Plasmonic Airy beam manipulation in linear optical potentials

We demonstrate, both theoretically and numerically, the efficient manipulation of plasmonic Airy beams in linear optical potentials produced by a wedged metal-dielectric-metal structure. By varying the angle between the metallic plates, we can accelerate, compensate, or reverse the self-deflection of the plasmonic Airy beams without compromising the self-healing properties. We also show that in the linear potentials the Airy plasmons of different wavelengths could be routed into different directions, creating new opportunities for optical steering and manipulation.     

Reshaping the trajectory and spectrum of nonlinear Airy beams

We demonstrate theoretically and experimentally that a finite Airy beam changes its trajectory while maintaining its acceleration in nonlinear photorefractive media. During this process, the spatial spectrum reshapes dramatically, leading to negative (or positive) spectral defects on the initial spectral distribution under a self-focusing (or defocusing) nonlinearity.     

Maslov index for power-law potentials

The Maslov index in the semiclassical Bohr–Sommerfeld quantization rule is calculated for one-dimensional power-law potentials V (x) = ?V ₀/x ^s, x > 0, 0 < s < 2 The result for the potential V(x)=-V ₀/x ^1/2 is compared with the recently reported exact solution. The case of a spherically symmetric power-law potential is also considered.     

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.     

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.     

Linear and nonlinear waves in surface and wedge index potentials

We study optical beams that are supported at the surface of a medium with a linear index potential and by a piecewise linear wedge-type potential. In the linear limit the modes are described by Airy functions. In the nonlinear regime we find families of solutions that bifurcate from the linear modes and study their stability for both self-focusing and self-defocusing Kerr nonlinearity. The total power of such nonlinear waves is finite without the need for apodization.     

激光器与轨道的相对位置对动态加热的影响

通过分析光束入射的角度因子将激光器在地平面上的安放位置进行分类,采用了几何分析和数值模拟的方法,探讨了聚焦激光束在加热运动圆柱体过程中,为了达到一定的加热功率水平和能量水平以取得最好的加热效果而应采取的措施,即应当以激光垂直入射的轨道点为中心,以激光的有效工作时间为取值范围,并参考大气对激光能量的衰减,相对于轨道选取适当的距离进行加热。该研究从理论上说明了激光器与圆柱体运动轨道的相对位置对激光动态加热的影响可以看作一个优化问题,存在最优解,进而对于合理使用激光器进行动态加热具有参考价值。     

激光器与轨道的相对位置对动态加热的影响

 通过分析光束入射的角度因子将激光器在地平面上的安放位置进行分类,采用了几何分析和数值模拟的方法,探讨了聚焦激光束在加热运动圆柱体过程中,为了达到一定的加热功率水平和能量水平以取得最好的加热效果而应采取的措施,即应当以激光垂直入射的轨道点为中心,以激光的有效工作时间为取值范围,并参考大气对激光能量的衰减,相对于轨道选取适当的距离进行加热。该研究从理论上说明了激光器与圆柱体运动轨道的相对位置对激光动态加热的影响可以看作一个优化问题,存在最优解,进而对于合理使用激光器进行动态加热具有参考价值。     

Airy Functions in the Thermodynamic Bethe Ansatz

Thermodynamic Bethe ansatz equations are coupled nonlinear integral equations which appear frequently when solving integrable models. Those associated with models with N=2 supersymmetry can be related to differential equations, among them Painlevé III and the Toda hierarchy. In the simplest such case, the massless limit of these nonlinear integral equations can be solved in terms of the Airy function. This is the only known closed-form solution of thermodynamic Bethe ansatz equations, outside of free or classical models. This turns out to give the spectral determinant of the Schrödinger equation in a linear potential.     

Higher-Order Airy Scaling in Deformed Dyck Paths

We introduce a deformed version of Dyck paths (DDP), where additional to the steps allowed for Dyck paths, ‘jumps’ orthogonal to the preferred direction of the path are permitted. We consider the generating function of DDP, weighted with respect to their half-length, area and number of jumps. This represents the first example of an exactly solvable two-dimensional lattice vesicle model showing a higher-order multicritical point. Applying the generalized method of steepest descents, we see that the associated two-variable scaling function is given by the logarithmic derivative of a generalized (higher-order) Airy integral.     

An analysis of the exactly solvable linear differential equations by the Modified Airy Function (MAF) method

Appropriate second order Linear Differential Equations (LDEs) which can be solved exactly by the Modified Airy Function (MAF) method, which normally gives approximate solutions in terms of Airy functions for Schrodinger-like LDEs, have been studied in three possible cases according to the MAF theory. The results of the exactly solvable LDEs have been classified in terms of two different family of LDEs with turning point and/or singular point parameter, one of which being a new class other than the known Time Independent Schrodinger’s Equation (TISE) with a linear potential.     

Klein–Gordon particles in mixed vector–scalar inversely linear potentials

The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the eigenfunctions which ensure that the effective Hamiltonian is Hermitian for all the points of the space. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist.     

Local interactions of higher-spin potentials that are gauge invariant in linear approximation

We study connected Wightman functions of N conserved currents, each of which is formed from a scalar field and has even spin l _i . The UV divergence of this vertex function is regularized by the analytic continuation in the space dimension D → D − ε. We evaluate the residue of ε ⁻¹ only, which is a local interaction Lagrangian density and gauge invariant in linear approximation. The text was submitted by the author in English.     

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。     

Some approximations in the linear dynamic equations of thin cylinders

Theoretical analysis is performed on the linear dynamic equations of thin cylindrical shells to find the error committed by making the Donnell assumption and the neglect of in-plane inertia. At first, the effect of these approximations is studied on a shell with classical simply supported boundary condition. The same approximations are then investigated for other boundary conditions from a consistent approximate solution of the eigenvalue problem. The Donnell assumption is valed at frequencies high compared with the ring frequencies, for finite length thin shells. The error in the eigenfrequencies from omitting tangential inertia is appreciable for modes with large circumferential and axial wave lengths, independent of shell thickness and boundary conditions.     

线阵CCD用于实时动态测量技术研究

本文研究的是在连续光条件下线阵ＣＣＤ实时动态测量技术,除了考虑ＣＣＤ像元响应非均匀性、非线性等影响因素外,还应认真考虑采样频率、测量精度、动态范围、快速电路等问题。本文还详细讨论了测量精度和动态范围问题,推导了测量精度公式与动态范围公式。为了减小测量误差和提高被测信号的频率,必须相应减小积分时间。精度公式是进行线阵ＣＣＤ电路设计的基本依据公式。动态范围与频率无关,只与结构参数有关,为了充分利用ＣＣＤ的动态范围,激光功率要可调。     

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.     

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.     

Scintillation of Airy beam arrays in atmospheric turbulence

We investigate the scintillation properties of Airy beam arrays in atmospheric turbulence. By utilizing the "self-bending" propagation property of Airy beams, the constituent beamlets propagate through relatively independent regions of turbulence but still largely overlap at the on-axis detector. Through numeric simulations, it is shown that the scintillation of an Airy beam array is significantly reduced and close to the theoretical minimum.     

Oblique Airy wave packets in bidispersive optical media

Using hyperbolic rotations, we show that a new class of skewed, nonspreading, accelerating Airy wave packets is possible in optical bidispersive systems. Their obliquity factor is found to have a profound effect on their spatiotemporal acceleration dynamics. Pertinent examples are provided.