互易定理计算分层半空间上方任意取向偶极子的远区场

利用互易定理推导了考虑直达波和界面反射波时半空间分层界面上任意取向偶极子在上半空间远区辐射场的解析表达式. 进一步考虑电偶极子距离分界面为某一高度情形, 在考虑直达波和反射波程差基础上导出相应辐射场公式. 辐射场解析表达式中分层半空间TM和TE波反射系数可以通过连分数方法或传播矩阵法计算获得. 本文推导过程物理概念清晰, 所得解析结果适于计算观察点远离界面情形下偶极子的远区辐射场. 数值计算结果表明, 利用本文结果可以快速分析半空间上方任意取向偶极子的远区辐射场.     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

开孔矩形腔体电磁泄漏特性的解析研究

本文提出了一种用于计算开孔矩形腔体电磁泄漏场的解析理论模型.该理论模型先基于模式展开法求解封闭腔场,进而依据Bethe小孔耦合理论将泄漏场与封闭腔场用等效偶极子关联.该模型可以考虑波频率、场源位置、开孔位置及场强观测点位置等因素的影响,计算结果与全波仿真结果一致.本文计算分析了相关因素对电磁屏蔽效能的影响规律,并给出了物理解释.结果表明近场屏蔽效能小于远场屏蔽效能,且近场区电场屏蔽效能与磁场屏蔽效能并不相同.     

Scattering of an arbitrarily oriented dipole field by an infinite and a finite length PEMC circular cylinder

Electromagnetic scattering from an infinite and a finite length PEMC circular cylinder, illuminated by an arbitrarily oriented dipole, is investigated theoretically. An electric dipole as a source of excitation is considered first, and then a magnetic dipole as a source of excitation is treated. In contrast to the case of an axially directed dipole, it is shown that no additional terms are needed to incorporate the cross-polarized component of the field for the case of radial and circumferential dipoles. Numerical verifications are presented to verify the validity of derived results and numerical code by comparing results with the published literature.      

Optical self-induced transparency in anisotropic dielectric crystals

Optical self-induced transparency for extraordinary waves in anisotropic crystals is theoretically studied. Crystals in which dipole moments of impurity optically active atoms are arbitrarily oriented relative to the optic axis are analyzed in detail. Explicit analytic expressions for the parameters of nonlinear extraordinary wave are presented, which yield known results in limiting cases.     

Anisotropic local-field effects of nanoparticles in plasmonic optics and magneto-optics

A theory of anisotropic optical local-field effects caused by resonantly polarizable small particles in multilayer polarizable media is developed. Considered is the model of a rectangular lattice of ellipsoidal nanoparticles with taking account of “image forces” at an interface in a layered medium. The lattice sums for anisotropic dipolar interactions are found using the Green’s function method in the quasi-point dipole approximation, and the effective polarizabilities of particles in a layer located near an interface are calculated self-consistently. The manifestation of an anisotropic local field of nanoparticles in optical radiation and propagation of evanescent waves responsible for optical near-field effects is investigated. Applications of the obtained results in the polar magneto-optical Kerr effect and reflectance anisotropy spectroscopy in propagating the polarized light along the normal to layers are considered. The resonant features in the spectra due to enhancement of the optical effects under excitation of surface (local) plasmons in nanoparticles of a noble metal are studied.     

Average scattered field from a random PEC cylinder buried below a slightly rough surface

Scattering from a perfect electric conducting cylinder with random radius buried below a half space dielectric homogenous interface is studied. The cylindrical wave scattered by cylinder is expanded in terms of plane wave spectrum. Small perturbation method is used to study the interaction of each plane wave with the interface. The zeroth order term yields solution for a flat interface, whereas scattering from a rough surface is given by first-order term. Results are obtained for both TM and TE polarizations. Analytical expressions of the average scattered field are obtained and verified using numerical evaluation. Different scattering scenarios are simulated by varying the distribution of the radius. It is observed that average scattering cross section of an ensemble with normal/uniform distribution is almost equal to that of a cylinder with mean radius.     

介质球的各向异性瑞利散射

基于电磁场的多尺度理论,研究了各向异性介质球内、外电场的规律,导出了各向异性目标散射场的表达式,得到了各向异性介质目标散射振幅、散射截面等的解析表达式,并对其正确性进行了检验.仿真结果表明:各向异性介质球的散射具有偶极辐射的特点,介电常量越大,产生的偶极矩也愈大,散射也越强.其结果可为各向异性目标监测、各向异性光散射研究等提供理论支持.     

