Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell T-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell T-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The T-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.     

广义Helmholtz方程的Green函数及旋波介质色散关系的另一求解方法

运用并矢法求解广义Helmholtz方程,结合Fourier变换、留数定理等数学处理,给出方程的并矢Green函数解析表达式;并进一步就旋波介质给出其中色散关系的另外一种求解方法．     

单边噪声源环境下的格林函数提取

对单边噪声源环境下空间中存在散射体时的格林函数到达时间结构提取展开了实验性研究。通过对位于沙滩上的传声器上记录的海浪噪声进行互相关处理,成功提取出两传声器间的格林函数到达时间结构。到达时间结构中观察到伪散射路径,并且伪散射路径在幅值上远高于散射路径。针对上述现象给出了理论及仿真解释:当传声器对受噪声源单边照射时,广义光学定理失效,伪散射路径将会出现;同时,由于伪散射路径由所有方向噪声源贡献,散射路径仅有稳相点附近声源贡献,因此伪散射路径在幅值上可能高于散射路径。结果表明,在单边噪声源环境下,基于互相关技术可以提取伪散射路径。伪散射路径的短时稳定提取可以为散射体无源成像提供更多信息,在海洋声学、地震学等领域具有潜在应用价值。      

Cancellation of spurious arrivals in Green's function retrieval of multiple scattered waves

The Green's function for wave propagation can be extracted by cross-correlating field fluctuations excited on a closed surface that surrounds the employed receivers. This study treats an acoustic multiple scattering medium with discrete scatterers and shows that for a given source the cross-correlation of waves propagating along most combinations of scattering paths gives unphysical arrivals. Because theory predicts that the true Green's function is retrieved, such unphysical arrivals must cancel after integration over all sources. This cancellation occurs because the scattering amplitude of each scatterer satisfies the generalized optical theorem. The cross-correlation of scattered waves with themselves does not lead to the correct retrieval of scattered waves, because the cross-terms between the direct and scattered waves is essential.     

Analyzing the coda from correlating scattered surface waves

The accuracy of scattered Rayleigh waves estimated using an interferometric method is investigated. Summing the cross correlations of the wave fields measured all around the scatterers yields the Green's function between two excitation points. This accounts for the direct wave and the scattered field (coda). The correlations themselves provide insights into the location of the scatterers, as well as which scatterer is responsible for particular parts of the coda. Furthermore, these measurements confirm a constant-time arrival in the correlations, not part of the Green's function, but which has previously been derived as a result of the generalized optical theorem.     

Unified Green's function retrieval by cross correlation

It has been shown by many authors that the cross correlation of two recordings of a diffuse wave field at different receivers yields the Green's function between these receivers. Recently the theory has been extended for situations where time-reversal invariance does not hold (e.g., in attenuating media) and where source-receiver reciprocity breaks down (in moving fluids). Here we present a unified theory for Green's function retrieval that captures all these situations and, because of the unified form, readily extends to more complex situations, such as electrokinetic Green's function retrieval in poroelastic or piezoelectric media. The unified theory has a wide range of applications in "remote sensing without a source."     

Rayleigh reciprocity relations:Applications

Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of classical Rayleigh reciprocity relation: higher derivative reciprocity relations as a generalization of the classical one and a theoretical proof on the Green's function retrieval from volume noises.     

A representation for Green's function retrieval by multidimensional deconvolution

Green's function retrieval by crosscorrelation may suffer from irregularities in the source distribution, asymmetric illumination, intrinsic losses, etc. Multidimensional deconvolution (MDD) may overcome these limitations. A unified representation for Green's function retrieval by MDD is proposed. From this representation, it follows that the traditional crosscorrelation method gives a Green's function of which the source is smeared in space and time. This smearing is quantified by a space-time point-spread function (PSF), which can be retrieved from measurements at an array of receivers. MDD removes this PSF and thus deblurs and deghosts the source of the Green's function obtained by correlation.     

