Near-field and far-field modeling of scattered surface waves. Application to the apertureless scanning near-field optical microscopy

The detection of surface waves through scanning near-field optical microscopy (SNOM) is a promising technique for thermal measurements at very small scales. Recent studies have shown that electromagnetic waves, in the vicinity of a scattering structure such as an atomic force microscopy (AFM) tip, can be scattered from near to far-field and thus detected. In the present work, a model based on the finite difference time domain (FDTD) method and the near-field to far-field (NFTFF) transformation for electromagnetic waves propagation is presented. This model has been validated by studying the electromagnetic field of a dipole in vacuum and close to a dielectric substrate. Then simulations for a tetrahedral tip close to an interface are presented and discussed.     

Signal Analysis by Time-Frequency Distributions–Applications to Impulse Radar Scattering Echoes of Plate and Dihedral Corner

The scattering phenomenology of the plate and the dihedral corner are investigated using the time-frequency processing of simulated data. The FDTD method is applied to carry out the simulated data. The simulated data are next analyzed in joint time-frequency plane by using the STFT (short time Fourier transformation) technology to provide further insight into the scattering phenomenology. In addition, the time-frequency distribution series, which improves the resolution of the STFT while overcoming the cross-term interference problem of the Wigner-Ville distribution, is applied to better identify back scattering returns that are difficult to resolve in the joint time-frequency plane.     

Enhanced optical transmission through a silver plate with a slit array

The near- and far-field properties of a large-scale silver plate with a slit array are studied by applying the FDTD method. The far region scattering properties with different incident angles are also discussed. We find out that the silver plate with a suitable placed narrow slit array can excite the enhanced optical transmission (EOT) by the excitation of the surface plasmon polarition (SPP) and the Fabry-Perot resonance, and the cutoff angle is much larger than the ordinary LEDs. These unique properties suggest possible applications to the light-transparent metal contact.     

金属-电介质复合结构实现荧光远场增强

本文提出一种大尺度的金属-电介质复合微纳结构(银-硅结构),用于提高荧光生物检测的灵敏度及解决荧光物质距离结构远场范围时荧光增强的近场局限。这种大尺度的金属-电介质复合微纳结构与之前的金属-电介质复合微纳结构不同,其通过光的散射和干涉实现了荧光物质距离结构远场范围时的荧光增强。在本文中,通过采用时域有限差分法,主要从荧光激发和荧光发射两个过程研究银-硅结构。结果表明,在激发过程中,银-硅结构的荧光强度高于玻璃结构且位于银-硅结构两柱之间的狭缝中的电场分布比金属结构(银结构)更均匀,因此在银-硅结构中可以实现荧光增强,而且分子运动行为的检测更准确。在发射过程中,当荧光纳米粒子距离结构远场范围内时,与玻璃相比,银-硅结构可以实现更好的荧光增强效果。利用银-硅结构实现荧光增强的机理是光的散射和干涉,荧光被银膜向上散射,同时,结构两侧的银/硅柱也散射一部分荧光,荧光相互干涉传播至远场实现荧光增强。此外,银-硅结构易于制备和集成。因此,其可以很好地应用于生物传感领域。     

Coupling of Dirichlet-to-Neumann boundary condition and finite difference methods in curvilinear coordinates for multiple scattering

The applicability of the Dirichlet-to-Neumann technique coupled with finite difference methods is enhanced by extending it to multiple scattering from obstacles of arbitrary shape. The original boundary value problem (BVP) for the multiple scattering problem is reformulated as an interface BVP. A heterogenous medium with variable physical properties in the vicinity of the obstacles is considered. A rigorous proof of the equivalence between these two problems for smooth interfaces in two and three dimensions for any finite number of obstacles is given. The problem is written in terms of generalized curvilinear coordinates inside the computational region. Then, novel elliptic grids conforming to complex geometrical configurations of several two-dimensional obstacles are constructed and approximations of the scattered field supported by them are obtained. The numerical method developed is validated by comparing the approximate and exact far-field patterns for the scattering from two circular obstacles. In this case, for a second order finite difference scheme, a second order convergence of the numerical solution to the exact solution is easily verified.     

Inverse scattering with far-field intensity data: random surfaces that belong to a well-defined statistical class

We consider the inverse scattering problem of retrieving the surface profile function from far-field angle-resolved intensity data. The problem is approached as a nonlinear constrained optimization problem. The surface, assumed one-dimensional and perfectly conducting, is also assumed to be a realization of a Gaussian random process with a Gaussian correlation function with known standard deviation of heights (δ) and correlation length (a). Starting from rigorously calculated far-field angle-resolved scattered data, we search for the optimum profile using evolutionary strategies. Examples that illustrate the proposed scheme are presented. Aspects of the convergence and lack of uniqueness of the solution are discussed.     

Finite-difference time-domain modeling of curved material interfaces by using boundary condition equations method

To deal with the staircase approximation problem in the standard finite-difference time-domain(FDTD) simulation,the two-dimensional boundary condition equations(BCE) method is proposed in this paper.In the BCE method,the standard FDTD algorithm can be used as usual,and the curved surface is treated by adding the boundary condition equations.Thus,while maintaining the simplicity and computational efficiency of the standard FDTD algorithm,the BCE method can solve the staircase approximation problem.The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders.The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors.Moreover,the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities.     

