菲涅耳公式的研究及数值模拟

菲涅耳公式阐述了光在两种不同透明介质的分界面上,发生反射和折射现象时,反射光、折射光的振幅变化规律。本文通过对菲涅尔公式的变形处理,得到了新的表达形式,并且应用Matlab软件进行了数值模拟,使菲涅耳公式的物理意义更清晰明了。     

平面偏振光的布儒斯特入射

菲涅耳公式给出了两种透明介质界面处,平行入射面的光矢量(P矢量)和垂直入射面的光矢量(S矢量),在分界面上的振动状态[1].     

带电平面的反射与透射研究——菲涅耳公式的修正

根据一般条件下电磁场的边界条件,研究了两种介质分界面存在面电荷分布时的反射与透射,证明了这一条件下反射定律和折射定律仍然成立,推导得到存在面电荷分布时入射波平行分量和垂直分量的振幅反射系数和振幅透射系数,即修正的菲涅耳公式。由于不同界面的导电特性不同,两种介质界面的面电荷分布会影响界面的面电导率,修正后的菲涅耳公式与面电导率和自由空间阻抗有关。计算结果表明当面电荷密度或界面特性使面电导率发生较大变化时,振幅反射系数和振幅透射系数及反射率和透射率发生变化。     

菲涅耳公式的几何图示与应用

电磁波通过两种透明介质的分界面时,反射波、折射波和入射波的电矢量分量的大小和方向之间的关系可由菲涅耳公式说明,作通过分析和推导,给出了菲涅耳公式的几何图示,这使得在分析光学问题时,谱得简单和直观。     

有关菲涅耳公式的两个问题

早在上世纪初,就有了关于光在电介质界面处反射和折射的菲涅耳公式。到上世纪后半叶,有了电磁场的麦克斯韦方程组以及光的电磁理论之后,对菲涅耳公式能够给出严格的理论推导。目前它已成为普通物理光学课中的基本内容,然而在对这些公式的理解和运用之中往往会产生一些误会和混淆的地方,本文将对此进行一些讨论。 一、坐标系的选取与相位突变问题 菲涅耳公式可写成式中θ1、θ2分别为入射、折射角,A、A分别表示光矢E的振幅矢量A在垂直和平行于入射面方向的分量。对于正入射情形,上式取01、0,02+02而01/礼一。。/nl(折射定律的极限),得确切…     

光在光轴取向任意条件下的晶体表面透射率

为了分析一束光在晶体表面的能量损失以及两束折射光的能量比,给出了一种求解反射率和透射率的方法。讨论了光从各向同性介质入射到单轴晶体表面时的折射和反射,注意到了e光线与e光波方向的不同,e光折射率与e光波法线折射率的不同,得出了在界面处应该满足的边界方程。在晶体光轴取向任意的条件下,给出了表明各光束间能量关系的折射率和反射率的理论表达式,为晶体器件特性的研究提供了有力的理论工具。数值模拟表明:得到的结果满足能量守恒;反射到各向同性介质中的光的电场(或磁场)与原入射光的电场(或磁场)不再平行;光轴的取向和入射角的大小对折射的o光、e光的能量比有很大的影响。     

光在高速运动界面上的反射和折射

依据闵可夫斯基运动介质电磁场理论，从物质方程和边界条件出发，导出了平行于入射面电场分量反、折射分配的Ｅｒ－Ｅｉ、Ｅｔ－Ｅｉ菲涅耳公式．用几何方法求得运动界面上法线方位角反、折射定律，进而导出光线的反、折射定律．基于光线速度满足洛伦兹变换，由光在静止界面上反、折射定律也可导出运动界面上光线的反、折射定律，最后给出了光线反、折射定律实例曲线，它们明显地依赖于界面速度．     

