介质波导并矢格林函数的本征模展开式

本文对于任意形状阶梯折射率光波导和任意缓变折射率光波导,利用算符理论方法,推导出介质波导的并矢格林函数本征模展开式的通用表达式。得到的电型并矢格林函数表达式由包括九个并矢分量的本征模展开式和一个奇异项组成。根据这个表达式,只要给定介质波导的本征模,就可以得到该波导的并矢格林函数。     

求解格林函数的本征函数法

从本征函数理论出发，本文介绍了求解第一类格林函数的本征函数法。从而对格林函数的本征函数法建立进行一般的理论概括。最后举例说明应用。     

二维光子晶体波导与单模平面介质波导间的喇叭波导接头

提出并优化了用于二维介质柱光子晶体波导与单模平面介质波导对接的基于分布布拉格反射波导的喇叭波导接头，提高了这两种波导之间的传输效率.二维时域有限差分仿真结果表明，在大部分光子晶体波导导模的频谱范围内，传输效率高于98％.传输效率最高可以达到99.85％. 关键词： 光子晶体波导 平面介质波导 时域有限差分     

并矢格林函数下的球形超透镜

应用并矢量格林函数法完成了球形超透镜的数值模拟,证明了球形超镜的亚波长成像能力.并矢格林函数法是处理电磁场问题的一种系统理论和有效方法,它弥补了坐标变换法的不足.与平板透镜相比,球形超透镜有几个优点,包括有限的横截面,能成放大或者缩小的像,很高的分辨率,进行二维成像等. 关键词： 球形超透镜 并矢量格林函数法 表面模 高分辨率     

半空间电大涂敷目标散射的高频分析方法

研究了半空间内(海面,地面)电大尺寸涂敷目标散射的高频求解方法.将半空间并矢格林函数引入物理光学方法中,对半空间复杂环境影响进行考虑,并利用阻抗边界条件考虑涂敷目标表面的复杂电磁散射,推导出半空间物理光学分析方法,同时结合图形电磁学,对半空间电大涂敷目标进行消隐判断,提取像素面元法矢量和深度缓存等有效信息,快速有效地计算了半空间电大涂敷目标的雷达散射截面.数值结果证明了方法的有效性和准确性. 关键词： 半空间物理光学方法 半空间并矢格林函数 图形电磁学 雷达散射截面     

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.     

对称单负介质包层平面波导的模式特征

系统研究了负μ材料(MNG)作为包层的对称三层平板波导的传输特性. 研究发现,这种波导既支持快波的传播,又支持TE₀,TE₁模式的慢波传输. 其模式特性不同于左手介质波导和传统介质波导,导模存在的模折射率范围要比它们的大. MNG波导的TE₀快波模缺失,且TE_m模(m>1)的传播常数大于TM_m模的传播常数. TE_m模具有双模特征,且与波导的结构参数密切相关,导致波导中的净能流出现负值. 关键词： 单负介质 平板波导 快波与慢波 传播常数     

具有对称性象差的光学系统成象积分算子谱分析

本文对有限视场成象积分算子的理论进行讨论,利用在零级本征函数空间展开的方法,得到积分算子本征函数的近似表达式,并借助于实验中测得的脉冲响应(点扩散函数)的数据,算出具有对称性象差的显微物镜的本征值和本征函数,并进行讨论。 关键词：     

考虑棱边散射的半空间复杂导体目标高频分析方法

研究了半空间内复杂导体目标棱边散射的高频求解方法.分析半空间电磁波的传播规律和复杂目标棱边的电磁散射特性,将半空间并矢格林函数引入等效电磁流方法中,给出了基于等效电磁流法和物理绕射理论的半空间棱边散射场计算式,同时结合图形电磁学,对半空间复杂目标进行消隐处理,判断目标的棱边像素及获得棱边参数,与半空间目标的面元散射场相叠加,快速有效地计算了半空间复杂目标的雷达散射截面.数值结果证明了方法的有效性和准确性. 关键词： 半空间等效电磁流方法 半空间并矢格林函数 图形电磁学 雷达散射截面     

精细积分法在含各向异性介质波导不连续性问题中的应用

用精细积分法对含各向异性介质的波导不连续性问题进行了数值模拟与分析. 从矢量波动方程相对应的单变量变分形式出发, 推导出了含有各向异性介质波导横截面离散系数矩阵的表达式, 引入对偶变量, 在Hamilton体系下, 利用精细积分法求出出口刚度矩阵, 进行有限元拼装, 求解了含各向异性介质的波导不连续性问题. 算例表明了该方法的准确性和高效性. 利用本文方法还讨论了介电系数和导磁系数张量的各个分量对波导传输特性的影响. 关键词： 波导不连续性 各向异性介质 Hamilton体系 精细积分法     

