Physics in plasmonic and Mie scattered near-field for efficient surface-enhanced Raman scattering template

We describe the physics of the SERS based on the optical near-field intensity enhancement on the metallic (plasmonic) and the nonmetallic (Mie scattering) nanostructured substrates with two-dimensional (2D) periodic nanohole arrays. The calculation by the Finite-Difference Time-Domain (FDTD) method revealed that the optical intensity enhancement increases with the increase of the thickness of a gold film coating on the nonmetallic (dielectric) nanostructured Si, GaAs, and SiC substrates. The resonance spectrum shifts with the changes in the geometrical structure of the void diameter and inter-void distance. It was clarified that the optical intensity enhancement obtained with the gold-coated substrate is equivalent to that with a gold substrate at 70-nm thick gold coating on the dielectric substrates in this structure. The resonance spectral bandwidth for Mie scattering and plasmonic near-fields is different. Therefore, if the Stokes line of the Raman scattering is located within the resonance bandwidth, the SERS signal is enhanced proportionally to the fourth power of the electric near-field. However, if the Stokes shift is located out of the resonance bandwidth, the SERS signal enhancement is only proportional to the square of the scattered near-field.     

Diffraction radiation from an inhomogeneous dielectric film on the surface of a perfect conductor

Diffraction radiation generated by a charged particle moving uniformly parallel to the surface of a perfect conductor coated with a dielectric film is considered; the thickness of the film is an arbitrary function of coordinates. A particular case is considered when this function is periodic in one coordinate. The dependence of radiation on the profile of an individual irregularity of the periodic film is analyzed in detail for an arbitrary energy of the particle.     

Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles

We have applied a method of reducing the number of iterations required to solve a system of linear equations in the discrete dipole approximation. This method obtains an initial guess of dipole polarization from those with similar particle characteristics (e.g., the size parameter and refractive index) calculated a priori. If the initial guess is closer to the solution, the number of iterations of the linear equation solution becomes smaller than that calculated with an arbitrary initial value.

This method was applied to various particle orientations using spline interpolation of the initial guess of dipole polarization from orientations calculated a priori.

We studied three types of particle model: an aggregate, a deformed sphere with moderate surface roughness, and a particle with a large number of edges. For the particle with a large number of edges, we propose a new model called the overlapping mixture of multiple tetrahedra (OMMT).

The proposed method is most advantageous for particles with moderate surface roughness (e.g., a deformed sphere), for which the calculation time was reduced to 20–40% of the original calculation time. For OMMT and an aggregate, the computation time was reduced to 30–60% and 40–90%, respectively. The differences in the scattering coefficient, absorption coefficient, intensity and polarization introduced by our method were less than 0.008%, 0.03%, 0.1%, and 0.08%, respectively.

If the light scattering properties vary slowly with the orientation variation, interpolation of the results is more efficient than the proposed method and produces only a small difference in the results. However, the interpolation of the results fails for particles such as BCCA64, for which our proposed method produces more accurate results.     

Influence of particle size on XRF wear analysis in plastics processing

Wear has to be quantified by the analytical characterization of particles in a plastic film generated by an extruder. The influence of particle size, film (matrix) thickness and particle location on the intensity of the Fe Kα peak, the Fe Kβ/Kα intensity ratios and the Compton scattering peak intensity are discussed. Experimental results are given for two synthetic matrices, vaseline and transparent tape. A comparison of the measured results with those of a simulation is made. Copyright © 2005 John Wiley & Sons, Ltd.     

Light scattering by a sphere with variable optical properties of the intermediate layer

A two-parameter model of a scattering spherical particle with a layer of a variable thickness (the first parameter), inside which the refractive index is specified by an arbitrary continuous function (the second parameter), is proposed. An algorithm for calculating the extinction and backscattering efficiency factors with the help of a developed piecewise-hyperbolic approximation of the scattering coefficients is presented. A correct choice of the parameters allowed us to obtain good agreement between the experimental and calculated data on the extinction and backscattering efficiency for typical polydisperse systems of particles of irregular shape.     

Relative intensities in X-ray photoelectron spectra: Part VII. The effect of elastic scattering in a solid on the angular distribution of photoelectrons escaping from samples covered with thin films of various thicknesses

The angular distributions of X-ray photoelectron peak intensity for (1) a semi-infinite sample, (2) a substrate sample covered with a film, and (3) an overlayer sample are calculated by the Monte-Carlo method. The elastic as well as the inelastic scattering of electrons in a solid is taken into account. In all cases the elastic scattering is shown to have a significant effect on both the absolute value of peak intensity and the angular distribution of photoelectrons. The electron mean free paths without inelastic collisions (λ_n) calculated using formulas derived without taking account of elastic scattering are shown to differ significantly from the real values. Moreover, the λ_n values calculated in this way are not physical constants at all, but depend for example on the film thickness and the intervals of photoelectron take-off angles under consideration. The elastic scattering effect is shown capable of explaining some difficulties which arise in the interpretation of experimental data reported in the literature on the basis of expressions derived taking into account only the inelastic interactions of photoelectrons with a solid.     