基于目标三角面元模型生成FDTD共形网格的方法

 提出了一种基于目标三角面元数据的FDTD共形网格生成方法，该方法通过投影求交计算得到目标表面各三角面元与网格线的交点，将每条网格线与三角面元的交点按坐标进行排序，根据交点的坐标及其编号的奇偶性确定FDTD共形网格的位置，并生成相应的共形FDTD计算所需的元段长度。结合处理理想导体曲面的CFDTD方法修正共形网格上的磁场递推式。数值结果证实了共形网格生成方法的正确性和在提高FDTD方法计算精度方面的有效性。     

Fourier-transform light scattering of individual colloidal clusters

We present measurements of the scalar-field light scattering of individual dimer, trimer, and tetrahedron shapes among colloidal clusters. By measuring the electric field with quantitative phase imaging at the sample plane and then numerically propagating to the far-field scattering plane, the two-dimensional light-scattering patterns from individual colloidal clusters are effectively and precisely retrieved. The measured scattering patterns are consistent with simulated patterns calculated from the generalized multiparticle Mie solution.     

Reconstruction of the characteristics and determination of the parameters of a statistical surface roughness from light scattering data in an integrated waveguide in the presence of noise

A computer simulation is used to obtain the solution to the direct and inverse problems of the waveguide scattering of laser radiation by a stationary statistical surface roughness of the substrate of an integrated optical waveguide in the presence of additive or multiplicative white noise. It is shown that the procedure developed for processing far-field scattering data is capable of providing the necessary information on the statistical properties of the surface roughness even when the signal-to-noise ratio is very low (SNR≈1). For a given additive or multiplicative noise with SNR≥1, the proposed method allows one, in the model calculations, to reconstruct the autocorrelation function with an error within 50–80% when the roughness correlation interval varies from λ/50 to 10λ (correspondingly). In this case, the correlation interval can be determined with an error no greater than 10–30%, and an rms height of the order of 1–500 Å, with an error less than 5–15%.     

Plasmonic modes of nanobox,nanocage, and nanoframe

The scattering, absorption, and extinction cross sections of Ag nanobox, nanocage, and nanoframe illuminated by a polarized plane wave are studied using the finite element method. Our numerical results show that the plasmon modes (dipole and quadrupole modes) of a single Ag nanocage are red-shifted as the thickness of the wall decreases. In addition, the plasmon modes of porous nanocage and nanoframe are red-shifted relative to the nanobox as the surface porosity of nanocage increases. In particular, the wavelengths at the peaks of these modes almost linearly depend on the surface porosity. Moreover, the scattering efficiency of the dipole mode is much higher than the absorption one. The former is broadband, while the latter narrowband. These modes are confirmed by their far-field scattering patterns, and the corresponding surface electric field distributions are also investigated.     

Investigation of composite electromagnetic scattering from ship-like target on the randomly rough sea surface using FDTD method

Composite electromagnetic scattering from a two-dimensional (2D) ship-like target on a one-dimensional sea surface is investigated by using the finite-difference time-domain (FDTD) method. A uniaxial perfectly matched layer is adopted for truncation of FDTD lattices. The FDTD updated equations can be used for the total computation domain by choosing the uniaxial parameters properly. To validate the proposed numerical technique, a 2D infinitely long cylinder over the sea surface is taken into account first. The variation of angular distribution of the scattering changing with incident angle is calculated. The results show good agreement with the conventional moment method. Finally, the influence of the incident angle, the polarization, and the size of the ship-like target on the composite scattering coefficient is discussed in detail.     

Aberration correction for time-domain ultrasound diffraction tomography

Extensions of a time-domain diffraction tomography method, which reconstructs spatially dependent sound speed variations from far-field time-domain acoustic scattering measurements, are presented and analyzed. The resulting reconstructions are quantitative images with applications including ultrasonic mammography, and can also be considered candidate solutions to the time-domain inverse scattering problem. Here, the linearized time-domain inverse scattering problem is shown to have no general solution for finite signal bandwidth. However, an approximate solution to the linearized problem is constructed using a simple delay-and-sum method analogous to "gold standard" ultrasonic beamforming. The form of this solution suggests that the full nonlinear inverse scattering problem can be approximated by applying appropriate angle- and space-dependent time shifts to the time-domain scattering data; this analogy leads to a general approach to aberration correction. Two related methods for aberration correction are presented: one in which delays are computed from estimates of the medium using an efficient straight-ray approximation, and one in which delays are applied directly to a time-dependent linearized reconstruction. Numerical results indicate that these correction methods achieve substantial quality improvements for imaging of large scatterers. The parametric range of applicability for the time-domain diffraction tomography method is increased by about a factor of 2 by aberration correction.     

