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。     

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.     

Reflection and transmission of an Airy beam in a dielectric slab

The reflection and transmission of a finite-power Airy beam incident on a dielectric slab are investigated by an analytical method. Based on the plane-wave angular spectrum expansion and Fresnel approximation, the analytical expressions of the reflected field, internal field as well as transmitted field in each region are obtained. Through numerical simulations, the intensity distributions of the incident beam, reflected beam, internal beam as well as transmitted beam are presented at oblique incidence. Besides, we also compare the intensity distributions of the geometrical-optics beam field, the first order beam mode field and the actual beam field, which indicates that the contribution of each order beam mode field to the actual beam field is related to the refractive index of the dielectric slab. Meanwhile, the reflection characteristics of the Airy beams in the special cases of Brewster incidence and total reflection are investigated. Finally, the effects of the optical thickness and refractive index of the dielectric slab on the peak intensity distributions and beam shifts of the reflected and transmitted beams are also discussed in detail. The analytical and numerical results will be useful to analyze the propagation dynamics of Airy beam in the dielectric slab and provide some theoretical supports to the design of optical film.     

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.     

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.     

Dressed Airy Vortex Beam in a Hot Atomic Medium

Introducing vortices into an Airy beam by the interference between the lobes of the Airy beam for the first time, the modulation of Airy vortices is experimentally and theoretically investigated by electromagnetically induced transparency (EIT) effect and changing the number of side lobes of the Airy beam. The formation and disappearance of vortices in Airy beams can be caused by changing the number of side lobes. The EIT effect can induce the movement of vortex phase singularity by regulating the intensities of lobes in Airy beams. However, changing the number of side lobes can change the energy distribution of the lobes through the energy flow due to the self-healing of Airy beams, thus causing the displacement of vortex phase singularity. In addition, the simulation of the Poynting vector shows that the less the side lobes are blocked, the more energy can be retained in the main lobe and the unblocked side lobes, so that the overall shape of the Airy beam can be better maintained. Such studies provide a new method to acquire and adjust Airy vortex beams and can be applied in the realm of optical micromanipulation.     

Vacuum electron acceleration driven by two crossed Airy beams

Using numerical simulation, we have studied in detail vacuum electron acceleration driven by two crossed Airy beams with identical characteristics except for opposite accelerating directions. An electron injected along the longitudinal central axis is only affected by the combined longitudinal electric field. In addition, a suitable crossed Airy beams scheme is more beneficial to the energy gain of an electron than the single Airy beam acceleration scheme [Opt. Lett. 35, 3258 (2010)]. Meanwhile, the cross angle, the injection energy of the electron, and the initial phase of the Airy beams play significant roles in the energy gain of the electron.     

克尔介质中艾里孤子的形成及控制

利用分步傅里叶法,数值研究了艾里光束在自聚焦克尔非线性介质中的传输。结果表明,当较强的非线性作用于艾里光束时,主瓣能量在传输过程中会发生脱落形成具有周期振荡的空间孤子。随着非线性的增强,该孤子的振荡周期与半高宽都减小。调节艾里光束的入射角度时,脱落孤子的传输轨迹随之发生变化,不同于艾里光束的是,艾里孤子的传输始终保持直线传输。     

The fractional Fourier transform of Airy beams using Lohmann and quadratic optical systems

Based on the generalized Huygens–Fresnel integral, the analytical expressions for Airy beams through three types of fractional Fourier transform (FRFT) optical systems (Lohmann I, Lohmann II and quadratic graded-index systems) are derived. Using the two analytical expressions, the propagation properties of Airy beams for the three types of FRFT optical systems are discussed in detail with numerical examples. Results indicate that the intensity of Airy beams periodically changes and remains form-invariant with the changing of fractional order p for the three types of FRFT optical systems.     

Generation and tight-focusing properties of cylindrical vector circular Airy beams

Tight-focusing properties of cylindrical vector circular Airy beams [i.e., azimuthally polarized (AP) circular Airy beam and radially polarized (RP) circular Airy beam] passing through a high numerical aperture thin lens are investigated in detail. It is found that a super long subwavelength dark channel with full width at half maximum about 0.49λ and depth of focus (DOF) about 52λ can be achieved near the focal region for the case of tight focusing of an AP circular Airy beam, and a super long needle with DOF about 27.5λ of strong longitudinally polarized field can be obtained near the focal region for the case of tight focusing of a RP circular Airy beam. Furthermore, we report experimental generation of an AP circular Airy. Our results will be useful for atom guiding and trapping, particle acceleration and fluorescent imaging.     

