Influence of turbulence on the beam propagation factor of Gaussian Schell-model array beams

The analytical expression for the beam propagation factor (M²-factor) of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the M²-factor of GSM array beams depends on the beam number, the relative beam separation distance, the beam coherence parameter, the type of beam superposition, and the strength of turbulence. The turbulence results in an increase of the M²-factor. However, for the superposition of the intensity the M²-factor is less sensitive to turbulence than that for the superposition of the cross-spectral density function. The M²-factor of GSM array beams is larger than that of the corresponding Gaussian array beams. However, the M²-factor of GSM array beams is less affected by turbulence than that of the corresponding Gaussian array beams. For the superposition of the cross-spectral density function a minimum of the M²-factor of GSM array beams may appear in turbulence, which is even smaller than that of the corresponding single GSM beams.     

Polarization properties of two Gaussian Schell-model beams in the turbulent atmosphere

General expressions are derived for the spectral degree of polarization of a beam generated by the superposition of two Gaussian Schell-model (GSM) beams propagating in a turbulent atmosphere by adopting the beam coherence-polarization matrix and Young's interference theory. We analyzed the distance of two beams, atmospheric turbulence intensity, and the location of the imaging plane affect the degree of polarization by numerical calculation. In particular, when the correlation coefficients of x and y components of the electric field are the same (i.e. δ_xx = δ_yy), the degree of polarization will obtain the same value.     

大气湍流中光束束宽扩展和角扩展的比较研究

以厄米-双曲余弦-高斯（H-ChG）光束为例,对H-ChG光束通过大气湍流传输时的束宽扩展和角扩展做了详细研究.用相对束宽和相对角扩展代替束宽和角扩展来研究湍流对光束影响的灵敏程度.研究表明,折射率结构常数C²_n越小,光束束宽扩展和角扩展越小.有较大阶数m,n,较小参数Ω₀和束腰宽度w₀ H-ChG光束的角扩展受湍流影响较小.当传输距离足够远时,这一结论对H-ChG光束的束宽扩展也成立.当传输距离不长时,对H-ChG光束相对束宽随Ω₀和w₀的变化规律做了分析.用数值计算例做了说明,并对结果的正确性做了物理解释.厄米-高斯,双曲余弦高斯和高斯光束在大气湍流中的扩展可作为H-ChG光束的特例来处理. 关键词： 束宽扩展和角扩展 大气湍流 厄米-双曲余弦-高斯光束     

Propagation of partially coherent beams carrying an edge dislocation through atmospheric turbulence along a slant path

This paper derives the explicit expressions for the average intensity, beam width and angular spread of Gaussian Schell-model (GSM) beams with edge dislocation propagating through atmospheric turbulence along a slant path. The propagation of GSM beams with edge dislocation through horizontal atmospheric turbulence can be treated as a special case through a slant one. The propagation properties of GSM beams with edge dislocation through slant atmospheric turbulence are studied, where the influence of edge dislocation parameters including the slope p and off-axis distance d on the spreading of GSM beams with edge dislocation in atmospheric turbulence is stressed. It shows that the spreading of the intensity profile of GSM beams with edge dislocation along a slant path is smaller than that along a horizontal path in the long-distance atmospheric propagation. The larger the slope vert pvert and the smaller the off-axis distance vert dvert are, the less the beam-width spreading and angular spread of GSM beams with edge dislocation are affected by turbulence. The GSM beams with edge dislocation is less affected by turbulence than that of GSM beams without edge dislocation. The results are illustrated numerically and their validity is interpreted physically.     

Electron screening in backward elastic scattering

Abstact: The elastic scattering cross sections, σ (E,θ), for the systems He+Ta and He+W have been measured at θ_lab=165° and E _lab=76.1 keV to 3.988 MeV using targets with a thickness of a few atomic layers. The results are smaller than the results given by the Rutherford scattering law, σ_R(E,θ), due to the effects of electron screening and can be described by σ(E,θ)/σ_R(E,θ)=(1+U_e/E)⁻¹, where U _e is an atomic screening potential energy. The deduced average value, U _e=28 ± 3 keV, is consistent with the Moliére- and Lenz-Jensen-models as well as electron binding energies. Received: 25 May 1998     

部分相干厄米-双曲正弦-高斯光束通过湍流大气传输的平均光强分布演化和角扩展

推导出部分相干厄米-双曲正弦-高斯(H-ShG)光束通过湍流大气的平均光强和角扩展的解析表示式,并用以研究了部分相干H-ShG光束在湍流中的平均光强分布演化和角扩展. 结果表明,折射率结构常数C²_n的增加和空间相关长度σ₀的减小都会加速演化过程. 引入相对角扩展来定量描述光束抗拒湍流的能力. 空间相关长度σ₀,束腰宽度w₀和双曲 关键词： 平均光强分布演化 角扩展 湍流大气 部分相干厄米-双曲正弦-高斯(H-ShG)光束     

Photoproduction of πmesons off protons from the Δ(1232) region to Eγ = 3 GeV

Photoproduction of π⁰-mesons was studied with the Crystal-Barrel detector at ELSA for incident energies from 300MeV to 3GeV. Differential cross-sections dσ/dΩ, dσ/dt, and the total cross-section are presented. For E _γ < 3GeV, the angular distributions agree well with the SAID parametrization. At photon energies above 1.5GeV, a strong forward peaking indicates t-channel exchange to be the dominant process. The rapid variations of the cross-section with energy and angle indicate production of resonances. An interpretation of the data within the Bonn-Gatchina partial-wave analysis is briefly discussed.     

