Parametric characterization of rotationally symmetric hard-edged diffracted beams

The truncated second-order moments and generalized M2 factor (M(G)2 factor) of two-dimensional beams in the Cartesian coordinate system are extended to the case of three-dimensional rotationally symmetric hard-edged diffracted beams in the cylindrical coordinate system. It is shown that the propagation equations of truncated second-order moments and the M(G)2 factor take forms similar to those for the nontruncated case. The closed-form expression for the M(G)2 factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams is derived that depends on the truncation parameter beta and beam order N. For N --> infinity, the M(G)2 factor equals 4/square root of 3 corresponding to the value of truncated plane waves, which guarantees consistency of the formalism.     

Approximate method for the generalized M2 factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams

On the basis of the truncated second-order moments method in the cylindrical coordinate systems and the expansion of the hard-edged aperture function into a finite sum of complex Gaussian functions, an approximate method used to calculate the generalized beam propagation factor (M2 factor) is proposed. The approximate analytical expressions of the generalized M2 factor for rotationally symmetric hard-edged diffracted flattened Gaussian beams defined by Gori [Opt. Commun. 107, 335 (1994)] and Li [Opt. Lett. 27, 1007 (2002)] are derived, respectively; we show that it depends on the beam order N and the beam truncation parameter delta. Some typical numerical examples are given to illustrate its applications that we compare by using the obtained analytical method and the numerical integration method.     

Generalized M* factor of truncated partially coherent controllable dark-hollow beams

On the basis of the fact that a hard-edged aperture function can be expanded into an approximate sum of complex Gaussian functions with finite numbers and the method of truncated second-order moments, the generalized beam propagation factor of truncated partially coherent controllable dark-hollow beams is derived. Some typical numerical simulations are given to illustrate the relations of the generalized beam propagation factor to four parameters: beam parameter ε, beam order N, truncation parameter F and coherence parameter T.     

M2-factor of truncated partially coherent beams propagating through atmospheric turbulence

A method of studying the M2-factor of truncated partially coherent beams both in free space and in turbulence is proposed, i.e., the method of the window function being expanded into a finite sum of complex-valued Gaussian functions. Taking the Gaussian Schell-model (GSM) beam as a typical example of partially coherent beams, the analytical formula of the M2-factor of truncated GSM beams propagating through atmospheric turbulence is derived. It is shown that the M2-factor decreases as the truncation parameter δ and the coherence parameter α increase. However, the M2-factor in turbulence is more sensitive to δ than that in free space. On the other hand, the M2-factor of truncated partially coherent beams with smaller δ is more affected by turbulence. In addition, the effect of turbulence on the M2-factor of truncated GSM beams is less sensitive to the coherence parameter α than that of nontruncated GSM beams.     

Generalized M2 factor of a partially coherent beam propagating through a circular hard-edged aperture

The second-order intensity moments and the beam-propagation M2 factor of partially coherent beams that propagate through a circular-symmetry hard-edged aperture are in the cylindrical coordinate system. AJo-correlated Schell-model beam with a Gaussian intensity distribution is an example. The analytical expression for the generalized M2 factor is derived. The numerical calculation results are analyzed.     

Generalized beam-propagation factor of partially coherent beams propagating through hard-edged apertures

The second-order intensity moments and beam-propagation factor (M2 factor) of partially coherent beams have been generalized to include the case of hard-edged diffraction. A laser beam with amplitude modulation and phase fluctuation and a Gaussian Schell-model beam are taken as two typical examples of partially coherent beams. Analytical expressions for the generalized M2 factor are derived.     

Complex Gaussian functions expansion method applied to truncated Gaussian beams

An analytical expression for the beam propagation factor (M ² factor) of truncated Gaussian beams was derived by using the complex Gaussian functions expansion method. The reasonability of the approximation of complex Gaussian functions expansion method is studied, and a comparison of this method with the generalised truncated second-order moments method and the asymptotic analysis method is also made. In general, an easy analytical expression for the M ² factor of truncated laser beams can be derived by using the complex Gaussian functions expansion method. The M ² factor obtained by using the complex Gaussian functions expansion method is more consistent with that in practice than that obtained by using two other methods. The analytical results obtained by using the complex Gaussian functions expansion method can be reduced to that for the non-truncated case when the truncation parameter is sufficiently large. Therefore, the complex Gaussian functions expansion method is a suitable approximation method for studying the M ² factor of truncated laser beams.     

Effect of Pressure on Elastic Constants,Generalized Stacking Fault Energy,and Dislocation Properties in Antiperovskite-Type Ni-Rich Nitrides ZnNNi3 and CdNNi3

The elastic properties and generalized stacking fault energy curves of antiperovskite-type Ni-rich nitrides MNNi₃ (M = Zn, Cd) under different pressure have been obtained from the first-principles calculations. By using the variational method, the core width and Peierls stresses of \(\frac {1}{2}\langle 110\rangle \{110\}\) edge dislocation and screw dislocation in ZnNNi₃ and CdNNi₃ within the improved Peierls-Nabarro (P-N) model in which the lattice discrete effect is taken into account have been investigated. Whatever the material or the pressure range, the Peierls stress of edge dislocation is smaller than that of screw dislocation. This also demonstrates that the edge dislocation is considered to be the dominant factor in determining the plastic behavior of MNNi₃ (M = Zn, Cd) in the pressure range of 0–30 GPa.     

