in Phys. Rev. Lett. 99, 213907 (2007). Comments on other well known approaches to the investigation of the nonparaxial propagation of definite paraxial beams are also given.     

The deflected angle and reflected displacement of Airy beams

The deflected angle of airy beams is defined to describe their bending degree. Based on this parameter, we analyze the lateral displacement of airy beams and the changes of deflected angles during reflection process. In multi-reflections of airy beams, we find that deflected angles increase linearly with the times of reflection, which is useful to study the propagation properties of airy beam in parallel plate waveguides and other waveguides. Also we can use this parameter to control the incident and reflected routes to realize airy beam bypassing obstacles and reflecting back at predictable location.     

Propagation of Airy Gaussian vortex beams in uniaxial crystals

The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated.     

Propagation of Airy beams from right-handed material to left-handed material

Based on the ABCD matrix formalism,the propagation property of an Airy beam from right-handed material(RHM) to left-handed material(LHM) is investigated.The result shows that when the Airy beam propagates in the LHM,the intensity self-bending due to its propagation in the RHM can be compensated.In particular,if the propagation distance in the RHM is equal to that in the LHM and the refractive index of the LHM is n L =-1,the transverse intensity distribution of the Airy beam can return to its original state.     

Airy光束在Kerr介质中的传输特性

通过对非线性薛定谔方程的研究,得出Airy光束在Kerr介质中的崩塌功率及有效束宽演化的解析表达式。经过数值计算发现,Airy光束在聚焦的Kerr介质中,其主瓣在开始传播时始终是会聚的;当输入功率小于临界崩塌功率时,Airy光束主瓣的中心部分出现局部崩塌。在不同的Kerr介质中, Airy光束的形状和传输轨道均能保持不变,如同在自由空间中传播,但光场大小的分布,随着不同的Kerr介质会发生改变:在Kerr的聚焦介质中,光场向中心聚焦;而在散焦的Kerr介质中,光场会发散。     

The optical Airy transform and its application in generating and controlling the Airy beam

We propose an optical Airy transform in this paper, and obtain the analytical expressions for the Airy transform of fundamental Gaussian beams and finite energy Airy beams. The setup for performing the optical Airy transform is presented. The Airy transform for Gaussian beams and finite energy Airy beams are theoretically calculated and analyzed. Our results show that the Airy beam can be conveniently generated and controlled through the optical Airy transform of the Gaussian beam. The optical Airy transform also can be used to directly modulate the beam parameters of the incident Airy beam, and it can transform the incident Airy beam into the Gaussian beam.     

Canonical momentum,angular momentum,and helicity of circularly polarized Airy beams

We report a study of the momentum, angular momentum, and helicity of circularly polarized Airy beams propagating in free space. By using the vector angular spectrum representation, the explicit analytical expressions for the electric and magnetic field components of circularly polarized Airy beams are derived in detail. To overcome the drawbacks of classical kinematics formulae when applied to structured light beams, a general canonical approach is introduced to describe the momentum, angular momentum and helicity of Airy beams. Numerical simulation results for the spatial distributions of the canonical momentum, spin and orbital angular momentum, as well as the helicity densities are presented and discussed. This study may provide useful insights into the dynamical properties of Airy beams that may be important in several applications, including the optical control, micromanipulation, and information processing.     

Evolution of self-healing characteristic on optical Airy beam

We investigate and analyze the evolution of self-healing characteristic on diffraction-free Airy beams. We also show that different internal structure of Airy beams contribute to self-healing by breaking the integrity of Airy beams. A numerical simulation is performed and demonstrate that each independent structure undertakes different roles. It is believed that the intriguing characteristic of Airy beams can be applied in many fields such as optical tweezers, atom trapping and manipulating.     

Collapse arrest in a two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam in nonlocal nonlinear media

Propagation dynamics of a two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam are investigated numerically in local and nonlocal nonlinear media. The self-healing and collapse of the beam crucially depend on the distribution factor b and the topological charge m. With the aid of nonlocality, a stable Airy Gaussian beam and an Airy Gaussian vortex beam with larger amplitude can be obtained, which always collapse in local nonlinear media. When the distribution factor b is large enough, the Airy Gaussian vortex beam will transfer into quasi-vortex solitons in nonlocal nonlinear media.     

Manipulation of Airy Beams in Dynamic Parabolic Potentials

The propagation of finite energy Airy beams in dynamic parabolic potentials, including uniformly moving, accelerating, and oscillating potentials, is investigated. The propagation trajectories of Airy beams are strongly affected by the dynamic potentials, but the periodic inversion of the beam remains invariant. The results may broaden the potential applications of Airy beams, and also enlighten ideas on Airy beam manipulation in nonlinear regimes.     

Broadband acoustic focusing by symmetric Airy beams with phased arrays comprised of different numbers of cavity structures

We realize broadband acoustic focusing effect by employing two symmetric Airy beams generated from phased arrays,in which the units of the phased arrays consist of different numbers of cavity structures, each of which is composed of a square cavity and two inclined channels in air. The exotic phenomenon arises from the energy overlapping of the two symmetric Airy beams. Besides, we demonstrate the focusing performance with high self-healing property, and discuss the effects of structure parameters on focusing performance, and present the characteristics of the cavity structure with straight channels. Compared with other acoustic lenses, the proposed acoustic lens has advantages of broad bandwidth(about 1.4 kHz), high self-healing property of focusing performance, and free adjustment of focal length. Our finding should have great potential applications in ultrasound imaging and medical diagnosis.     

