电磁场递推算法及微纳光学元件中的应用

提出一种电磁场递推算法来分析微纳光学元件体内电磁场的传输.该方法基于Maxwell方程组和电磁场横向的边界条件给出了严格解.以高斯光束在亚波长矩形浮雕光栅体内的传输为例,分析了非匀幅光束在微纳光学元件体内的传输. 关键词： 递推算法 非匀幅光束 微纳光学元件     

On the longitudinal polarization of non-paraxial electromagnetic fields

Within the framework of the angular plane-wave spectrum of the electromagnetic field, the general form is given for the freely-propagating beams, exact solution of the Maxwell equations, that closely approach (in an algebraic sense) to a purely-longitudinal vectorial distribution at some transverse plane. In the rotationally symmetric case, such a field is written as the combination of radial and longitudinal components, whose propagation can be analysed independently. Several illustrative examples are also considered.     

电磁波方程及折射、反射定律的一些思考

本文由电磁波的麦克斯韦方程组出发,介绍导出折射定律和反射定律的一种证明方法.其证明方法,使用了空间微元近似,然后推广至全空间传播的方法,从而简化了麦克斯韦方程组求解的烦琐过程,提出了一种可教学推广的实用性方法.通过使用微元法,求解得到麦克斯韦方程的行波解形式,即得出电磁场是一种行波.由电磁场的向量形式推导空间中电磁波的折射、反射定律,得到折射、反射定律的证明并不需要电磁波的解析形式,在连续函数的情形下是普遍成立的.求解过程中加深对麦克斯韦方程组的理解,体现了电磁过程的深刻物理图像,也为由几何光学向波动光学过渡提供一种思想上的指导.     

Colliding Plane Waves in Einstein–Maxwell Theory

Recently, a simple solution of the vacuum Einstein–Maxwell field equations was given describing a plane electromagnetic shock wave sharing its wave front with a plane gravitational impulse wave. We present here an exact solution of the vacuum Einstein–Maxwell field equations describing the head-on collision of such a wave with a plane gravitational impulse wave. The solution has the Penrose–Khan solution and a solution obtained by Griffiths as separate limiting cases.     

Electrodynamics of a continuous medium in a system with specified structure

It is shown that electrodynamics can be considered not only in Minkowski space but also in Riemannian space-time. The exact solutions for the electric field within and beyond a charged plate and a sphere and the space-time geometry are found without applying the Einstein equations. The space-time geometry of a Born-rigid noninertial frame of reference (NFR) with global linear acceleration in space-time having constant curvature is obtained on the basis of the structural equations (integrability conditions). A new Lorentz-covariant condition of stationarity for possible solutions to the Maxwell equations for the particles frozen in a Born-rigid NFR is formulated. In an inertial frame of reference this condition is equivalent to zero four-curl of the field of four-accelerations of particles. This condition provides zero relativistic generalized radiation friction force. The propagation of electromagnetic waves in this NFR and the Doppler effect are described. The limitations imposed on the energy-momentum tensor in the Einstein equations are derived.     

声诱导电磁场的赫兹矢量表示与多极声电测井模拟

在假设声场不受电磁场影响的前提下，将Pride声电耦合方程组化为具有电流源的麦克斯韦方程组.与空间位置固定的电流源产生的电磁场不同，孔隙地层中声波诱导的电磁场是由空间波动的电流源产生的.通过引入赫兹矢量，将求解麦克斯韦方程组问题转化为求解关于赫兹矢量的非齐次矢量赫姆霍兹方程组.通过求解该方程组，得出电磁场表达式.利用此方法，针对声电效应测井，分别计算了由单极声源、偶极声源、四极声源激发的井内声场及其诱导电磁场的全波波形. 关键词： 孔隙介质 诱导电磁场 测井 多极声源     

Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes

The exact vector integral solution for all the electromagnetic field components of a general flattened Gaussian laser mode is derived by using the angular spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The integrals are of the form of Gegenbauer's finite integral and are computed analytically for each case, yielding fields satisfying the Maxwell equations exactly in the form of quickly converging Fourier-Gegenbauer series.     

Theory of ferromagnetic antiresonance in parallel configuration in metals

A solution of Maxwell equations for the propagation of electromagnetic waves in a metallic ferromagnet is presented for the region of ferromagnetic antiresonance; the magnetization vector motion is described by the Landau-Liftshitz equation, the metal sample is in the form of a flat disc statistically magnetized in its surface plane (parallel configuration). The dispersion relations for the three waves of (complex) electromagnetic spin wave origin, the surface impedance and the shifts of antiresonance point due to the damping and electrical conductivity are computed in the analytical form.     

Two-dimensional electromagnetic breathers in an array of nanotubes with multilevel impurities

The propagation of a two-dimensional bipolar electromagnetic pulse in an array of semiconductor carbon nanotubes with multilevel impurities is studied. The electromagnetic field in the array of nanotubes is described by Maxwell’s equations reduced to a non-one-dimensional wave equation. The numerical solution to the wave equation demonstrates the possibility of the propagation of a two-dimensional electromagnetic breather in the array of nanotubes. The character of the evolution of the shape of the breather is elucidated, and the time dependence of the maximum intensity of its field is obtained. It is demonstrated that the introduction of multilevel impurities causes a significant change in the parameters, thereby providing an additional possibility for the stabilization of a laser pulse propagating in an array of semiconducting carbon nanotubes.     