Stochastic analysis of groundwater flow in a two‐dimensional generalized fractal field

Abstract

Stochastic analysis of groundwater flow in a generalized fractal field is performed in this study. The random field is described by fractional Levy motion (fLm), which is a generalized version of traditional fractional Brownian motion (fBm) and is superior to describe a field with a high degree of variability. A truncated power variogram of the fLm is derived using the weighted superposition of mutually uncorrelated exponential variograms. When the Levy index of fLm α equals 2, the fBm is recovered. When the upper and lower cutoffs of the truncated power variogram are close, the stationary exponential model can be well approximated. First‐order perturbation analyses of flow in a two‐dimensional fLm field are performed and results are compared to those in the stationary exponential and fractal fBm fields. Since the proposed general fractal model has broader applications than the stationary and fBm models, it is versatile enough to simulate flow in different scenarios and provide more accurate modeling results.     

Encircled energy for systems with truncated-Gaussian apertures of different Fresnel numbers. II. Maximizing beam energy concentration on a target

In Part I of this study [J. Opt. Soc. Am. A24, 2023 (2007)] the Q(2n) functions of E. Wolf and the Y(n) functions of H. H. Hopkins have been generalized for evaluating the fraction of the total energy in systems with focused truncated Gaussian beams by apertures of different Fresnel numbers and different ratios of aperture radius to beam radius. The generalized special functions provide a mathematical basis for a rigorous study of maximizing beam energy concentration on a target. This subject is addressed under two subtitles: (1) active focusing of a Gaussian beam onto a distant target and (2) optimizing photodetection in a focused field.     

Numerical analysis of the effects of aberrations on coherently combined fiber laser beams

Numerical analysis of the effects of aberrations on coherently combined fiber laser beams is presented. We prove that traditional beam quality criteria, such as the M2 factor and the Strehl ratio, do not consider necessary information to evaluate the quality of a coherently combined laser beam. The beam propagation factor (BPF) is introduced and studied as a proper beam quality factor for the coherently combined beam. Two main categories of aberrations, geometry and nongeometry factors, are numerically studied to investigate their effect on beam quality by using the BPF criterion. For a ring-distributed fiber laser array with certain vacancy factor and a RMS value of tilt error, we obtain a semianalytical equation to evaluate their effect on beam quality. We present a brief discussion of those aberrations at the end of this paper. Our generalized methodology offers a good reference for investigating coherent combining of fiber laser beams in a comprehensive way.     

χ-拟连续模

定义了 Q-模及 Q(χ) -模 ,证明了 M是 Q-模当且仅当 M是拟连续模以及给出了 1型χ-拟连续模和 2型χ-拟连续模的等价条件 ,并且推广了已有的一些相关的结果     

复振型导数计算的可变移频值方法

实际结构系统由于存在多种不同性质的阻尼其动态特性很复杂,振型导数的计算也比较困难。采用模态加速和移频的思想发展了一种基于模态叠加的复振型导数计算方法。首先对控制方程进行移频处理,利用广义幂级数展开式获得模态迭代公式,并利用迭代结果与各阶振型表示复振型导数;然后把系统的广义动柔度矩阵表示为已知的低阶模态与截断的高阶模态之和,高阶模态部分采用多个矩阵多项式与一个广义幂级数的乘积表示,并利用系统的低阶模态和系统矩阵进行计算;各阶移频值表示为相应的移频系数与复特征值的乘积,它们仅与最低阶模态移频值的模和本阶模态的单位复特征值有关,而最低阶模态的移频系数通过精度分析获得。给出了合适的模态加速迭代次数。该方法仅需进行一次系统矩阵的分解就可获得高精度的多个复振型导数。算例表明方法正确、高效。     

MLnBO_4陶瓷中K_2NiF_4型层状钙钛矿结构的稳定性

通过固相反应法制备了MLnBO_4(M=Ba,Sr,Ca;Ln=La,Nd,Sm,Y;B=(Zn0.5Ti0.5),(Mg_(0.5)Ti_(0.5)))陶瓷粉末,使用X射线衍射仪(XRD)分析其相组成,并结合文献中B位为Ga和Al时的结果,探讨了MLnBO_4中K_2NiF_4型层状钙钛矿结构的稳定性。当M~(2+)和B~(3+)固定时,K_2NiF_4型结构的稳定性随钙钛矿层许容因子t偏离1程度的增加而降低;但当M~(2+)或B~(3+)改变时,两者之间并无直接联系。而考虑M~(2+)、Ln~(3+)、B~(3+)离子半径的对比时,则发现K_2NiF_4型结构均出现在以r(M~(2+))/r(Ln~(3+))=1.1、r(Ln~(3+))/r(B~(3+))=2为中心的一定范围内。因此,用M~(2+)、Ln~(3+)、B~(3+)离子半径的对比衡量MLnBO_4中K_2NiF_4型层状钙钛矿结构的稳定性远较用钙钛矿层的许容因子更可靠,这对于相关材料的设计和开发具有重要意义。     