Binding energies of impurity states in strained wurtzite GaN/Al_xGa_(1-x)N heterojunctions with finitely thick potential barriers

Ground state binding energies of donor impurities in a strained wurtzite GaN/AlxGal_xN heterojunction with a po- tential barrier of finite thickness are investigated using a variational approach combined with a numerical computation. The built-in electric field due to the spontaneous and piezoelectric polarization, the strain modification due to the lattice mismatch near the interfaces, and the effects of ternary mixed crystals are all taken into account. It is found that the binding energies by using numerical wave functions are obviously greater than those by using variational wave functions when impurities are located in the channel near the interface of a heterojunction. Nevertheless, the binding energies using the former functions are obviously less than using the later functions when impurities are located in the channel far from an interface. The difference between our numerical method and the previous variational method is huge, showing that the former should be adopted in further work for the relevant problems. The binding energies each as a function of hydrostatic pressure are also calculated. But the change is unobvious in comparison with that obtained by the variational method.     

Optics of magnetic multilayers

Optical response of layered lossy anisotropic media displaying magnetic order is considered. The analysis is based on classical optical terms. Planar magnetic multilayers (ML) are represented by Yeh's 4×4 matrices which relate the field amplitudes in the isotropic half spaces on both sides of a ML structure. Each layer is characterized by a complex permittivity tensor of general form while magnetic permeability assumes its vacuum value. The basic assumption is that the electromagnetic field in a layer can be represented by a linear combination of four eigenmodes following from the wave equation of the layer. Then the boundary conditions at interfaces along with a set of four field amplitudes completely determine ML electric and magnetic field distributions. Alternatively, two orthogonally polarized incident wave amplitudes in each of the isotropic half spaces may be specified. The approach is more general than those published so far. Assuming minimum previous experience in the ML optics the case of polar magnetization is treated in detail to provide a simple way to the solution of the problems most often encountered in practice.     

电力线谐波辐射在分层各向异性电离层中的传播特点

电力线谐波辐射特指在电离层或磁层中观测到的来源于地面电力系统输电线的电磁波辐射, 其在电磁场时频功率谱中表现为400 Hz至5 kHz范围内, 频率间隔为50/100 Hz或60/120 Hz 的平行谱线, 已成为近地空间环境的一种人为污染源. 对于该现象的形成机理尚缺乏定量研究. 本文研究了非理想导电大地上方由电偶极子源产生的电磁场在分层各向异性电离层中的传播模型, 提出了一种新的求解方法, 有效解决了编程计算中的数值溢出问题, 并利用已有解析解对所提方法进行了验证. 在此基础上, 利用实际电力线、大地、电离层的相关参数, 研究了偶极子源频率、电离层下边界高度、大地电导率、地磁场方向等对电力线谐波辐射在电离层中的传播的影响. 结果表明, 频率等于地-电离层波导导波模截止频率时透入电离层的电力线谐波辐射强度更大; 谐波电流一定时, 大地电导率小的地区, 电力线谐波辐射的功率更大; 电力线谐波辐射在电离层中沿地磁场方向传播. 本文所得结果有益于阐释电力线谐波辐射现象的形成机理.     

基于新型混合场积分方程的半空间三维均匀介质目标电磁散射分析

利用介质半空间格林函数,将一种混合场积分方程(JMCFIE)推广应用到有耗半空间的均匀介质的散射分析中,以减少离散矩阵方程迭代求解时所需的迭代步数,提高矩量法(MoM)对半空间介质目标散射分析的求解效率.数值算例验证了方法的准确性和有效性.     

Radiation of the Point Source from an Anisotropic Plasma Cylinder

We obtain and analyze an analytical solution to the problem of electromagnetic-wave radiation of the point electric dipole from an anisotropic plasma cylinder to free space. Two cases of the dipole orientation are considered, where the electric dipole is directed along and across a horizontal magnetic field whose direction does not coincide with the axes of a cylindrical coordinate system. We analyze how the conditions and characteristics of the resonance influence of the anisotropic plasma cylinder depend on the strength of the magnetic field and its direction with respect to the dipole moment of the source. Comparative analysis of the resonance influence of the plasma cylinder with horizontal and axial external magnetic fields is performed.     

Guided wave propagation in multilayered piezoelectric structures

A general formulation of the method of the reverberation-ray matrix (MRRM) based on the state space formalism and plane wave expansion technique is presented for the analysis of guided waves in multilayered piezoelectric structures. Each layer of the structure is made of an arbitrarily anisotropic piezoelectric material. Since the state equation of each layer is derived from the three-dimensional theory of linear piezoelectricity, all wave modes are included in the formulation. Within the framework of the MRRM, the phase relation is properly established by excluding exponentially growing functions, while the scattering relation is also appropriately set up by avoiding matrix inversion operation. Consequently, the present MRRM is unconditionally numerically stable and free from computational limitations to the total number of layers, the thickness of individual layers, and the frequency range. Numerical examples are given to illustrate the good performance of the proposed formulation for the analysis of the dispersion characteristic of waves in layered piezoelectric structures. Supported by the National Natural Science Foundation of China (Grant Nos. 10725210 and 10832009), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20060335107), the National Basic Research Program of China (Grant No. 2009CB623204), and the Scientific Research Foundation for Tsuiying Talents of Lanzhou University     

Shear-horizontal transverse-electric seismoelectric waves in cylindrical double layer porous media

