Interface response and scattering matrix theories for composite systems

The main general results of a new interface response theory for composite systems in d-dimensional discrete spaces are given. A scattering matrix theory is then proposed also for the first time for any composite system     

Laboratory measurements of single light scattering by ensembles of randomly oriented small irregular particles in air. A review

In this paper we present an overview of light scattering experiments devoted to measure one or more elements of the scattering matrix as functions of the scattering angle of ensembles of randomly oriented small irregular particles in air. A summary of the most important findings in light scattering experiments on ensembles of randomly oriented particles in air is given. The particles of interest are relevant for studies of atmospheres of planets and satellites and also for other astronomical bodies and environments. Some applications of light scattering experiments are also presented.     

Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack

A theoretical method is described for calculating the bidirectional scattering characteristic for any given thin-film multilayer geometry in which the surfaces and interfaces are assumed to be rough, and where statistical inhomogeneities in the optical permittivities may also exist in each layer. The light energy scattered in any direction depends on geometrical thickness, the permittivities of the ideal layer stack and also on the corresponding auto- and cross-correlation functions. The expressions that are obtained for the scattered field are completely general in the sense of the Born approximation of first order in the imperfections and the exciting fields. The contributions of interface and volume scattering can be assumed arbitrarily because both are derived in a unique way. The main new result consists in the occurrence of four different possibilities of coupling between the scattered and exciting waves due to the standing wave character of both light waves. It is easy to show that the case of a columnar structure reduces the theoretical effort and leads to a similarity of this volume case to that of normal interface scattering. The matrix formalism used in analogy to the normal calculations of reflection and transmission coefficients allows a simple physical interpretation of the light propagation through the layer system and straightforward numerical calculations.     

Modification of the matrix-operator method for solving the equation of radiative transfer

Our proposed method shortens the time needed to calculate the radiation field when the albedo for single scattering is not close to unity. An algorithm is given for reflection-operator calculations in a semi-infinite medium. The reflection and transmission matrices may be expressed in terms of this operator for any value of the optical depth. The calculation time is shorter because the doubling algorithm is reduced to a single matrix multiplication, while in the classical method, five matrix multiplications and one inversion must be carried out for each step of optical-depth doubling.     

Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack

Abstract

A theoretical method is described for calculating the bidirectional scattering characteristic for any given thin-film multilayer geometry in which the surfaces and interfaces are assumed to be rough, and where statistical inhomogeneities in the optical permittivities may also exist in each layer. The light energy scattered in any direction depends on geometrical thickness, the permittivities of the ideal layer stack and also on the corresponding auto- and cross-correlation functions. The expressions that are obtained for the scattered field are completely general in the sense of the Born approximation of first order in the imperfections and the exciting fields. The contributions of interface and volume scattering can be assumed arbitrarily because both are derived in a unique way. The main new result consists in the occurrence of four different possibilities of coupling between the scattered and exciting waves due to the standing wave character of both light waves. It is easy to show that the case of a columnar structure reduces the theoretical effort and leads to a similarity of this volume case to that of normal interface scattering. The matrix formalism used in analogy to the normal calculations of reflection and transmission coefficients allows a simple physical interpretation of the light propagation through the layer system and straightforward numerical calculations.     

Scattering Matrix Modeling of Photon Migration in Turbid Media

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Scattering Matrix Modeling of Photon Migration in Turbid Media

A lattice random walk model based on walkers wandering on discrete lattice of scattering space by discrete spatial and temporal step is presented. The scattering matrix and linking matrix of the lattice random walk are given for the scattering and absorption processes in homogenous and inhomogeneous turbid media. All the results obey the principle of causality.     

Study on light scattering by a multilayered infinite cylinder immersed in an absorbing medium

On the basis of the theory of electromagnetic scattering of plane waves by a multilayered cylinder, analytic solutions are developed for single scattering properties of an inhomogeneous cylinder embedded in an absorbing medium with normal incidence, and the rapid recursive algorithm is given. Results show that computations for scattering field in our code are extended to fairly large parameters, up to 10,000 and 10⁶ in number of layers. Some examples are simulated to validate the code, and compared with the published results with good agreement. The variations of the scattering matrix with the scattering angles of the homogeneous and inhomogeneous cylinders are simulated. The results show that the scattering matrix depends closely on the refractive index of the surroundings, and the explanation of the scattering mechanism is given.     

最弱受约束电子势模型散射态的精确解

研究了最弱受约束电子势模型的散射态性质，获得了扭曲库仑波的解析解．给出了精确的按“k/2π标度”归一化的散射态波函数及相移表达式．讨论了散射振幅的解析性质，给出了束缚-连续跃迁矩阵元的解析计算公式．结果可广泛应用于处理原子的散射问题 关键词：     

Quantum theory of transverse galvano-magnetic phenomena

A quantum theory of electrical conduction in crosfsed electric and magnetic fields is given for the limit of very weak scattering. A density matrix formulation of the problem is used, and an arbitrary scattering mechanism is considered. The theory is found to be completely equivalent to theories given earlier by and by and .

Formulae are given for the resistivity in the quantum limit for both longitudinal and transverse orientations of electric field, for degenerate and non-degenerate statistics, and for several different scattering mechanisms. The oscillatory conductivity is calculated for acoustical and ionized-impurity scattering mechanisms. Formulae obtained for the quantum transport effects are in disagreement with the formulae of and of . The discrepancy is attributed to unwarranted approximations in those authors' treatments of scattering.     