Uncertainty products for nonparaxial wave fields

Although maximal localization is a basic notion in the consideration of phase-space representations of fields, it has not yet been pursued for general wave fields. We develop measures of spatial and directional spreads for nonparaxial waves in free space. These measures are invariant under translation and rotation and are shown to reduce to the conventional ones when applied to paraxial fields. The associated uncertainty relation sets limits to joint localization in coordinate and frequency space. This relation provides a basis for the definition of a joint localization measure that is analogous to the beam propagation factor (i.e., M2) of paraxial optics. The results are first developed for two-dimensional fields and then generalized to three dimensions.     

改进的基本解法在薄体各向异性位势Cauchy问题中的应用

该文提出一种改进的基本解法,应用于薄体各向异性位势边界条件识别反问题的研究。基本解法求解反问题所产生的线性系统往往是高度病态的,我们采用截断奇异值分解方法来求解,广义交叉校验准则用来确定正则化参数。正则化方法的使用大大地拓展了源点与真实边界间距离的选取范围,同时有效地降低了解的精度对"距离选择"的敏感度。算例的数值实验表明,该文方法简单、效率高,即使薄体结构的厚度小到纳米级,仍然可获得非常高精度的数值解。该文为二维薄体各向异性位势反问题的研究开辟了新的途径,也拓展了基本解法的应用领域。     

Decontamination of sandy soils from 137Cs by reagent treatment with agitation leaching

The simplest and the most efficient method for decontamination of sandy soils is separation of the finely dispersed fraction (<0.1 mm), with which ∼90% of the contaminating radionuclides are associated, by gravity sedimentation in water. However, for sandy soils from the Russian Research Centre Kurchatov Institute, the decontamination factor in this case is as low as 4–5. The decontamination factor can be further increased by using reagent treatment. The main parameters of the process are reagent composition and concentration, temperature, and liquid to solid ratio. The decontamination factor of 10–14 can be attained by reagent treatment with 2 M H₂SO₄ + 1 M H₃PO₄ or 3–4 M H₂SO₄ solutions for 7 h at 80°C, at the liquid to solid ratio of no less than 2 : 1. Two times higher decontamination factor can be attained by treatment with a 2 M H₂SO₄ + 0.6 M NH₄F solution, but high toxicity of fluorides restricts the possibility of using this reagent.     

‘Fairy Chimney’‐Shaped Tandem Metamaterials as Double Resonance SERS Substrates

A highly tunable design for obtaining double resonance substrates to be used in surface‐enhanced Raman spectroscopy is proposed. Tandem truncated nanocones composed of Au‐SiO₂‐Au layers are designed, simulated and fabricated to obtain resonances at laser excitation and Stokes frequencies. Surface‐enhanced Raman scattering experiments are conducted to compare the enhancements obtained from double resonance substrates to those obtained from single resonance gold truncated nanocones. The best enhancement factor obtained using the new design is 3.86 × 10⁷. The resultant tandem structures are named after “Fairy Chimneys” rock formation in Cappadocia, Turkey.     

Group-theoretic approach to the enhancement of the Fourier modal method for crossed gratings: C2 symmetry case

A new formulation of the Fourier modal method for crossed gratings with symmetry considerations is established by using the group-theoretic approach that we have developed recently. Considering crossed gratings with the C2 symmetry (invariance after rotation about the normal of the mean grating plane through angle pi), we present in detail the construction of the new algorithm, illustrate the improved computation efficiency, and discuss its application. It is shown theoretically and numerically that when the grating is Littrow mounted and the truncated reciprocal lattice of the diffracted field also has the C2 symmetry, the maximum effective truncation number of the algorithm is doubled and the computation time is reduced by a factor of 4. The time saving factor is increased to 8 for the special case of normal incidence.     

Structural and morphological characterization of cerium oxide nanocrystals prepared by hydrothermal synthesis

Colloidal cerium oxide (CeO2) nanocrystals prepared by hydrothermal synthesis were characterized by high-resolution transmission electron microscopy (HRTEM) and three-dimensional electron tomography (3D-ET). HRTEM images of individual CeO2 nanocrystals were then simulated by Blochwave and multislice simulations to determine the atomic arrangement and terminating atoms. The edge length distributions were between 5.0 and 8.0 nm with an average edge length of 6.7 nm. The HRTEM images showed that the CeO2 particles were slightly truncated revealing {220} facets. 3D-ET revealed that the CeO2 nanocrystals exposed predominantly {200} cubic facets. The nanocrystals were truncated at the corners exposing {111} octahedral facets and at the edges {220} dodecahedral facets. Furthermore, 3D-ET revealed the presence of some tetragonal-shaped CeO2 nanocrystals.