Radiation pressure in the case of the scattering of an arbitrary field by a complex-shaped inclusion

The radiation pressure on a complex-shaped inclusion in an ideal liquid in the primary field of an arbitrary configuration is calculated. The solution is sought in terms of the scattering problem in the linear approximation. For the components of radiation pressure in an arbitrary primary field, expressions involving the resulting scattering amplitude are presented. The expressions are simplified for a number of particular cases. The results of the study can be used for inclusions with complicated scattering amplitudes, and the derived expressions considerably extend the ranges of fields and scatterers for which the radiation pressure can be calculated. An example of calculation is presented.     

微小颗粒的光散射数值模拟

简单介绍了以经典Mie理论为基础的光散射测量技术在颗粒直径和颗粒浓度测量中广泛的应用。分别以Mie理论和离散偶极子近似理论(DDA)为基础, 用数值计算方法分析了球型颗粒的光散射特性，给出了微小颗粒对平行入射光散射的强度函数和散射偏振度的数值计算方法。得到了强度函数和偏振度随相关物理参量变化的三维图，为微小颗粒散射研究提供了一种三维视图。计算结果表明：当尺度参量x＜4时，2种方法所得结果差异不大；随尺度参量增大，2种方法所得结果出现较大差异。与经典Mie理论相比，由于离散偶极子近似理论可以解决各种形状的颗粒散射问题，其应用前景更广泛。     

Scattering from a Multi-Layered Sphere Located in a High-Order Hermite-Gaussian Beam

Scattering of a high-order Hermite-Gaussian beam by a multi-layered sphere is analyzed. The incident high- order Hermite-Gaussian beam field is expressed by the complex-source-point method and expanded in terms of spherical vector wave functions. The beam shape coefficients of the Hermite-Gaussian beam are obtained. Under electromagnetic field boundary conditions, coefficients in the expressions of scattering fields are derived. Results of the numerical calculation of scattering intensity are presented. The effects of the particle parameters and beam parameters on scattering intensity are discussed in detail.     

Mie光散射理论的数值计算方法

Mie散射级数的计算速度和精度对颗粒测量结果有着重要的影响。针对不同颗粒直径和相对折射率，一般采用前向递推，后向递推，连分式法等计算Mie散射级数。在这3种方法的基础上提出一种改进算法，即首先通过连分式法计算Mie散射级数的初始值，然后后向递推其余各值。该算法在Matlab中实现时，数据以数组的数据类型存储和调用，程序采用递归算法。通过比较计算结果发现，该算法耗时短且结果不易溢出，具有快速、稳定、不受颗粒直径和折射率范围影响等优点。     

Enhanced scattering from a thin film with one-dimensional disorder

This paper deals with a TE plane wave scattering from a thin film with one-dimensional disorder by means of the stochastic functional approach. The thin film is one-dimensionally inhomogeneous in the horizontal direction with infinite extent, and is homogeneous in the vertical direction with finite thickness. Based on an approximate wavefield representation in terms of a Wiener–Hermite expansion in a preceding paper (Tamura et al., 2004, Waves in Random Media, 14, 435–465), the first- and second-order incoherent scattering cross-sections are presented in explicit forms and scattering properties are discussed. The scattering properties vary entirely with the film thickness. In a case where the thickness is smaller than a few wavelengths in the thin film, enhanced scattering and associated enhanced scattering may appear as sharp peaks or dips on the second-order incoherent scattering distribution if the thin film has guided wave modes. When the thickness becomes sufficiently larger than the wavelength inside the film, a new enhanced scattering phenomenon appears as gentle peaks on the second-order incoherent scattering distribution in four special directions. Such four directions are the directions of forward scattering, specular reflection, backscattering, and the symmetrical direction of forward scattering with respect to the normal of the film surface.The first-order incoherent scattering occurs distinctly in four such directions. Such enhanced scattering is independent of the existence of the guided wave modes inside the thin film, and deeply relates to the structure of the thin film with one-dimensional disorder that has infinite correlation in the vertical direction. For SiC and glass thin films having one-dimensional disorder with a Gaussian correlation and three types of exponential correlation, the first- and second-order incoherent scattering cross-sections are illustrated in figures. The narrow enhanced scattering peaks appear for the glass film in a thin case. The gentle enhanced peaks turn up for both the SiC and glass films in a thick case. Furthermore, the optical theorem is calculated for several cases. It is then found that the error of the optical theorem decreases and the performance of the wavefield is improved by taking into account the second-order incoherent scattering.     

