Lagrange method and boundary conditions for the intensity correlation functions in turbulent media*

Abstract

An exact functional integral representation for the two-point intensity correlation function was previously obtained by the author for a collimated beam wave by solving the moment equation. The variable functions of integration involved therein can be effectively limited to a set of functions determined so that the entire phase term of the integrand becomes stationary against arbitrary variation of the variable functions, exactly according to the Lagrange variational principle in dynamics. The result is free from any expansion and is presented with a set of unperturbed equations of closed form. When making a formal expansion, it leads to the zeroth- and first-order expressions similar to those obtained by an improved two-scale method. With exactly the same procedure, the three-point intensity correlation and the two-frequency intensity correlation were also obtained.The Lagrange method leads to the ‘equation of motion’ subjected to boundary conditions to continue the phase term from the incident beam wave. The boundary conditions were previously found based on a physical reasoning, while the same conditions are found here purely based an the variational principle. A focused beam wave is assumed for the incident wave, including both spherical and plane waves as special cases.     

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.     

A variational principle for the scattered wave

A Schwinger-type variational principle is presented for the scattered field in the case of scalar wave scattering with an arbitrary field incident on an object of arbitrary shape with homogeneous Dirichlet boundary conditions. The result is variationally invariant at field points ranging from the surface of the scatterer to the farfield and is an important extension of the usual Schwinger variational principle for the scattering amplitude, which is a farfield quantity. Also, a generic procedure, physically motivated by the general principles of boundary conditions and shadowing, is presented for constructing simple trial functions to approximate the fields. The variational principle and the trial function design are tested for the special case of a spherical scatterer and accurate answers are found over the entire frequency range.     

二维高斯波束对多层球粒子电磁散射的解析解

基于矢量波函数在球和柱坐标系中表达式之间的转换关系,提出了一种求解球坐标系中二维高斯波束波形因子的方法,得到了二维高斯波束波形因子在球坐标系中的解析公式.结合广义米理论推导了在轴二维高斯波束入射多层球粒子的电磁散射的解析解,并对散射强度随散射角的分布进行了数值模拟,结果与平面波入射情况进行了比较. 关键词： 矢量波函数 波形因子 电磁散射 广义米理论     

Gaussian beam scattering by a chiral sphere

Based on the generalized Lorenz–Mie theory that provides the general framework, an analytic solution to Gaussian beam scattering by a chiral sphere is constructed, by expanding the incident Gaussian beam, scattered fields and internal fields in terms of spherical vector wave functions. The unknown expansion coefficients are determined by a system of equations derived from the boundary conditions. For a localized beam model, numerical results of the normalized differential scattering cross section are presented.     

A General Spectral-Domain Formulation of the Electromagnetic Scattering by a Perfectly Conducting Circular Cylinder

A full-wave method for the two-dimensional scattering problem by a perfectly conducting circular cylinder is presented, providing an exact solution for the Helmholtz equation in very general cases. The method is based on the Fourier series expression of the boundary conditions (Dirichlet and Neumann) generated by an arbitrary, finite-power, incident beam, and the analysis is performed in the complex plane of the analytic continuation of a space spectral variable. This approach allows us to define an analytic continuation for cylindrical wave expansions, working with lossy propagation media and with a full incident spectrum, including inhomogeneous waves, both in E and in H polarization. Convergence of the modal expansion is investigated, to verify that very weak hypotheses are needed, and no geometrical or paraxial approximation is required. Extact expressions for the expansion coefficients are given, in terms of complex intergrations involving the Fourier spectrum of the incident beam.     

A variational treatment of the mixed boundary condition for the equilibrium diffusion equation

We formulate the asymptotic boundary layer analysis which leads to a mixed (Robbin) boundary condition for the equilibrium diffusion equation of radiative transfer. The information required from the nonlinear boundary layer equations to obtain the boundary condition is obtained by deriving and applying an appropriate variational principle. Based upon an examination of certain limiting cases and the good accuracy previously reported in the literature for similar variational treatments, the accuracy of this variational procedure is expected to be quite good over a wide range of conditions.     

