一种新空心光束的理论及实验研究

提出了一种用来描述空心光束的新理论模型——空心高斯光束模型，通过控制光束参数可以方便地调制空心光束黑斑的大小.导出了空心高斯光束经傍轴光学系统的解析传输变换公式.利用导出的公式计算分析了空心高斯光束在自由空间的传输特性.在实验上利用矩阵本征值方法设计了能输出空心高斯光束的光学谐振腔，对实验上得到的空心高斯光束进行了传输特性的研究.结果表明，理论和实验相吻合.该空心高斯光束产生的光势阱为控制冷原子提供了一条新途径. 关键词： 空心高斯光束 光学谐振腔 传输特性     

Propagation of cosh Gaussian laser beam in plasma with density ripple in relativistic – ponderomotive regime

Self-focusing of cosh Gaussian laser beam in plasma with periodic density ripple has been investigated. The pondermotive force on electron and the relativistic oscillation of the electron mass causes periodic self-focusing/defocusing of the cosh Gaussian laser beam. The beam converges in the region of high plasma density due to dominance of self-focusing effect over diffraction effect and diverges in the low density region. Non-linear partial differential equation governing the evolution of complex envelope in slowly varying approximation is solved using paraxial ray approximation. The variation of beam-width parameter is studied with distance of propagation for different values of ripple wave number d and decentred parameter b. In order to get strong self-focusing, wavelength and intensity parameters of cosh Gaussian laser beam are optimized.     

Effect of tilt and astigmatism aberration of turbulent atmosphere on the intensity distributions of a LG11 beam

The effects of turbulent aberration such as z-tilt aberration, and astigmatism on the intensity distribution of double ring shaped LG₁₁ beam have been investigated using the Fresnel–Kirchhoff diffraction integral and the quadratic approximation. The effect of turbulent aberration on the intensity distributions at the focal plane with different turbulent strength, and propagation distance is analyzed numerically. It is observed that the effect of tilt aberration gives major effect on the intensity distribution of the LG_(1,1) beam in the turbulent atmosphere.     

Distribution regimes of intense laser beam in a self-consistent plasma channel

In the present work, we investigate the distributed regimes of an intense laser beam in a self-consistent plasma channel. As the intensity of the laser beam increases, the relativistic mass effect as well as the ponderomotive expulsion of electrons modifies the dielectric function of the medium due to which the medium exhibits nonlinearity. Based on Wentzel–Kramers–Brillouin and paraxial ray theory, the steady-state solution of an intense, Gaussian electromagnetic beam is studied. A differential equation of the beamwidth parameter with the distance of propagation is derived, including the effects of relativistic self-focusing (SF) and ponderomotive self-channeling. The nature of propagation and radial dynamics of the beam in plasma depend on the power, width of the beam, and Ω _p, the ratio of plasma to wave frequency. For a given value of Ω _p (<1), the distribution regimes have been obtained in beampower–beamwidth plane, characterizing the regimes of propagation as steady divergence, oscillatory divergence, and SF. The related focusing parameters are optimized introducing plasma density ramp function, and spot size of the laser beam is analyzed for inhomogeneous plasma. This results in overcoming the diffraction and guiding the laser beam over long distance. Numerical computations are performed for typical parameters of relativistic laser–plasma interaction studies.     

Formation of optical vortices using coherent laser beam arrays

We present a proposal to generate an optical vortex beam by using the coherent-superposition of multi-beams in a radially symmetric configuration. In terms of the generalized Huygens-Fresnel diffraction integral, we have derived the general propagation expression for the coherent radial arrays of laser beams. Using the derived formulae, we have analyzed the effects of the beamlet number N, the separation distance ρ of the beamlets and the topological charge m on the intensity and phase distributions of the resultant beams. Our simulation results show that optical vortices could be efficiently generated due to the coherent-superposition effect of all beamlets, during the propagation process of the coherent radial array of laser beams with the initial well-organized phase distributions through the free space. In the focusing system, the resultant beam near the focusing plane has the strong rotational effect with the phase helicity.     