光偶极天线的远场方向性研究

用时域有限差分方法模拟了两种光偶极天线模型的场分布,研究了光偶极天线的远场辐射特性随其长度增加而变化的规律以及影响其远场方向性的因素,发现光偶极天线的远场方向性随其长度增加而变化的规律类似于经典对称振子天线的相应规律.但高阶局域表面等离激元模式的存在使得光偶极天线的远场辐射图更快地出现了旁瓣.这些发现对于提高光天线的性能具有重要意义. 关键词： 光偶极天线 局域表面等离激元 金纳米粒子 远场方向性     

指数型粗糙地面与上方矩形截面柱宽带电磁散射的时域有限差分法研究

采用土壤介电常数的四成分模型表示实际地面的介电特性,应用指数型分布粗糙面模型和Monte Carlo方法模拟实际的粗糙地面,运用时域有限差分方法研究了微分高斯脉冲波照射时粗糙地面与上方目标的宽带电磁散射问题,得出了后向复合散射系数的频率响应曲线,计算了后向复合散射系数随粗糙地面高度起伏均方根、相关长度、土壤湿度、目标尺寸、高度、倾角等几何参数及介电参数等的变化情况,并做了详细分析与讨论,得到了指数型粗糙地面与上方目标宽带电磁散射特性.     

Slat noise modeling and prediction

This paper presents a model for aircraft slat noise prediction, based on the theory of aerodynamic sound generation and the first principles of source flow physics. Starting from the theory of acoustic analogy, the noise from the high Reynolds number and low Mach number flows in the slat cove region is formulated as a general solution by the method of dimensional analysis, far-field asymptotic expansion and statistical modeling. The solution relates the far-field noise spectrum to the surface pressure statistics, the characteristic length and time scales in the surface pressure statistics and Green's function that accounts for the sound-flow coupling and propagation effects. The general solution is then used to extract scaling laws and correlation models for the individual functional dependences between the far-field noise and various parameters, including the slat noise spectral shape, its Mach number dependence and its far-field directivity. The simple scaling laws and correlation models are validated by test data and serve as building blocks to construct a slat noise prediction model.     

三维海洋波导中散射目标快速声学远场成像

研究用声传播远场分布信息成像海洋波导环境中三维散射目标的反问题,提出一种指示器样本成像方法,在不需要预先知道散射目标的任何声学和几何特性的情况下,可以快速得到其位置、形状等几何信息的一个理想的像.数值试验表明,该方法对成像海洋波导中三维散射目标是有效的,即使在有限孔径测量方式和具有噪声测量数据时,也能够得到散射目标的一个理想成像,表明海洋波导边界的多重反射效应对成像效果具有一定的正面影响.     

Lorenz-Mie Theory for Spheres Immersed in an absorbing host medium

Light scattering by particles is often used to determine velocities or concentrations of particles in gaseous or liquid streams. Within the Lorenz-Mie theory, light scattering is well understood both for a single compact spherical particle and a single multilayered particle in a non-absorbing surrounding medium. However, in some cases of practical importance the Lorenz-Mie theory in its present form may fail to describe the scattering because the host medium is absorbing (e.g. water droplets in oil). In this case, a new treatment of the scattering theory is required. In previous work, solutions were obtained in the far-field of the scattering sphere. In this paper, a rigorous solution is derived from the calculation of the total absorption rate of the particle in the host medium, which is valid for all distances from the surface of the encapsulated particle. It is shown that it is necessary to consider finite sizes R of the integrating sphere when dealing with absorbing host media. Cross-sections are defined which are characteristic quantities not only for the particle, depending on the size of a conceptual sphere around the scatterer and the imaginary part of the refractive index of the host medium. The results obtained are discussed for the case of non-absorbing host media and in the far-field approximation. Some numerical examples are given which are also related to experimental results.     

FDTD方法分析高功率微波粗糙地面散射特性

采用时域有限差分方法(FDTD)对高功率微波(HPM)近地面传输进行了仿真,其中提出的一种完全匹配层-广义完全匹配层混合吸收边界,较好地抑制了常规FDTD方法在计算低掠射角入射时产生的边缘绕射现象。将理想水平地面数值计算结果与解析法结果对比验证计算模型的正确性,通过数值计算结果分析高功率微波粗糙地面的散射特性。理论分析和仿真结果表明:粗糙地面对散射系数变化影响较明显,从宏观角度上看,散射系数曲线同理想水平地面散射系数曲线相似,即随掠射角的增大散射系数先减小后增大;从微观角度上看,由于粗糙地面的作用,其散射系数曲线并不存在布鲁斯特角,且在某一区域并非单调增加或减小。     

Closed solution to electromagnetic scattering of a plane wave by an eccentric cylinder coated with metamaterials

Closed series solution of electromagnetic scattering by an eccentric coated cylinder is achieved in matrix form. Diffracted field patterns are examined for an incident plane transverse magnetic (TM) wave. The solution is found by the classical separation of variables technique and the translational addition theorems. Wave transformation and orthogonality of the complex exponentials are employed to produce an infinite series. Numerical results are then shown by shortening the infinite series to a limited number of terms. Solutions are discussed for a dielectric or a metamaterial coating.