Recovering the acoustic Green's function from ambient noise cross correlation in an inhomogeneous moving medium

We study long-range correlation of diffuse acoustic noise fields in an arbitrary inhomogeneous, moving fluid. The flow reversal theorem is used to show that the cross-correlation function of ambient noise provides an estimate of a combination of the Green's functions corresponding to sound propagation in opposite directions between the two receivers. Measurements of the noise cross correlation allow one to quantify flow-induced acoustic nonreciprocity and evaluate both spatially averaged flow velocity and sound speed between the two points.     

水平层状介质并矢Green函数的递推矩阵方法

采用递推矩阵方法计算任意数目水平层状介质的并矢Green函数.根据层界面处电场和磁场的连续性条件得到3个确定Sommerfeld积分待定系数的矩阵方程组,分别对应于垂向单位电偶极子产生的TM波、水平方向单位电偶极子产生的TE波和TM波,这些方程组均可通过递推方法快速求解.只需改变3个方程组中源项元素的位置,就可以方便地得到当源点和场点在任意层时的并矢Green函数.本文给出的并矢Green函数表达式形式简洁且不含指数增加项,计算时不会出现溢出现象.     

On the electromagnetic dyadic Green''s functions for planar multi-layered anistropic uniaxial material media

A complete, plane-wave spectral, vector-wave function expansion of the electromagnetic, electric, and magnetic, dyadic Green's function for electric, as well as magnetic, point currents for a planar, anisotropic uniaxial multi-layered medium is presented. It is given in terms ofz-propagating, source-free vector-wave functions, where is normal to the interfaces, and it is developed via a utilization of the Lorentz reciprocity theorem. The electromagnetic dyadic Green's function for periodic electric as well as magnetic point current sources is also presented. Some salient features of the Green's dyadics, along with a physical interpretation are also described.This work was supported by the IIarry Diamond Laboratories under Contract DAAL02-88-C-0065 with Sabbagh Associates, Inc.     

Ocean acoustic interferometry

Ocean acoustic interferometry refers to an approach whereby signals recorded from a line of sources are used to infer the Green's function between two receivers. An approximation of the time domain Green's function is obtained by summing, over all source positions (stacking), the cross-correlations between the receivers. Within this paper a stationary phase argument is used to describe the relationship between the stacked cross-correlations from a line of vertical sources, located in the same vertical plane as two receivers, and the Green's function between the receivers. Theory and simulations demonstrate the approach and are in agreement with those of a modal based approach presented by others. Results indicate that the stacked cross-correlations can be directly related to the shaded Green's function, so long as the modal continuum of any sediment layers is negligible.     

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

Speckle fields are the random light wave distributions produced when the light fields are scattered from random surfaces or a random medium. They appear in many optical phenomena that are related to light propagations[1,2] and have found wide appli-cations in a variety of scientific and technical fields. The examples of the recent impor-tant applications of speckles include the analysis of the movement of the granules[3], the three-dimensional imaging for the microstructures of metal nanocryst…     

Dyadic Green‘s function for an unbounded gyroelectric chiral medium in cylindrical coordinates

The dyadic Green‘s function for an unbounded gyroelectric chiral medium is formulated in the Fourier domain in cylindrical coordinates.After a triple Fourier integral of the dyadic Green‘s function has been obtained,the integral is reduced by performing the integration over the transverse Fourier variable.     

亚波长间距理想导体球阵列近区时间反演电磁场的快速求解

为快速求解亚波长间距分布的理想导体球阵列近区的时间反演电磁场,提出一种基于等效偶极子模型的解析分析方法.首先,通过分析球面波照射理想导体小球的散射场解析解发现,散射场可以近似等效为电磁偶极子辐射场的叠加.等效偶极子的强度与初始激励源的幅度成正比关系.通过建立不同小球等效偶极子矢量间的耦合方程组可以直接求解得到相应矢量的大小.然后,结合时间反演腔理论得到相应的时间反演并矢格林函数,继而得到小球阵列近区的时间反演场分布.最后,通过与数值仿真软件的计算结果进行对比,验证了方法的正确性及高效性.研究表明,时间反演技术结合近场亚波长间距小散射体加载能够实现超分辨率的场聚焦.     