The effect of tilt aberration and astigmatism of turbulent atmosphere on the intensity distribution of a vortex carrying Gaussian beam

The effect of tilt and astigmatism aberration of the turbulent atmosphere on the intensity distribution of a focused vortex carrying Gaussian beam was investigated based on the extended Fresnel-Kirchhoff diffraction integral and the quadratic approximation of phase structure function. Our results have shown that the intensity distribution on the focal plane in the effect of tilt aberration changes with the turbulent strength, the propagation distance and the topological charge of the initial beam. The propagation distance is larger, the focal spot size will be larger, and the central dip will be less deep. It is also noticed that the intensity distribution of a beam with single topological charge is affected more by tilt aberration in comparison to the beam with double topological charge. The effect of astigmatism on the intensity distribution is quite less than that of tilt aberration. For focused beam propagation in atmosphere, the effect of the tilt aberration on the intensity distribution of optical vortex beam is the main effect of total turbulent aberration.     

Conversion of high-order Laguerre-Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon

We propose a new method for transformation of a Laguerre-Gaussian beam of azimuthal index l and radial index n = 0 (LG_l,0) into a vortex, diverging or nondiverging Bessel beam, which can have increased or decreased phase singularity order, or into a zeroth order Bessel beam, by means of a helical axicon. The Bessel beam divergence or nondivergence depends upon the waist position of the input Laguerre-Gaussian beam, regarding the plane where the helical axicon is situated.The expressions for the amplitude and the intensity distribution of the diffracted wave field, in the process of Fresnel diffraction, are deduced using the stationary phase method. The theoretical analysis for the vortex radius and the maximum propagation distance of the Bessel beams obtained is presented.     

Astigmatic telescopic transformation of a high-order optical vortex

Properties of an optical vortex light beam formed after the astigmatic telescopic transformation of a circular Laguerre-Gaussian mode are considered both theoretically and experimentally. The beam evolution is found to be in conformity with the general notions on the high-order optical vortex symmetry breakdown. Upon propagation, the asymmetric beam shows a sort of rotation of its transverse profile in accord with the energy circulation in the original circular mode; this process is described on the base of the beam intensity moments and the vortex and asymmetry components of its orbital angular momentum. An l-charged optical vortex converts into |l| secondary first-order vortices positioned on a straight line crossing the beam axis. Orientation of this straight line in the beam cross section and spatial separation of the secondary vortex cores depend on the propagation distance. Morphology (orientation and anisotropy) of all the secondary vortices is the same and depends on the propagation distance; the anisotropy can be characterized by the vortex component of the beam angular momentum. At certain distance, relative separation of secondary vortices with respect to the beam transverse size reaches its maximum that corresponds to the minimum anisotropy of the vortices. The results can be useful in the context of current research of the optical vortex arrays.     

The relay propagation of partially coherent cosh–Gaussian–Schell beams in turbulent atmosphere

We have studied the relay propagation of a partially coherent cosh–Gaussian–Schell beam in turbulent atmosphere. Analytical expressions for both the cross-spectral density at the relay system and average intensity at the target are derived. By using the analytical expressions some special cases are studied and some numerical simulation comparisons are made, especially the effects of the coherence of the beam, turbulence strength, aperture and its size on the relay propagation. Our study shows that the effects of diffraction and coherence of initial beam on the intensity profiles at the relay system are so small that they can be neglected when the effects due to turbulence are large enough. Even though the correction to the receiving beam at relay system is important, it is not necessary to improve the receiving beam when the effect of turbulence over the travel path is strong. A high peak intensity at target can be obtained by optimizing these factors, such as propagation distance, aperture and spatial correlation length.     