介质表面运动时的菲涅耳公式

论述了电磁波在运动介质界面反射和折射时电磁场场量间的振幅关系,得到了修正后的菲涅耳公式。     

菲涅尔公式的几何表示

:通过在两种不同的透明介质的分界面处光的反射、折射和入射的电矢量振幅和方向之间的关系,给出了菲涅尔公式的几何表示法,使在分析光学问题时变得简单和直观。     

菲涅尔公式的实验研究

菲涅耳公式是通过理论推导而得出的,在光学理论中占有重要地位,很多光学现象都可以用其解释,但这一公式却难于用实验直接验证。本文利用折射定律将菲涅耳公式形变处理,消除了不易测量的折射角,把不可测量的电矢量振幅转化为可测量的光强,并且选择在空气和水的分界面进行实验研究,使得菲涅尔公式的完整实验验证成为可能,实验曲线与mathematica软件数值模拟曲线完全吻合。     

矩孔光栅的矢量模式理论

本文引入满足均匀矢量亥姆霍兹（Ｈｅｌｍｈｏｌｔｚ）方程的矢量波函数作为基矢，对矩孔光栅的孔内外光场分别进行矢量模式展开和矢量平面波展开，并由耦合条件导出了求解展开系数的方程组，从方程组中求解出相应的振幅系数，可研究光栅的衍射场分布，该方法可研究入入射扬方向和偏振任意时的衍射效率和偏振特性等问题。     

Fresnel boundary and interface conditions for polarized radiative transfer in a multilayer medium

In many applications of the theory of radiative transfer, it is important to consider the changes in the index of refraction that occur when the physical domain being studied consists of material regions with distinct optical properties. When polarization effects are taken into account, the radiation field is described by a vector of four components known as the Stokes vector. At an interface between two different material regions, the reflected and transmitted Stokes vectors are related to the incident Stokes vector by means of reflection and transmission matrices, which are derived from the Fresnel formulas for the amplitude coefficients of reflection and transmission. Having seen that many works on polarized radiative transfer that allow for changes in the index of refraction exhibit discrepancies in their expressions for the transmission matrix, we present in this work a careful derivation of the relations between the reflected and transmitted Stokes vectors and the Stokes vector incident on an interface. We obtain a general form of a transmission factor that is required to ensure conservation of energy and we show that most of the discrepancies encountered in existing works are associated with the use of improper forms of this factor. In addition, we derive explicit and compact expressions for the Fresnel boundary and interface conditions appropriate to the study of polarized radiative transfer in a multilayer medium.     

Reflexion und Brechung des Lichtes an einer anisotropen Schicht

Reflection and Refraction of Light by an Anisotropic Layer The linear problem of reflection and refraction of plane monochromatic electromagnetic waves by a plane-parallel homogeneous anisotropic layer between (in general different) homogeneous optically isotropic semiinfinite media is treated on the basis of MAXWELL 's equations and the boundary conditions following from them. The permittivity tensor of the anisotropic layer is assumed to be widely arbitrary and therefore asymmetric, neglecting only the spatial dispersion, i. e., the dependence on the wave vector. The electrical fields of reflected, refracted, and transmitted waves are calculated in dependence on the electric field of the incident wave. The conditions for waveguide modes of the layer in the absence of incident waves are obtained from the vanishing of a determinant. The general formulae are specialized to the cases of normal incidence and also of perpendicular and parallel polarisation, relatively to the plane of incidence, of the refracted partial waves in the anisotropic layer thus obtaining simplifications in these cases. The interesting cases of uniaxial layers, when the optic axis lies either parallel or perpendicular to the plane of incidence, belong to the last mentioned special cases of perpendicular and parallel polarisation relatively to the plane of incidence.     

有耗介质层上多导体传输线的电磁耦合时域分析方法

目前,针对空间电磁场作用有耗介质层上传输线的电磁耦合,仍缺乏有效的数值分析方法.因此,本文提出一种高效的时域混合算法,很好地解决了有耗介质层上传输线电磁耦合建模难的问题.首先,对经典传输线方程进行改进,推导了适用于有耗介质层上多导体传输线电磁耦合分析的修正传输线方程.然后,结合时域有限差分方法和相应插值技术,求解修正传输线方程,获得多导线及其端接负载上的电压和电流响应,并实现空间电磁场辐射与多导线瞬态响应的同步计算.最后,通过相应计算实例的数值模拟,与CST软件的仿真结果进行对比,验证了时域混合算法的正确性和高效性.     