Wave-obstacle interaction in a lossy medium: energy perturbations and negative extinction

The concept of a generalized extinction cross-section introduced in a previous paper is given in detail and exemplified by the problem of scattering by an elastic cylinder embedded in a viscoelastic matrix. It is shown that under certain conditions the presence of inclusion may have a supporting effect on wave propagation (negative extinction). The derived low-frequency expansions indicate that the Rayleigh law may not hold in the case of a lossy medium. Numerical results as well as discussions concerning separation between scattering and intrinsic viscoelastic losses are also given.     

涂层目标1.06μm偏振双向反射分布函数测量方法研究

为了获取复杂涂层目标的光学散射特性,介绍了一套全自动偏振双向反射分布函数测量系统,可以测量半球空间内几乎所有角度下的偏振双向反射分布函数。采用双波片旋转法实现了对光的偏振调制,利用离散傅里叶变换反演出了涂层目标的Muller矩阵。给出了某涂层样品的测量结果与模型的计算比较。结果表明,这种方法是一种测量涂层目标偏振双向反射分布函数的有效方法。     

A dispersion relation for the density of states with application to the Casimir effect

The trace of a function of a Schrödinger operator minus the same for the Laplacian can be expressed in terms of the determinant of its scattering matrix. The naive formula for this determinant is divergent. Using a dispersion relation, we find another expression for it which is convergent, but needs one piece of information beyond the scattering matrix: the spatial integral of the potential. Except for this ‘anomaly’, we can express the Casimir energy of a compact body in terms of its optical scattering matrix, without assuming any rotational symmetry for its shape.     

n维氢原子的散射态

研究了n维氢原子的散射态性质．给出了精确的按“k/2π标度”归一化的散射态的精确解波函数及相移表达式，讨论了相移的解析性质，获得了束缚-连续跃迁矩阵元的解析计算公式．普通氢原子(n=3)散射态的有关结果作为特例包含在本文的一般结论之中． 关键词： n维氢原子 散射态 精确解 相移 束缚-连续跃迁矩阵元     

散射介质超衍射极限技术研究进展

综述了已有散射介质超衍射极限聚焦和成像技术的研究现状及进展。首先介绍了这一领域的研究背景及意义,以及已有超衍射极限成像技术的发展现状;然后给出了应用于超衍射极限成像的散射介质定义;其次分析了时间反演技术在声学、微波领域聚焦上的应用,介绍了时间反演法在光学领域超衍射极限聚焦应用中的实现方法,总结了散射介质加入到光学系统中的作用,分析了利用反馈控制调节和光学相位共轭方法进行散射介质超衍射极限聚焦方法的特点;讨论了基于空域和空频域传输矩阵测量的散射介质宽场成像方法及在该目的下的散射介质制备方法;最后给出了散射介质光学超衍射极限成像技术研究前景及展望。     

自旋梯可积模型的研究

通过对自旋梯可积模型的研究,求出该模型的能量本征值和两体散射矩阵.用可积模型中的坐标Bethe Ansatz方法,首先由薛定谔方程求得能量的本征方程.设定波函数的具体形式,求出本征能量,然后利用能量本征方程和波函数的连续性求出两体散射矩阵.求出单粒子、双粒子和N₀个粒子的本征能量,同时求得粒子的两体散射矩阵.自旋梯可积模型的本征能量和两体散射矩阵可通过Bethe Ansatz的方法求得.     

时间相关的多道散射理论

本文把Lippmann-Schwinger等人关于散射理论的时间相关方案扩充到多道情况。Ekstein在1956年也曾试图进行这样的扩充工作。值得特别提到,他所指出并着重引用的事实,即多道情况下的射出(或射入)本征态组的广泛的正交性质,是极为重要的,这是建立散射矩阵概念的基础。但是,Ekstein没有充分利用Lippmann-Schwinger等人的方案所包含的相当普遍的出发点,原方案的简明性没有保留下来。而且由于无法用一个单独的相互作用表示来建立散射算符,就认为散射矩阵不能看作某种线性算符的表示,使散射矩阵的概念含混起来。本文保持原有Lippmann-Schwinger方案的基本精神及简明性而把它扩充为多道理论。给出了散射算符的明显形式。跃迁几率与散射矩阵的关系可以按照单道情形的方法来推导。 关键词：     

Light transmission in inhomogeneous birefringent medium as a function of propagation and observation angles

We use the Mueller matrix for inhomogeneous linear birefringent media derived in Savenkov et al. [Mueller-matrix model of an inhomogeneous linear birefringent medium: single scattering case. JQSRT 2007;106:475–86] to generate new results on the forward scattering of light using Cloude's coherence matrix method. We show that the intensity of scattered light (m₁₁) as a function of observation angle depends on the difference between refractive indices along the eigen polarizations resulting in intensity lost when unpolarized light propagates parallel to the optical axes compared to propagation orthogonal to the optical axis. For a given inhomogeneity (roughness), depolarization strongly depends on the direction of light propagation in the medium. The depolarization at 90° propagation angle is minimal for any value of inhomogeneity. Sample calculations are based on calcite.     

Application of the Sherman-Morisson formula to scattering problems by multi-component systems

The scattering matrix for multi-component systems is recalculated using the extended form of the Sherman-Morisson formula. The matrix elements are given explicitly in closed form. The Gibbs-Duhem relation separates the density and composition contributions. Received 5 April 2002     

Eigenvectors of the multichannel scattering matrix at resonance energy values

Explicit representations for the T matrix and the scattering matrix analytically continued to unphysical energy sheets in a multichannel problem featuring binary channels are discussed. From these representations, it follows that a resonance on a given unphysical sheet arises at the (complex) energy value for which the appropriately truncated scattering matrix considered on the physical sheet has zero eigenvalue. It is shown that the channel components of that eigenvector of the truncated scattering matrix which corresponds to zero eigenvalue at a resonance energy value have the meaning of breakup amplitudes for the respective resonance state of the multichannel system being considered.