湍流等离子体鞘套中高斯光束的传播特性分析

为了研究高斯光束在湍流等离子体鞘套中的传输特性,根据广义惠更斯-菲涅耳原理,采用基于快速傅里叶变换的功率谱反演法,用多随机相位屏来模拟湍流带来的影响.根据超声速飞行器绕流等离子体流场厚度在厘米级别的特点,光束在两个相位屏之间的传输过程中采用菲涅耳衍射积分的两次快速傅里叶变换算法(double fast Fourier transform algorithm),利用多随机相位屏模拟等离子体鞘套湍流对光束传输产生的影响,解决了多随机相位屏模拟湍流研究中的超短距离传输问题.当飞行高度为45 km,飞行速度为18马赫时,通过对超声速飞行器绕流等离子体流场的统计分析,发现在此飞行条件下折射率起伏方差的强度范围10~(–11)—10~(–14).对高斯光束在湍流等离子体流场中的传输特性进行了数值仿真.结果表明:在等离子体鞘套湍流中折射率起伏强度、波长、传输距离等都是影响高斯光束质量的重要因素.折射率方差越大,传输距离越长,光斑弥散越严重,光强起伏越大,光强减弱也越明显.光束的波长越长,高斯光束抑制湍流的能力越强,光斑弥散程度越小,光强起伏也越小.     

The intensity distribution of hollow Gaussian beams focused by a lens with spherical aberration

We developed an expression that describes the hollow Gaussian beams (HGBs) passing through a spherically aberrated lens by using the Collins formula. The radial intensity distribution in both spherical aberration SA free lens, lens that exhibits relatively large in both positive spherical aberration PSA, and negative spherical aberration NSA is calculated. Numerical calculations are made and the results show that the PSA and NSA have a strong influence on the intensity distribution especially at the focus. The study showed remarkable results for which there is no hollow Gaussian beam at a large NSA along the optical axis at the focus. In addition, we found that the DSS, and w_r of focused hollow Gaussian beams in the focal region depend not only on the beam radius, and beam order; but also on the spherical aberration.     

Influence of atmospheric turbulence on the propagation of superimposed partially coherent Hermite-Gaussian beams

The influence of atmospheric turbulence on the propagation of superimposed partially coherent Hermite-Gaussian (H-G) beams is studied in detail. The closed-form propagation equation of superimposed partially coherent H-G beams through atmospheric turbulence is derived. It is shown that the turbulence accelerates the evolution of three stages which superimposed partially coherent H-G beams undergo. The turbulence results in a beam spreading and a decrease of the maximum intensity. However, the larger the beam number M, the beam order m, the separate distance x_d, and the smaller the beam correlation length σ₀ are, the less the power focusability of superimposed partially coherent H-G beams is affected by the turbulence. Specially, superimposed partially coherent H-G beams are less sensitive to turbulence than superimposed fully ones, and than partially coherent H-G beams if the beam power focusability and the maximum intensity are taken as beam criterions. However, the maximum intensity of superimposed partially coherent H-G beams is less sensitive or more sensitive to turbulence than that of superimposed Gaussian Schell-model (GSM) beams depending on σ₀.     

Hollow Gaussian beams and their propagation properties

A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB.     

双轴棱锥产生长距离近似无衍射光的新技术

提出了一种利用会聚透镜、轴棱锥等简单光学元件产生长距离近似无衍射光的新技术. 分别利用几何光学和衍射理论分析了该方法产生长距离近似无衍射光束的原理, 通过软件模拟了长距离近似无衍射光束的形成过程,得出了该光束在不同距离处的横向光强分布. 模拟结果显示该光束在较长距离处的横向光强分布满足Bessel分布. 从实验上获得了传播距离长达80 m、中心光斑发散角约为0.12 mrad的近似无衍射光束, 相比于国外学者最近的研究成果(Belyi et al. 2010 Opt. Exp. 18 1966)将传播距离延长了50多米,而光束发散角压缩了22倍.实验中, 对光束沿光轴传播时在不同距离处的光斑进行了拍摄,所得实验结果与理论分析基本符合.     

Propagation distances of surface electromagnetic waves on Ni,Pd, Pt,and W metal surfaces

The propagation distances, L_x, of surface electromagnetic waves (SEW) on Ni, Pd, Pt, and W were measured using the two-prism coupling technique at wavelengths from 9.3 to 10.6 microm. Metal samples consisted of films, deposited on glass substrates by electron beam deposition, and metal foils. The measured L_x values for the Pd and Pt firms and Pt foil agree to within 20% of the calculated values from the two-media dispersion relation. The measured values of the propagation distance for the Ni film and foil and the W foil agree to within 50% of the calculated L_x. Scanning electron microscope (SEM) photographs and Auger analysis indicate that film imperfections and foil surface roughness contributed to the lower propagation distances observed for Pt and Pd while imperfections, roughness, and oxidation contributed to the disagreement between measured and calculated propagation distance for Ni and W.     