Focusing of electromagnetic waves into a uniaxial crystal

We derive integral representations suitable for studying the focusing of electromagnetic waves through a plane interface into a uniaxial crystal. To that end we start from existing exact solutions for the transmitted fields due to an arbitrary three-dimensional (3D) wave that is incident upon a plane interface separating two uniaxial crystals with arbitrary orientation of the optical axis in each medium. Then we specialize to the case in which the medium of the incident wave is isotropic and derive explicit expressions for the dyadic Green's functions associated with the transmitted fields as well as integral representations suitable for asymptotic analysis and efficient numerical evaluation. Relevant integral representations for focused 3D electromagnetic waves are also given. Next we consider the special case in which (i) the incident field is a two-dimensional (2D) TM wave and (ii) the optical axis in the crystal lies in the plane of incidence, implying that we have a 2D vectorial problem, and derive dyadic Green's functions, integral representations suitable for asymptotic and numerical treatment, and integral representations for focused TM fields. Numerical results for focused 2D TM fields based on these integral representations as well as corresponding experimental results will be presented in forthcoming papers.     

基于有限元法的光子并矢格林函数重整化及其在自发辐射率和能级移动研究中的应用

任意微纳结构中量子点的自发辐射率和能级移动均可用并矢格林函数表达.当源点和场点在同一位置时,格林函数的实部是发散的.为解决这一发散问题,可采用重整化格林函数方法.本文提出一种计算重整化格林函数和散射格林函数的方法.该方法利用有限元,计算点电偶极子的辐射场,将其在量子点体积内做平均得到重整化的并矢格林函数,减去均匀空间中解析的重整化格林函数,得到重整化的散射格林函数.在均匀空间情况下,本方法所得数值结果与解析解一致.将该方法应用到银纳米球系统,以解析的散射格林函数作为参考,结果表明该方法能准确处理散射格林函数的重整化问题.将该方法应用到表面等离激元纳米腔中,发现有极大的自发辐射增强和能级移动,且该结果不依赖于量子点的体积.这些研究在光与物质相互作用领域具有积极的意义.     

利用环境噪声互相关实现散射体无源成像

最近研究表明利用环境噪声的互相关可以恢复两点之间的时域格林函数(声脉冲响应),这一原理在文献中被称为格林函数恢复。基于此原理,通过对多个传声器所接收的环境噪声进行互相关处理,获取与散射体相关联的散射波的到达时延信息,结合最小二乘反演算法和改进克希霍夫移位算法,分别获得道路交通噪声场中石柱以及海浪噪声场中塑料桶的空间位置,且其估计结果与实际测量相一致。实验结果表明将环境噪声作为探测信号进行散射体无源成像是可行的。这为设计室内无源声监测系统以及通过海洋环境噪声实现对水中静默目标成像提供了新思路和有益参考。      

The dyadic Green's function for the cylindrical chirostrip antenna

Using the eigenfunction expansion of dyadic Green's function in unbounded chiral medium, and the method of scattering superposition, the expressions of dyadic Green's function for the one and two—layer cylindrical chirostrip antennas are derived, when the field sources are placed in any layer of cylindrical chirostrip antenna. Also, using the method of saddle point integration, the asymptotic expression of dyadic Green's function for the wraparound chirostrip antenna is obtained. The results can be directly used to analyse the radiation characteristics of cylindrical chirostrip dipolc antenna, et al.     

Imaging theory of an aplanatic system with a stratified medium based on the method for a vector coherent transfer function

A simple formalism relating image fields to object fields, similar to that of the scalar and paraxial case, is presented for an aplanatic system obeying the sine condition, which shows that the vector plane-wave spectrum of image fields is equal to the product of the vector coherent transfer function due to the x- and y-polarized point electric field source and the scalar spectrum of the corresponding transverse object fields. Utilizing this formula and dyadic Green's function, a rigorous imaging theory of an aplanatic system for the point electric current source through a stratified medium is readily developed.