叶绿素中用简并的四波混频产生位相复共轭后向反射波

本文报道在叶绿素溶液中用简并的四波混频得到位相复共轭后向反射波的首次实验。实验表明,转换效率在作用长度为5毫米时达22％,这是一种高效率的四能级系统。在泵浦波强度恒定的情况下,入射物波强度与复共轭反射波强度成线性关系。研究了后向反射波的位相复共轭特性。在有畸变(相位和振幅的)介质存在时,由于这种位相复共轭特性仍能获得金属丝网格高质量的再现象。 关键词：     

Self-consistent RPA based on a many-body vacuum

Self-Consistent RPA is extended in a way so that it is compatible with a variational ansatz for the ground-state wave function as a fermionic many-body vacuum. Employing the usual equation-of-motion technique, we arrive at extended RPA equations of the Self-Consistent RPA structure. In principle the Pauli principle is, therefore, fully respected. However, the correlation functions entering the RPA matrix can only be obtained from a systematic expansion in powers of some combinations of RPA amplitudes. We demonstrate for a model case that this expansion may converge rapidly.     

Diffraction of an obliquely incident wave beam by a rectangular aperture

The diffraction problem of an obliquely incident wave beam on a rectangular aperture can be reduced to that of normal incidence by expressing the incident wave beam in a form convenient for the discussion of the problem. In this paper the diffraction field is obtained by using this expression. The field is then expanded into a series of beam mode functions. The expansion coefficient of the series can be expressed in a simple form. A numerical example of the coefficient is shown for the diffraction by a half plane.     

AN EXACT METHOD FOR THE FREE VIBRATION ANALYSIS OF TIMOSHENKO-KELVIN BEAMS WITH OSCILLATORS

In this paper, a modern exact method is proposed for solving the problem of free vibrations of a Timoshenko-type viscoelastic beam with discrete rigid bodies, connected to the beam by means of viscoelastic constraints. The phenomenon of free vibrations of this discrete-continuous system is described by a set of three partial and two subsystem ordinary differential equations with generalized boundary conditions and initial conditions. Vector notation of the equations allows one to identify the self-adjoint linear operators of inertia, stiffness and damping. In this case, these operators are not homothetic hence a separation of variables in this set of equations is possible only in a complex Hilbert space. Such separation of variables leads to ordinary differential equations of motion with respect to time as well as to a set of three ordinary differential equations with respect to a spatial variable and two subsystem algebraical equations. Solution of the boundary-value problem was carried out in the classical way, but its results are complex conjugated. Using these results and the fundamental principle, describing the orthogonality property of complex eigenvectors, the problem of free vibrations of the system with arbitrary initial conditions has been finally solved exactly.     

Wave propagation in double-walled carbon nanotubes on a novel analytically nonlocal Timoshenko-beam model

This paper is concerned with the characteristics of wave propagation in double-walled carbon nanotubes (DWCNTs). The DWCNTs is simulated with a Timoshenko beam model based on the nonlocal continuum elasticity theory, referred to as an analytically nonlocal Timoshenko-beam (ANT) model. The governing equations of the DWCNTs beam consist of a set of four equations that are derived from the variational principle of the beam with high-order boundary conditions at the both ends, in which the effects of the nano-scale nonlocality and the van der Waals interaction between inner and outer tubes are inclusive. The characteristics of the wave propagation in the DWCNTs beam were analyzed with the new ANT model proposed and the comparisons with the partially nonlocal Timoshenko-beam (PNT) models in publication were made in details. The results show that the nonlocal effects of the ANT model proposed in the present study on the wave propagations are more significant because it is in stronger stiffness enhancement to the DWCNTs beam.     

Evolution of Bright Screening-photovoltaic Spatial Optical Solitons

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　Ｓｐａｔｉａｌｓｏｌｉｔｏｎｓｉｎｐｈｏｔｏｒｅｆｒａｃｔｉｖｅｍｅｄｉａｈａｖｅａｔｔｒａｃｔｅｄｍｕｃｈｉｎｔｅｒｅｓｔｉｎｔｈｅｐａｓｔｆｅｗｙｅａｒｓ[1～ 10 ] .Ａｔｐｒｅｓｅｎｔ,ｔｈｒｅｅｔｙｐｅｓｏｆｓｃａｌａｒｓｏｌｉｔｏｎｓ ( ｑｕａｓｉ ｓｔｅａｄｙ ｓｔａｔｅ[1～ 3 ] ,ｓｃｒｅｅｎｉｎｇ[4～ 8] ａｎｄｐｈｏｔｏｖｏｌｔａｉｃｓｏｌｉｔｏｎｓ[9～ 10 ] )ｈａｖｅｂｅｅｎ ｐｒｅｄｉｃｔｅｄａｎｄｆｏｕｎｄ .Ｓｏｆａｒ ,ｐｈｏｔｏｖｏｌｔａｉｃｓｏｌｉｔ…     