Influence of the reagent vibration on the stereo-dynamics of the reactions D- + H2 and H- + D2

Employing the quasi-classical trajectory method and the potential energy surface of Panda and Sathyamurhy [Panda A N and Sathyamurthy N 2004 J. Chem. Phys. 121 9343], the effect of the reagent vibration on vector correlation of the ion-molecule reactions D^- + H₂ and H^- + D₂ is studied at a collision energy of 35.7 kcal/mol. Four generalized polarization-dependent differential cross sections (2π/σ)(dσ₀₀/dω_t),(2π/σ)(dσ₂₀/dω_t),(2π/σ)(dσ₂₂/dω_t), and (2π/σ)(dσ₂₀/dω_t) are presented in the centre-of-mass reference frame, separately. At the same time, the effects on the product angular distributions P(θ_r), P(φ_r) and P(θ_r,φ_r) of the title reactions are also analysed. The calculated results show that the scattering tendencies of the product HD, the alignment and the orientation of j' sensitively depend on reagent molecule vibration.     

Turbulence distance of radial Gaussian Schell-model array beams

The effect of turbulence on the spreading of radial Gaussian Schell-model (GSM) array beams is studied quantitatively by examining the mean-squared beam width. The analytical expression for the turbulence distance z _T of radial GSM array beams is derived by using the integral transform technique, which indicates within what ranges radial GSM array beams will be less affected by turbulence. It is shown that the effect of turbulence on the spreading of radial GSM array beams can be reduced by choosing the suitable array beam parameters and the type of the beam superposition. In addition, a comparison with the previous work is also made.     

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.     

The Beam Propagation Factor of Nonparaxial Truncated Flattened Gaussian Beams

By using the second-order moment of the power density, the beam width, far-field divergence angle and M² factor of nonparaxial truncated flattened Gaussian (FG) beams are derived analytically. It is shown that the M² factor of nonparaxial truncated FG beams depends not only on the truncation parameter δ and beam order N, but also on the initial waist-width to wavelength ratio w₀/λ. The far-field divergence angle approaches an asymptotic value of θ_max=63.435° when the truncation parameter δ → 0. For the special cases of N = 0 and δ → ∞ our results reduce to those of nonparaxial truncated Gaussian beams and nonparaxial untruncated FG beams, respectively.     

湍流对环状光束扩展的影响

采用积分变换技巧,推导出了环状光束通过湍流大气传输二阶矩束宽的解析表达式,并研究了湍流对环状光束扩展的影响.另一方面,通过分析二阶矩束宽给出了环状光束不受湍流影响的传输范围,指出环状光束将不受到湍流大气影响的条件.研究表明,光束遮拦比ε、阶数M（N）、波长λ越大,束宽w₀越小,则环状光束受湍流大气的影响就越小.并对所得到的主要结果给出了合理的物理解释. 关键词： 环状光束 大气湍流 二阶矩束宽     

矩形分布高斯-谢尔模型列阵光束的等效曲率半径

 推导出矩形分布高斯-谢尔模型（GSM）列阵光束通过湍流大气传输的等效曲率半径的解析表达式。研究表明,等效曲率半径由湍流强度、GSM列阵光束参数及光束的叠加方式等因素共同确定。湍流使得等效曲率半径减小,但湍流对交叉谱密度函数叠加时等效曲率半径的影响要比光强叠加时大。在自由空间中,交叉谱密度函数叠加时GSM列阵光束的等效曲率半径要比光强叠加时的大。但是,随着湍流的增强,交叉谱密度函数叠加时GSM列阵光束的等效曲率半径可以大于、等于或小于光强叠加时的等效曲率半径。此外,若光束相干参数和子光束数目越大,则等效曲率半径受湍流的影响越大。GSM列阵光束的等效曲率半径受湍流的影响比高斯列阵光束要小。     

Propagation of the off-axis superposition of partially coherent beams through atmospheric turbulence

The propagation properties of the off-axis superposition of partially coherent beams through atmospheric turbulence and their beam quality in terms of the mean-squared beam width w(z) and the power in the bucket (PIB) are studied in detail, where the effects of partial coherence, off-axis beam superposition and atmospheric turbulence are considered. The analytical expressions for the intensity, the beam width and the PIB are derived, and illustrative examples are given numerically. It is shown that the maximum intensity I_max and the PIB decrease and w(z) increases as the refraction index structure constant C_n² increases. Therefore, the turbulence results in a degradation of the beam quality. However, the resulting partially coherent beam with a smaller value of spatial correlation parameter γ and larger values of separate distance x_d and beam number M is less affected by the turbulence than that with a larger value of γ and smaller values of x_d and M. The main results obtained in this paper are explained physically.     