关于Airy光束衍射及自加速性质的研究

对Airy光束的特性做进一步探讨, 一方面对无限宽Airy光束的重心问题给出新的理论说明, 另一方面着重对有限宽情形下的Airy光束的奇特性质进行探讨. 文中采用反证法给出无衍射的讨论, 同时结合数值模拟给出高斯函数及矩形函数限定下的有限宽Airy光束的场分布, 并由此得到其重心位置的轨迹: 重心位置是不变的, 不可能整体自由加速. 最终得到有限宽Airy光束既不可能在自由空间加速, 也不可能是无衍射光束. 关键词： Airy光束 无衍射 自加速 数值模拟     

用傅里叶分析法研究艾里光束远场传播特性

为了从理论上深入分析新型无衍射光束艾里光束在有限能量条件下的远场传播特性,首先,从决定光波在自由空间传播的一维旁轴波动方程入手,采用傅里叶分析法,结合艾里函数的特殊性质,并利用经过指数衰减的有限能量初始条件,完整给出了有限能量条件下用于精确描述一维艾里光束在自由空间传播特性的波动方程解析解.然后,利用所得到解析解分别对一维和二维艾里光束在自由空间的传播特性进行了研究,重点分析了不同参量条件对艾里光束进行无衍射传播和横向自加速的影响.研究表明:当任意横向尺度为100μm,衰减系数为0.03、0.05、0.07、0.1、0.2时,二维艾里光束无衍射传播距离分别为1 014、624、455、338、193mm;当横向尺度保持不变时,衰减系数越小,艾里光束保持无衍射传播的距离越大;当衰减系数保持不变时,横向尺度越小,艾里光束横向自加速越大.所采用的研究方法也可用于研究艾里光束在介质中的传播特性.     

Off-Axis and Multi Optical Bottles from the Ring Airy Gaussian Vortex Beam with the Astigmatic Phase

A new type of off-axis and multi optical bottle (OB) from an astigmatic-phase ring Airy Gaussian vortex beam (APRAGVB) propagating in free space is derived numerically. By choosing appropriate parameters, different sizes and amounts of OBs can be obtained. More importantly, when the APRAGVB has the multi optical vortices at different locations, one can generate off-axis, multi, and complex OBs. It is believed that the results can diversify optical tweezers applications for multi microparticle manipulation.     

Self-Imaging Effect Based on Airy Beams with Quadratic Phase Modulation

The self-imaging effect based on Airy beams with quadratic phase modulation (QPM) in 1 + 1 and 2 + 1 dimensions is studied both numerically and analytically. It is demonstrated that, in spite of spatial spectral shape being kept invariant, both the intensity pattern and the accelerating trajectory of this self-imaging effect depend considerably on the QPM. When the QPM parameter is negative, the self-imaging accelerating wave exhibits deceleration and then acceleration, and the self-imaging scope can be expanded. In the opposite case, the self-imaging extent would be narrowed and the self-imaging accelerating wave will only accelerate during propagation. Numerical simulations agree with the theoretical results very well. This study shows the possibility of controlling the self-imaging effect based on 1D and circular Airy beams, by purposely choosing appropriate QPM parameters.     

相位连续可调诱导下双艾里光束形成的可控方形光瓶(英文)

提出一种利用相位连续可调诱导产生的双艾里光束形成方形光瓶的方法。该方法首先利用二值化后的相位调制出双艾里光束,为了能够实现光瓶能量分布,一个可调控的线性因子被引入到相位调制函数中形成新改进的相位,该相位能够灵活地调节光瓶的大小。数值模拟结果表明高斯光束通过该改进相位调制,能够形成光瓶能量分布的光束。该方形光瓶光束可应用于光镊、原子捕获与操纵。     

相位连续可调诱导下双艾里光束形成的可控方形光瓶

提出一种利用相位连续可调诱导产生的双艾里光束形成方形光瓶的方法。该方法首先利用二值化后的相位调制出双艾里光束,为了能够实现光瓶能量分布,一个可调控的线性因子被引入到相位调制函数中形成新改进的相位,该相位能够灵活地调节光瓶的大小。数值模拟结果表明高斯光束通过该改进相位调制,能够形成光瓶能量分布的光束。该方形光瓶光束可应用于光镊、原子捕获与操纵。     

Airy plasmons: non‐diffracting optical surface waves

Airy beams represent an important class of non‐diffracting waves which can be realized on a flat surface. Being generated in the form of surface‐plasmon polaritons, such Airy plasmons demonstrate many remarkable properties: they do not diffract while propagating along parabolic trajectories, and they recover their shape after passing through obstacles. This paper reviews the basic physics of Airy plasmons in both paraxial and non‐paraxial cases, and describes the experimental methods for generation of Airy surface waves on metal surfaces, including a control of their trajectories, as well as the interference of Airy plasmons and hot‐spot generation. Many unusual properties of Airy plasmons can be utilized for useful applications, including plasmonic circuitry and surface tweezers. Picture: Observation of two colliding Airy plasmons.