Exact calculation of the minimal thickness of the large optical path difference wind imaging interferometer

This paper gives the relation between spatial ray and its projection on paper plane based on the vector form of reflective law.Using the method of prism expansion,it obtains the exact expression of the exit height.The exit height can ensure that the incident rays,at arbitrary direction and arbitrary angle,after several transmission and reflection in the two right-angle reflectors,finally pass through the exit surface.Furthermore,it analyses the effects of different parameters on the exit height through computer simulation,and some important conclusions are obtained.The physical meaning of the sign of exit height is described,and the exact expression of the minimal thickness of the large optical path difference wind imaging interferometer is gained.This work is of great scientific significance to the static,realtime simultaneous detection of atmospheric wind field,and it will provide a theoretical and practical guidance for the miniaturization design and engineering realization of wind imaging interferometer.     

Ray dynamics of the propagation of sound in nonuniform moving media

This paper presents a new ray theory for the propagation of sound waves in nonuniformly moving media. It is found that the ray equations in weakly inhomogeneous and slowly moving media are analogous to the equations of motion of charged particles in nonuniform electric and magnetic fields. The adiabatic approximation is used to study the problem of the propagation of sound rays in a model of near-ocean-bottom waveguide with horizontal flow and slowly varying parameters along the direction of propagation of the wave. A general formula is derived that describes the transverse displacement of the trajectory of the ray relative to the direction of propagation of the wave.     

Electric-field and magnetic-field effects on electronic tunneling through magnetic-barrier nanostructures

We have theoretically investigated electric-field and magnetic-field effects on electronic transport properties in nanostructures consisting of realistic magnetic barriers created by lithographic patterning of ferromagnetic or superconducting films. The results indicate that the characteristics of transmission resonance are determined not only by the magnetic configuration and the incident wave vector but also strongly by the applied electric and magnetic fields. It is shown that transmission resonance shifts towards the low-energy region by applying the electric field, and that with increasing the electric field transmission resonance is suppressed for the entire incident wave vector in the magnetic nanostructures with antisymmetric magnetic profile, while for the magnetic nanostructures with symmetric magnetic profile transmission resonance is enhanced for certain incident wave vector. It is also shown that both transmission and conductance shift towards high-energy direction and are greatly suppressed with the increase of the external magnetic field.Received: 20 May 2003, Published online: 11 August 2003PACS: 73.40.Gk Tunneling - 73.23.-b Electronic transport in mesoscopic system - 75.70.Cn Interfacial magnetic properties (multilayers, superlattices)     

Electromagnetic wave refraction on the interface of absorptive and transparent isotropic media and non-resonant excitation of surface waves

New formulae for the angles of refraction at the interface of the absorbing/transparent isotropic media are derived from Maxwell's equations. Using the time-averaged Poynting vector for the direction of the beam of light, the noncoincidence of incidence and refraction planes is predicted for the mixed polarization of incident wave. The angle between the refracted beam and incidence plane is especially large for the condition of non-resonant excitation of surface electromagnetic waves at a flat interface of absorptive-transparent media.     

对称型闪耀光栅的矢量模态理论

本文将满足均匀矢量亥姆霍兹方程的标准矢量波函数作为基矢对对称型闪耀光栅槽内、外的电磁场分别进行矢量模式和矢量平面波展开。然后通过在槽内外分界面上的场耦合条件得到一组振幅系数方程组。从方程组中求解出相应的振幅系数,就可研究光栅的衍射场分布。该方法适用于对称型闪耀光栅对任意入射方向、任意偏振态入射场衍射问题的研究。在K_2=0入射情况下,其振幅方程组与已发表的文献[6]相同。