Absence of Magnetism in Continuous-Spin Systems with Long-Range Antialigning Forces

We consider continuous-spin models on the d-dimensional hypercubic lattice with the spins σ _x a priori uniformly distributed over the unit sphere in ℝ ⁿ (with n≥2) and the interaction energy having two parts: a short-range part, represented by a potential Φ, and a long-range antiferromagnetic part λ|x−y|^−s σ _x ⋅σ _y for some exponent s>d and λ≥0. We assume that Φ is twice continuously differentiable, finite range and invariant under rigid rotations of all spins. For d≥1, s∈(d,d+2] and any λ>0, we then show that the expectation of each σ _x vanishes in all translation-invariant Gibbs states. In particular, the spontaneous magnetization is zero and block-spin averages vanish in all (translation invariant or not) Gibbs states. This contrasts the situation of λ=0 where the ferromagnetic nearest-neighbor systems in d≥3 exhibit strong magnetic order at sufficiently low temperatures. Our theorem extends an earlier result of A. van Enter ruling out magnetized states with uniformly positive two-point correlation functions.     

Spectral changes of vector Gaussian Schell-model beams passing through an aperture lens

On the basis of the polarization matrix and propagation equation of the cross-spectral density matrix, the spectral changes in the focal plane of vector Gaussian Schell-model (GSM) beams focused by an aperture lens are studied, where the influence of correlation and polarizer on the behavior of the spectral switch is stressed. It is found that the critical position u_c, spectral minimum S_min, and transition height Δ of the spectral switch depend on the auto-correlation but do not depend on the cross-correlation of GSM beams if there is no polarizer. However, in the presence of the polarizer u_c, S_min and Δ depend on both auto- and cross-correlations. The polarizer affects the spectral switch of vector GSM beams, whereas it does not affect the spectral switch of scalar GSM beams.     

Beam quality of radial Gaussian Schell-model array beams

Taking the Rayleigh range z_R and the M²-factor as the characteristic parameters of beam quality, the beam quality of radial Gaussian Schell-model (GSM) array beams is studied. The analytical expressions for the z_R and the M²-factor of radial GSM array beams are derived. It is shown that for the superposition of the cross-spectral density function z_R is longer and the M²-factor is lower than that for the superposition of the intensity. For the two types of superposition, z_R increases and the M²-factor decreases with increase in beam coherence parameter, and both z_R and the M²-factor increase with increase in inverse radial fill-factor. For the superposition of the cross-spectral density function, z_R increases and the M²-factor decreases with increase in beam number, while for the superposition of the intensity both the z_R and M²-factor are independent of the beam number.     

Similarity parameters evaluation in the Po Valley during convective situations with Sodar data

Summary In well-developed convection, the surface sensible-heat flux can be evaluated from Sodar data; by using these flux values, it is possible to estimate some scale parameters in the mixed layer (likeθ _* andw _*). The use ofθ _*,w _* and the height of the mixed layerz _i, obtainable from other sources (i.e. radiosoundings), allows to verify some similarity relationships. We analysed the vertical profiles of the ratioσ _w ² /w _* ² : we found that it follows the theoretical behaviour depending onz/z _i if we use numerical coefficients slightly different from those usually referred to in the literature.     

Coherent and incoherent π0 photoproduction from the deuteron

Differential cross-sections for the reactions d (γ,π⁰)d and d (γ,π⁰)pn have been measured at MAMI with the TAPS detector setup in the energy range 140 MeV < E _γ < 306 MeV. By use of the Glasgow tagging spectrometer an 0.8 MeV energy resolution for photons incident on the target was achieved. The π⁰ missing energy resolution was sufficient for a reliable separation of coherent and incoherent channels. The data for the break-up channel exhibit very strong final state interaction effects, whereas the observed angular dependence of the inclusive process d (γ,π⁰)X is in quantitative agreement with predictions for a quasi-free process. The observed absolute d (γ,π⁰)X cross-sections, on the other hand, are significantly smaller than predicted by the quasi-free process for E _γ >∼ 250 MeV. Associating this failure with the π⁰ photoproduction on the neutron would suggest that its cross-section is up to 25% below the presently believed value. Received: 13 February 2001 / Accepted: 13 April 2001     

Propagation of random electromagnetic beams through axially nonsymmetrical optical systems

When random electromagnetic beams passing through axially nonsymmetrical ABCD optical systems, the analytical formula for the transformation of the elements of 2 × 2 cross-spectral density matrix is obtained with the help of vector integration. We derive analytical expressions of the spectral degree of polarization, the spectral degree of coherence, and the spectral density in any output plane z > 0. Some numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams propagating through such optical systems.