Lateral displacement of a Gaussian beam reflected from absorbing media

Lateral displacements of well-focused beams reflected from absorbing media are demonstrated in this paper. The incident beam is modeled as a tapered wave with a Gaussian spectrum. The field solutions are obtained on both sides of the interface by solving analytically from Maxwell's equations and by matching the boundary conditions at the interface. Numerical simulations are presented and the field values as well as the time-averaged power densities are computed. The influences of the polarization, the angle of incidence and the beam width on the displacement are discussed. The origin of the displacement lies in the absorption of the media, for which there is a phase shift between the incident and reflected waves. Because of this phase shift, the center of the reflected beam does not coincide with that of the incident one, similar to the Goos-Hänchen shift.     

可调分束角棱镜分束光强比研究

利用相位匹配条件,坐标转换和菲涅耳公式推导出了可调分束角棱镜的光强分束比的数学表达式,分析了光束的入射角、棱镜的结构角,以及入射波长对光强分束比的影响,给出了使光强分束比为1的条件,并进行了实验测试,测试结果与理论分析相一致,为设计出射光强相等或近似相等的可调分束角棱镜提供了理论依据。     

Energy Minigaps in the Quantum Wires with Lateral Surface Structures

Energy minigaps caused by lateral surface structures in quasi-one-dimensional GaAs/AlAs quantum wires are calculated with the variational and degenerate-pert urbational approaches. By a coordinate transformation, the structured interfaces of wires are transformed into planar ones so that the boundary conditions of the electronic wave functions can be satisfied exactly on the interfaces. The dependence of energy minigaps on lateral surface structures are discussed.     

Scattering of shaped beam by an arbitrarily oriented spheroid having layers with non-confocal boundaries

An approach to express an incident shaped beam with respect to an arbitrarily oriented spheroidal particle having layers with non-confocal boundaries is presented. To overcome the difficulty of non-confocal boundary conditions connected with different spheroidal coordinate systems, a theoretical procedure is developed to deal with the non-confocal boundary conditions by virtue of a transformation for vector wave functions. The unknown coefficients of scattered and internal electromagnetic fields are determined by solving a system of linear equations derived from the boundary conditions and relations between the spheroidal vector wave functions and spherical ones. Numerical results of the normalized scattering cross section for a two-layered non-confocal prolate spheroid are evaluated. PACS 42.25.Fx; 42.25.Bs     

Diffraction of X-ray spatially inhomogeneous beam in a crystal with cubic nonlinearity

Diffraction of a spatially inhomogeneous X-ray wave was theoretically studied in a crystal with cubic nonlinear response to the strength of an external electric field. Using numerical calculations in case of two-beam diffraction of a narrow incident beam, the intensity distributions on the output surface of the crystal was investigated depending on the thickness and intensity of the incident beam. The results of numerical calculations of integral (spatial) coefficients of transmission and reflection are given as functions of incident wave intensity for fixed thickness of the crystal.     

Analytic solution of the Boltzmann-equation for radiative transfer and neutron transport in plane geometry

A power series expansion method for solving the multi-group transport equation in plane-parallel geometry is presented. In this method, the radiation intensity is separated into forward and backward components, which are then expanded in powers of the space variable, while the angular variable is treated exactly. The generalized boundary conditions considered in the analysis allow radiative heat transfer and neutron transport problems to be handled by the same formalism. Analytical expressions are derived for the angular distribution and the angle-integrated intensities by solving a matrix problem in which the matrix elements are integrals over rational functions of the angular variable. Two test problems describing completely different physical situations illustrate the usefulness and generality of the present method.