Extremely short optical pulse in a thin-film topological insulator with a hexagonal lattice

The propagation of an extremely short optical pulse in a thin-film topological insulator has been considered. The electrons are described by a low-temperature long-wavelength effective Hamiltonian, whereas the electromagnetic field is treated classically within the Maxwell??s equations. The dependence on the velocity and maximum amplitude of the extremely short pulse has been revealed.     

Periodic current domains in a system of carbon nanotubes

The dynamics of propagation of periodic electromagnetic waves and the current induced by them in a system of carbon nanotubes is investigated. The study is performed on the basis of the analysis of the coupled equations for the classical distribution function of electrons in carbon nanotubes and the Maxwell equations for an electromagnetic field. An effective equation describing the electromagnetic field dynamics is obtained. Periodic changes in the form of an electromagnetic wave during its propagation are revealed. This effect is related to the energy exchange between periodic vibrations with different periods in the system under consideration. The corresponding regions of the current through carbon nanotubes form a regular periodic domain structure. The results of numerical calculations are reported, which make it possible to consider this effect at different problem parameters.     

Scattering of electromagnetic waves by ensembles of particles and discrete random media

Current problems of the theory of multiple scattering of electromagnetic waves by discrete random media are reviewed, with an emphasis on densely packed media. All equations presented are based on the rigorous theory of electromagnetic scattering by an arbitrary system of non-spherical particles. The main relations are derived in the circular-polarization basis. By applying methods of statistical electromagnetics to a discrete random medium in the form of a plane-parallel layer, we transform these relations into equations describing the average (coherent) field and equations for the sums of ladder and cyclical diagrams in the framework of the quasi-crystalline approximation. The equation for the average field yields analytical expressions for the generalized Lorentz-Lorenz law and the generalized Ewald-Oseen extinction theorem, which are traditionally used for the calculation of the effective refractive index. By assuming that the particles are in the far-field zones of each other, we transform all equations asymptotically into the well-known equations for sparse media. Specifically, the equation for the sum of the ladder diagrams is reduced to the classical vector radiative transfer equation. We present a simple approximate solution of the equation describing the weak localization (WL) effect (i.e., the sum of cyclical diagrams) and validate it by using experimental and numerically exact theoretical data. Examples of the characteristics of WL as functions of the physical properties of a particulate medium are given. The applicability of the interference concept of WL to densely packed media is discussed using results of numerically exact computer solutions of the macroscopic Maxwell equations for large ensembles of spherical particles. These results show that theoretical predictions for spare media composed of non-absorbing or weakly absorbing particles are reasonably accurate if the particle packing density is less than ∼30%. However, a further increase of the packing density and/or absorption may cause optical effects not predicted by the low-density theory and caused by near-field effects. The origin of the near-filed effects is discussed in detail.     

Non-paraxial Elliptical Gaussian Beam

By using the methods of Hertz vector and angular spectrum transormation, the exact solution of non-paraxial elliptical Gaussion beam with general astigmatism based on Maxwell′s equations is obtained. We discussed its propagation characteristics. The results show that the orientation of the elliptical beam spot changes continuously as the beam propagates through isotropic media. Splitting or coupling of beam spots may occur for different initial spot size. This is very different from that of paraxial elliptical Gaussian beam.     

Non-paraxial Elliptical Gaussian Beam

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Two-dimensional unitary waves in a nonuniform block of carbon nanotubes

The propagation and scattering of two-dimensional unitary electromagnetic waves on metallic discontinuity in a block of carbon nanotubes is considered. The electromagnetic field was considered on the basis of Maxwell equations, and the electron system of carbon nanotubes was based on Boltzmann kinetic equations in an approximation of the relaxation time.     

Design of antireflection composite coating based on metal nanoparticles

A design of ultrathin composite layer with metal nanoparticles on a dielectric surface is proposed for interference reduction of Fresnel reflection. The structural and material parameters of the antireflection composite are calculated within the Maxwell-Garnett effective-medium approximation. The results of the approximate analytical calculation are in good agreement with the exact numerical solution to the Maxwell equations.     

Letter: A Twisting Electrovac Solution of Type II with the Cosmological Constant

An exact solution of the current–free Einstein–Maxwell equations with the cosmological constant is presented. It is of Petrov type II, and its double principal null vector is geodesic, shear–free, expanding, and twisting. The solution contains five constants. Its electromagnetic field is non–null and aligned. The solution admits only one Killing vector and includes, as special cases, several known solutions.     

反铁磁体中电磁振荡的频散和衰减

本文是考虑到电磁波的相对效应(位移电流起作用)和介质的交换效应,对反铁磁体中的电磁振荡的频散作了一定的讨论,并计算了频谱的偏振态。另外,考虑到介质中有阻尼存在,对耦合振荡的传播和衰减作了讨论,并粗略地估计了振荡的穿透深度的数量级。     

Electrodynamics of multilayer media

Using an exact solution of the Maxwell equations, two classes of electromagnetic fields are found, generated by currents in media consisting of plane-parallel layers with given electrodynamical characteristics.Institute for Strong Current Electronics, Russian Academy of Sciences, Siberian Branch. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 89–96, December, 1992.     

电离层与卫星通信

利用电子流体动力学方程和麦克斯韦方程组推导了等离子体的特征频率、折射率，并讨论了电磁波在等离子体中传播的基本条件，从而得出了卫星通信的基本电磁学条件．