Enhanced scattering from a thin film with one-dimensional disorder

This paper deals with a TE plane wave scattering from a thin film with one-dimensional disorder by means of the stochastic functional approach. The thin film is one-dimensionally inhomogeneous in the horizontal direction with infinite extent, and is homogeneous in the vertical direction with finite thickness. Based on an approximate wavefield representation in terms of a Wiener-Hermite expansion in a preceding paper (Tamura et al., 2004, Waves in Random Media, 14, 435-465), the first- and second-order incoherent scattering cross-sections are presented in explicit forms and scattering properties are discussed. The scattering properties vary entirely with the film thickness. In a case where the thickness is smaller than a few wavelengths in the thin film, enhanced scattering and associated enhanced scattering may appear as sharp peaks or dips on the second-order incoherent scattering distribution if the thin film has guided wave modes. When the thickness becomes sufficiently larger than the wavelength inside the film, a new enhanced scattering phenomenon appears as gentle peaks on the second-order incoherent scattering distribution in four special directions. Such four directions are the directions of forward scattering, specular reflection, backscattering, and the symmetrical direction of forward scattering with respect to the normal of the film surface.The first-order incoherent scattering occurs distinctly in four such directions. Such enhanced scattering is independent of the existence of the guided wave modes inside the thin film, and deeply relates to the structure of the thin film with one-dimensional disorder that has infinite correlation in the vertical direction. For SiC and glass thin films having one-dimensional disorder with a Gaussian correlation and three types of exponential correlation, the first- and second-order incoherent scattering cross-sections are illustrated in figures. The narrow enhanced scattering peaks appear for the glass film in a thin case. The gentle enhanced peaks turn up for both the SiC and glass films in a thick case. Furthermore, the optical theorem is calculated for several cases. It is then found that the error of the optical theorem decreases and the performance of the wavefield is improved by taking into account the second-order incoherent scattering.     

偏振X射线荧光分析尾矿薄层样品的散射校正方法研究

了解尾矿浆中的重金属元素含量能为矿物浮选提供决策依据,不仅可以提高矿物的利用率,还可减少环境污染。X射线荧光光谱法是一种常用的重金属元素分析技术,对于地质类样品的分析,康普顿散射内标法是一种常用的定量方法。但对于薄层沉积样品,其康普顿散射峰强度会受到支撑滤膜的散射影响。由于样品紧密附着在支撑滤膜上,难以直接获得来自样品本身的康普顿散射强度,不利于直接应用康普顿散射峰强度进行定量分析。以尾矿薄层样品为分析对象,研究了不同聚丙烯滤膜厚度对康普顿散射峰强度的影响,并对薄层样品的康普顿散射强度进行了校正。实验结果表明,在0.34～3.06 mm厚度范围内,康普顿散射峰强度随聚丙烯滤膜厚度的增加线性增加,通过建立探测器获得的总康普顿散射强度与滤膜厚度的线性关系,计算出样品的净康普顿散射峰强度。为验证该修正方法的可靠性,利用蒙特卡洛方法模拟研究了无滤膜的尾矿样品和带有不同厚度滤膜的尾矿样品,结果显示经滤膜厚度影响修正后的净康普顿散射峰强度与无滤膜样品康普顿散射峰强度基本一致,相对偏差为0.41%。同时通过实验和模拟计算了0.34 mm厚聚丙烯滤膜时修正后的净康普顿散射峰强度占总康普顿散射峰的比例,分别为91.31%和89.91%,二者基本一致。最后,利用了上述基于滤膜厚度康普顿散射影响的校正方法,建立了基于康普顿散射内标法的定量校准曲线,对两种尾矿浆中的Cu,Zn和Pb元素的定量分析结果显示,未经滤膜厚度修正的康普顿内标校正相比校正前,部分元素定量结果与ICP-OES结果相比,其相对偏差反而增加3.18%～9.00%。而经滤膜厚度修正的康普顿内标方法的定量结果与ICP-OES结果的相对误差在1.14%～11.15%之间,相比于校正之前,相对偏差减少了0.30%～8.97%。     

非晶态Se薄膜的自发晶化研究

利用真空热蒸镀的方法制备了非晶Se薄膜,测试了稳定的非晶Se薄膜,不稳定的非晶Se薄膜和初始自发晶化的非晶Se薄膜的透射率光谱和拉曼光谱,对透射率光谱曲线进行了拟合,计算了薄膜的厚度和折射率随波长的变化关系。在自我晶化过程中,Se薄膜折射率逐渐增大;随波长增大,折射率则减小,初始自发晶体的Se薄膜中,出现标志Se8环和链的结构,不完整的环和链结构在自发晶化过程中得到了增强。     