The shear-horizontal(SH) waves excited by the shear source in a borehole are easy to analyze due to the simple waveform. The borehole-side structures make the formation properties discontinuous. We consider a cylindrical double layer structure and study the borehole shear-horizontal and transverse-electric(SH-TE) seismoelectric waves. We first derive the expressions of the basic field quantities, and simulate the acoustic field and electric field using the real axis integral method. Compared with the wave fields of an infinitely homogeneous porous medium outside the borehole, the cylindrical layered structure makes the multi-mode cylindrical Love waves and their accompanying electric fields excited.Next, in order to study the interface response law of the inducing electric fields, we use the secant integral method to calculate the interface converted electromagnetic waves and analyze the causes of each component. It is found that an interface response occurs each time the SH wave impinges the interface in the layered porous medium. The results show that the SH-TE mode has a potential application for borehole-side interface detection in geophysical logs.     

Seismoelectric waves in a borehole excited by an external explosive source

The conversion of energy between seismic and electromagnetic wave fields has been described by Pride’s coupled equations in porous media. In this paper, the seismoelectric field excited by the explosive point source located at the outside of the borehole is studied. The scattering fields inside and outside a borehole are analyzed and deduced under the boundary conditions at the interface between fluid and porous media. The influences of the distance of the point source, multipole components of the eccentric explosive source, and the receiving position along the axis of vertical borehole, on the converted waves inside the borehole are all investigated. When the distance from the acoustic source to the axis of a borehole is far enough, the longitudinal and coseismic longitudinal wave packets dominate the acoustic and electric field, respectively. The three components of both electric field and magnetic field can be detected, and the radial electric field is mainly excited and converted by the dipole component. Owing to the existence of borehole, the electric fields and magnetic fields in the borehole are azimuthal. The distance from the point where the maximum amplitude of the axial components of electric field is recorded, to the origin of coordinate indicates the horizontal distance from the explosive source to the axis of vertical borehole.     

Wave diffraction by rough interfaces in an arbitrary plane-layered medium

Abstract

The problem of electromagnetic wave scattering by a slightly rough interface in an arbitrarily layered medium is solved by a small-perturbation method. The bistatic amplitude of scattering as well as the scattering cross sections for statistically rough surfaces are calculated for linear polarized waves. Along with scattering into up-going waves in a homogeneous medium and scattering cross sections in down-going waves into a layered medium, scattering amplitudes from a rough interface in the arbitrarily layered medium are obtained.     

Time-Domain Numerical Solutions of Maxwell Interface Problems with Discontinuous Electromagnetic Waves

This paper is devoted to time domain numerical solutions of two-dimensional (2D) material interface problems governed by the transverse magnetic (TM) and transverse electric (TE) Maxwell's equations with discontinuous electromagnetic solutions. Due to the discontinuity in wave solutions across the interface, the usual numerical methods will converge slowly or even fail to converge. This calls for the development of advanced interface treatments for popular Maxwell solvers. We will investigate such interface treatments by considering two typical Maxwell solvers – one based on collocation formulation and the other based on Galerkin formulation. To restore the accuracy reduction of the collocation finite-difference time-domain (FDTD) algorithm near an interface, the physical jump conditions relating discontinuous wave solutions on both sides of the interface must be rigorously enforced. For this purpose, a novel matched interface and boundary (MIB) scheme is proposed in this work, in which new jump conditions are derived so that the discontinuous and staggered features of electric and magnetic field components can be accommodated. The resulting MIB time-domain (MIBTD) scheme satisfies the jump conditions locally and suppresses the staircase approximation errors completely over the Yee lattices. In the discontinuous Galerkin time-domain (DGTD) algorithm – a popular Galerkin Maxwell solver, a proper numerical flux can be designed to accurately capture the jumps in the electromagnetic waves across the interface and automatically preserves the discontinuity in the explicit time integration. The DGTD solution to Maxwell interface problems is explored in this work, by considering a nodal based high order discontinuous Galerkin method. In benchmark TM and TE tests with analytical solutions, both MIBTD and DGTD schemes achieve the second order of accuracy in solving circular interfaces. In comparison, the numerical convergence of the MIBTD method is slightly more uniform, while the DGTD method is more flexible and robust.     

Resolution of objects within subwavelength range by using the near field of a dipole

We analyze the far-field resolution of apertures that are illuminated by a point dipole located at subwavelength distances. It is well known that radiation emitted by a localized source can be considered a combination of traveling and evanescent waves, when represented by the angular spectrum method. The evanescent wave part of the source can be converted to propagating waves by diffraction at the aperture; thereby it contributes to the far-field detection. Therefore one can expect an increase in the resolution of objects. We present explicit calculations showing that the resolution at the far zone is improved by decreasing the source-aperture distance. We also utilize the resolution enhancement by the near field of a dipole to resolve two closely located apertures. The results show that without the near field (evanescent field) the apertures are not resolved, whereas with the near field of the dipole the far zone intensity distribution shows improved resolution. This method eliminates the requirements of near-field techniques such as controlling and scanning closely located tip detectors.