Derivatives on the isotropic tensor functions

The derivative of the isotropic tensor function plays an important part in continuum mechanics and computational mechanics, and also it is still an opening problem. By means of a scalar response function f(Λ_i, I ₁, I ₂) and solving a tensor equation, this problem is well studied. A compact explicit expression for the derivative of the isotropic tensor function is presented, which is valid for both distinct and repeated eigenvalue cases. Throughout the analysis, the formulation holds for general isotropic tensor functions without need to solve eigenvector problems or determine coefficients. On the theoretical side, a very simple solution of a tensor equation is obtained. As an application to continuum mechanics, a base-free expression for the Hill’s strain rate is given, which is more compact than the existent results. Finally, with an example we compute the derivative of an exponent tensor function. And the efficiency of the present formulations is demonstrated. We dedicate this work with deep respect and admiration to the memory of Prof. Gao Yuchen.     

Calculation of the electroelastic Green’s function of the hexagonal infinite medium

The electroelastic 4 × 4 Green’s function of a piezoelectric hexagonal (transversely isotropic) infinitely extended medium is calculated explicitly in closed compact form ((73) ff. and (88) ff., respectively) by using residue calculation. The results can also be derived from Fredholm’s method [2]. In the case of vanishing piezoelectric coupling the derived Green’s function coincides with two well known results: Kröner’s expressions for the elastic Green’s function tensor [4] is reproduced and the electric part then coincides with the electric potential (solution of Poisson equation) which is caused by a unit point charge. The obtained electroelastic Green’s function is useful for the calculation of the electroelastic Eshelby tensor [16].     

关于求各向异性介质中电磁场的格林张量函数的一个方法

本文提出一个方法,来推求在(3)式中所定义的、在全空间中的格林张量函数。它有时亦称为对应微分方程的基本解。这个方法是以富氏变换为基础。由于问题的复杂性,我们不得不作某些近似。首先,把各向异性介质分为两类,一类是磁迴旋介质,另一类是电迴旋介质。对于磁迴旋介质,如铁氧体,取μ为张量而ε为标量。而对电迴旋介质,如等离子体,取ε为张量而μ为标量。其次,由于矩阵μ_p非常小(在(15)式中定义),我们可以把解展为μ_p的冪级数,并计算出一级近似。具体结果在式(23)、(25)、(28)、(32)和(33)中表示。最后对Г函数的物理意义和它的渐近展开式的有效范围作了讨论。     

The gauge theory of dislocations: Static solutions of screw and edge dislocations

We investigate the T(3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations in terms of the elastic distortion tensor and dislocation density tensor for the force and pseudomoment stresses of an isotropic solid. The constitutive relations contain six material parameters. In this theory, both the force and pseudomoment stresses are asymmetric. The theory possesses four characteristic lengths ?₁, ?₂, ?₃ and ?₄, which are given explicitly. We first derive the three-dimensional Green tensor of the master equation for the force stresses in the translational gauge theory of dislocations. We then investigate the situation of generalized plane strain (anti-plane strain and plane strain). Using the stress function method, we find modified stress functions for screw and edge dislocations. The solution of the screw dislocation is given in terms of one independent length ?₁ = ?₄. For the problem of an edge dislocation, only two characteristic lengths ?₂ and ?₃ arise with one of them being the same ?₂ = ?₁ as for the screw dislocation. Thus, this theory possesses only two independent lengths for generalized plane strain. If the two lengths ?₂ and ?₃ of an edge dislocation are equal, we obtain an edge dislocation, which is the gauge theoretical version of a modified Volterra edge dislocation. In the case of symmetric stresses, we recover well-known results obtained earlier.     

General form of the full electromagnetic Green function in materials physics

In this article, we present the general form of the full electromagnetic Green function which is suitable for the application in bulk materials physics. In particular, we show how the seven adjustable parameter functions of the free Green function translate into seven corresponding parameter functions of the full Green function. Furthermore, for both the fundamental response tensor and the electromagnetic Green function, we discuss the reduction of the Dyson equation on the four-dimensional Minkowski space to an equivalent, three-dimensional Cartesian Dyson equation.     