Relation between Airy beams and triple-cusp beams

Airy beams and triple-cusp beams are two kinds of accelerating beams. The propagation characteristics and internal topological structures of accelerating Airy beams are well understood because of the developed mathematical theory about Airy function. However, limited information is available about the optical characteristics of accelerating triple-cusp beams. In this work, the relationship between Airy beams and triple-cusp beams is examined theoretically and experimentally. Results reveal some important optical characteristics of triple-cusp beams based on the optical characteristics of Airy beams. These findings are expected to provide a foundation for future applications of triple-cusp beams.     

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.     

附加球面相位引致Airy光束在单轴晶体传输时的两次镜像演化

利用单轴晶体光束传输理论,求得了具有附加球面相位Airy光束在单轴晶体中的传输公式.数值模拟计算结果表明,线偏振附加球面相位Airy光束在晶体中传输时仍为线偏振,但不是传输不变的.粗略地讲,具有附加球面相位的Airy光束在晶体中传输时,近场是传输不变的;而在由晶体寻常与非寻常折射率和球面半径共同确定的两个特定传输距离处,传输光束转换成了取向不同的Gaussian-Airy光束,且高斯依赖的束宽度敏感地与截断因子相关;而当光束依次穿过此两位置时光斑花样先后相对于两横向轴平面做镜像演化,且镜像演化顺序也与晶体寻常和非寻常折射率相对大小密切相关,其总的效果是远场强度花样能恢复原样但花样取向产生了关于对过横平面二、四象限平分平面的镜像演化.这些结果表明,通过恰当选择晶体材料(即折射率)和附加球面相位的半径R,可以调控光束花样的形状、取向及表征各向异性材料的相关性质.     

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.     

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.     

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.     

Airy trajectory engineering in dynamic linear index potentials

We study the propagation of Airy beams in transversely linear index potentials with a gradient that is dynamically changing along the propagation direction. We find exact solutions in the case of Airy and apodized (Gaussian and exponentially) Airy beams in 1+1 and 2+1 dimensions. More important, we find that the Airy beam can follow any predefined path, in which case the potential gradient is determined as a function of this path.     

Propagations of Airy Beams and Nonlinear Accelerating Optical Beams in Photorefractive Crystals with Asymmetric Nonlocality

The impact of the asymmetric nonlocal diffusion nonlinearity of Airy beams and nonlinear accelerating beams supported by photorefractive crystals is addressed. It is revealed how the asymmetric nonlocal response alters the evolution of these optical beams. It is found that the evolution of these beams presents a bending action under the influence of the diffusion nonlinearity. It is also shown that nonlinear accelerating beams can exist in photorefractive crystals with asymmetric nonlocality. These accelerating solutions have the same Airy‐like tail, and accelerate along parabolic trajectories. Soliton states are formed in the interaction of both in‐phase and out‐of‐phase Airy beams and nonlinear accelerating beams and also present a bending action because of the action of diffusion nonlinearity.     

Evolution of Airy beams in a chiral medium

We study the evolution of Airy beams in chiral media. We numerically demonstrate that the circularly polarized Airy beams of opposite handedness can be separated when traveling through the chiral media. The constructive interference of the Airy beams in the near- and far-zone is explicitly analyzed by varying the chirality parameter of the medium. It is interesting to find that the self-acceleration of the beam is sensitive to the interference term.     

Enhancement of Autofocusing Performance for Circular Arrayed‐Airy Vortex Beams

Numerically and experimentally circular arrayed‐Airy vortex beams (CAAVBs) are demonstrated, of which propagation dynamics and autofocusing performance are investigated. In contrast to the classical circular Airy beams, the focal intensity of CAAVBs can be abruptly enhanced several orders of magnitude by introducing vortex arrays (VAs) and increasing Airy arrays number, and the autofocusing performance markedly increases in the focal plane due to introducing VAs. The position of the focal point can be readily controlled by varying the circular arrayed Airy radius is also demonstrated. Experimental results agree with the numerical calculations. These advantages could be beneficial for potential applications in optical trapping, the generation of high intensity laser, medical treatment, and nonlinear effect.