Propagation analysis of flattened circular Gaussian beams with a circular aperture in turbulent atmosphere

The propagation properties of flattened Gaussian beam with aperture in turbulent atmosphere have been studied by using the extended Huygens-Fresnel principle. From the study and numerical calculation, the effects of aperture on the propagation of flattened Gaussian beams in turbulent atmosphere have been illuminated. It shows that when the value of the truncation parameter δ is bigger, for example δ?2, the effects of aperture on the propagation properties are too small to be neglected. But when the truncation parameter δ is smaller, for example δ<2, the effects of aperture are complex. The peak value of the average intensity descends more rapidly and the beam spot spreads quicker with aperture than that without aperture when the propagation distance increases. Meanwhile, with the propagation distance increasing, the average intensity profiles of flattened Gaussian beams gradually convert into Gaussian average intensity profiles. In addition, some limiting cases are also discussed. It agrees with the existing results.     

矢量空心高斯光束横纵向光场传输特性

基于矢量瑞利-索末菲衍射积分,研究了矢量空心高斯光束横向光场和纵向光场在自由空间中的传输特性.研究结果表明,空心高斯光束的横向光场与纵向光场在传输过程中光强分布情况并不相同,横向光场的光强分布具有旋转对称性,并且保持空心特性的距离受光束阶数的影响,而纵向光场不再具有旋转对称性,并且在理想状态下纵向光场可以一直保持空心特...     

衍射理论对局域空心光束及无衍射光束重建的描述

利用衍射理论导出了局域空心光束的传输表达式及光强分布,给出了局域空心光束的精细结构,详细分析了其演变过程。讨论了聚焦透镜的焦距f对径向暗域最大尺寸及轴上暗域长度的影响。结果表明,径向暗域最大尺寸及轴上暗域长度都随着f的增大而增大。通过轴棱锥-透镜系统获得局域空心光束,用体视显微镜和CCD照相机组成的系统拍摄光束强度分布。结果表明应用衍射理论可以较精确地描述局域空心光束的演变过程。找出了其应用中的不利因素,更清晰地展现无衍射光束的重建现象。这种描述方法弥补了几何理论和干涉理论的不足。     

Gaussian laser beam tailoring using acoustooptic cell

Profile shaping of a Gaussian laser beam by an acoustic wave is well described using Collins integral and ABCD matrix formalism. It is shown by a numerical simulation that the relative width of the laser beam to the ultrasonic wavelength and the acoustic pressure inside the acoustooptic cell act on the light intensity diffraction pattern.Obtained results show that the output intensity profile differs from the incident Gaussian beam shape, and it is more broadened with an increase in the acoustic pressure. The intensity of a focused laser beam is transformed in a flat form in the central region if the acoustic pressure is proprely controlled.On the other hand the intensity longitudinal range (ILR) of the flat shape is discussed along the propagation axes, we have found the ILR is about 2 mm for a focal length distance f=100 mm.     

Specific features of speckle structure formed by dispersed laser beams

The geometry of statistical average of intensity speckles formed by a broadband dispersed laser beam spatially coherent in initial plane z = 0 is studied theoretically. A computer simulation was used to obtain two-dimensional distributions of random intensity that provide a clear picture of the transformations experienced by the speckle structure upon laser beam propagation. Correlation functions and power spectra of random intensity are calculated in order to determine the characteristic size and shape of speckles as a function of longitudinal coordinate z, the width and shape of the frequency spectrum, and the degree of dispersion of the light beam. Analytical expressions that describe an increase in the speckle size along the beam axis and in the direction of beam dispersion as a function of distance from the initial plane are obtained. The ultimate (at z → ∞) width of speckles in the direction of beam dispersion is calculated.