QCD at finite temperature

Quantum chromodynamics is studied at finite temperatures and densities using the temperature Green functions method. For the Green functions the renormalized Schwinger-Dyson equations are obtained and their qualitative properties are discussed. The equality of the renormalization constants for the equations obtained at T, μ ≠ 0 with those for quantum field theory is pointed out. General properties of the gluon polarization tensor are investigated at T, μ ≠ 0. The temperature Green functions are calculated within the one-loop approximation using both relativistic and axial gauges. The fulfilment of the Slavnov-Taylor identities is verified. The asymptotic behaviour of the polarization tensor at T, μ ≠ 0 is established and the excitation spectrum of quark-gluon plasma is found. Both Fermi and Bose excitations are considered and the gauge invariance of the spectra is demonstrated. The renormalization group extension of the dispersion laws into the regions of high temperatures and densities is presented. The exact representation of the thermodynamical potential in QCD is found in terms of the temperature Green functions. For the quark-gluon plasma the thermodynamical potential is calculated with the g³-term taken into account. The equation of state of the hot quark-gluon plasma is found and its properties are discussed. The complete evolutional diagram of the hadronic matter is outlined. The phase curve asymptotics, which put bounds on the quark-gluon plasma domain, are found for the two limiting cases (μ = 0, T → T₀; T = 0, μ → μ₀). The phase transition of the hot quark-gluon plasma placed in external Abelian field is studied. The instability of such plasma has been found and the program of its stabilization is indicated. The infrared behaviour of the non-Abelian gauge theory is studied for finite temperatures when power divergencies are essential. The propagator of transverse gluons is shown to be singular for momenta |p| ˜ g²T and this cannot be avoided by summing the simplest bubble chains. The infrared asymptotic behaviour of the tree-gluon vertex is found and the results obtained are checked using the Slavnov-Taylor identities. The Green functions asymptotics found indicate either an instability of the quark-gluon plasma in the infrared momentum domain or the inconsistency of the perturbational methods. A non-perturbative approach to the infrared problem in QCD is developed within the axial gauge. The closed equations for the structure functions that determine the gluon polarization tensor are obtained by using the Slavnov-Taylor identities to found approximately the three-gluon vertex. It is shown that the solution of the equations obtained by iterations does not remove the infrared singularity from the temperature Green functions. The nonperturbative solution of such equations is discussed.     

Low energy atomic collisions

The Schrödinger equation for the system H⁺-H developed in a previous paper is considered using new expansion functions for electronic states obtained from H₂ ⁺ molecular ion electronic eigenfunctions by a unitary transformation. These new functions have the advantage of remaining orthonormal at all internuclear separations and asymptotically becoming symmetrized atomic hydrogen states. Although they are eigenfunctions of the H₂ ⁺ hamiltonian only in the limit of large internuclear distance, the effect of the H₂ ⁺ hamiltonian on these functions is readily found.

Due to coupling which remains non-zero in the limit of large interproton distance, each independent formal solution of the H⁺-H equations involves more than one expansion state in this limit. These solutions may be expressed asymptotically as column vectors multiplied by incoming or outgoing spherical waves.

The formal theory of scattering as developed by Gell-Mann and Goldberger has been utilized along with the projection formalism of Feshbach to obtain the correct asymptotic form of the scattering wave function. The procedure employed involves formulating the problem in terms of two-potential scattering and requires application of renormalization techniques for treating level shifts produced by the infinite-ranged coupling. This asymptotic form may be used in imposing scattering boundary conditions on numerical solutions of coupled equations for H⁺-H scattering.

Finally, it is shown that one cannot interpret coefficients of all outgoing spherical waves as scattering amplitudes. In addition, new interference phenomena are found to result from the presence of the infinite-ranged coupling. The present formalism is shown to reduce to the usual perturbed stationary-states method in the approximation that the infinite-ranged coupling is neglected.     

Theoretical analysis for dispersion characteristics of elliptic-groove waveguide with mode-matching method

In this paper, two kinds of elliptic-groove waveguides are presented. One of them has never been studied before. With the help of Mathieu function and mode-matching method, the field components and characteristic equation of the elliptic-groove waveguides are obtained for the first time. Then their dispersion characteristics for the dominant mode i.e. the mode TE _e11 ¹ are also studied. The gotten conclusions have very important values in theoretical study and actual application for the two kinds of the elliptic-groove waveguides.     

Exact short time dynamics for steeply repulsive potentials

The autocorrelation functions for the force on a particle, the velocity of a particle and the transverse momentum flux are studied for the power law potential v(r)=ε(σr)^ν (soft spheres). The latter two correlation functions characterize the Green–Kubo expressions for the self-diffusion coefficient and shear viscosity. The short-time dynamics is calculated exactly as a function of ν. The dynamics is characterized by a universal scaling function S(τ), where τ=t/τ_ν and τ_ν is the mean time to traverse the core of the potential divided by ν. In the limit of asymptotically large ν this scaling function leads to delta function in time contributions in the correlation functions for the force and momentum flux. It is shown that this singular limit agrees with the special Green–Kubo representation for hard-sphere transport coefficients. The domain of the scaling law is investigated by comparison with recent results from molecular dynamics simulation for this potential.