基于MATLAB与LabVIEW的 Mie散射参数分析系统

针对激光散射法测量0.1 m~10 m微小球形颗粒过程中,Mie散射理论各参数的分析、计算、最优化选取比较复杂和繁琐,通过收敛速度、折射率和尺度参数测量范围、叠加次数的比较,采用球形粒子Mie散射参量的MATLAB改进算法, 结合MATLAB较强的计算能力和LabVIEW良好的图形化界面,进行LabVIEW和MATLAB混合编程。设计了Mie散射理论参数分析系统,系统实现散射系数的计算,并分别对散射系数与颗粒直径关系曲线、散射强度分布曲线、入射光波长与散射光强关系曲线、颗粒直径与散射光强关系曲线、入射光偏振角与散射光强关系曲线进行分析。通过实验结果和结论对比验证系统可行,且散射系数、消光系数和散射光强的计算结果可精确到小数点后17位,从而达到减少大量计算和编程工作的目的。     

General derivation of the total electromagnetic cross sections for an arbitrary particle

This work concerns a common problem in electromagnetic scattering; calculation of the total scattering, extinction, and absorption cross sections for an arbitrary particle. Typical expressions for the cross sections are obtained in terms of the vector spherical wave function expansions for the incident and scattered waves. The unique aspect of this work is that the derivation is carried out specifically without use of the far-field zone approximation. The resulting expressions, valid at any distance, exactly match those obtained from the far-field approximation. This demonstrates that the cross sections are independent of the distance from the particle at which they are calculated as one would expect from energy conservation. Numerical simulations of the near and far-field zone energy flows due to a spherical particle are presented to illustrate several implications of this result.     

Elastic scattering amplitude of a scalar particle in a plane wave field

The elastic scattering amplitude of a scalar particle in an arbitrary plane wave electromagnetic field is obtained in the form of a double integral by the method of dispersion relations. Particular cases of giving the plane wave field are investigated. It is shown that the existence of scalar particle radiation in an arbitrary plane wave electromagnetic field results in elastic scattering, whose amplitude determines the change in particle mass in this field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 32–37, May, 1990.     

Locally enhanced light–matter interaction of MoS2 monolayers at density-controllable nanogrooves of template-stripped Ag films

Transition metal dichalcogenide (TMD) monolayers, such as MoS_2, possess a direct optical bandgap are useful for emerging ultrathin optoelectronics in the visible light range, whereas their thin thickness limits light absorption and emission properties. To address this drawback, one promising approach is to hybridize plasmonic nanostructures with monolayer TMDs to utilize local field enhancement effects owing to localized surface plasmon resonance (LSPR). Herein, we propose a strong enhancement of the local light–matter interaction in MoS₂ monolayers on naturally generated nanoscale grooves. The nanogrooves are formed at grain boundaries (GBs) of template-stripped metal film substrates that are fabricated by mechanically stripping Ag films deposited on an ultra-flat Si substrate, wherein the nanogroove densities are systematically modulated by the Ag film thickness. We observe an effective photoluminescence enhancement factor of 758 and a Raman spectroscopy intensity enhancement of approximately 5 times in MoS₂ on the subwavelength-scale nanogrooves, compared with that on grain planes, which is attributed to a strong local field enhancement of the LSPR effect. Moreover, this plasmonic enhancement effect is elucidated by dark-field scattering spectroscopy and optical simulations. Our results can facilitate the utilization of density-controllable plasmonic nanogrooves synthesized without nanopatterning techniques for plasmonic hybrids on 2D semiconductors.     

光学厚度对颗粒媒质的多重散射的影响

基于辐射传播方程及多重散射基础理论,利用Fraunhofer近似,对颗粒媒质的多重散射光强进行了计算。研究了光学厚度对多重散射的影响,揭示了多重光散射的角分布特征,光强大小随光学厚度的变化,以及单散射引起的误差等方面的规律。为实际的颗粒媒质的光学测量等提供了理论根据。     

反射干涉光谱法测量固体薄膜的光学常数和厚度

本文报道一种简单的方法,从平原介质薄膜的反射干涉光谱来计算薄膜的光学常数和厚度。当一束光照射在基板上的介质膜上时,由于膜上下界面反射光的相干,会使反射光谱的曲线有一定的波动。我们对反射相干光谱进行理论分析,给出计算公式,从测量曲线中的实验值得出薄膜的光学常数ｎ、ｋ以及厚度等参数。此种方法简单可行,而且易于编程处理。