A finite-difference time-domain method for solving electromagneticproblems with bandpass-limited sources

The complex-envelope representation of bandpass-limited signals is used to formulate a bandpass-limited vector wave equation and a new finite-difference time-domain (FDTD) scheme that solves the bandpass-limited vector wave equation is presented. For narrow-band electromagnetic systems, this new method allows the time step to be several orders of magnitude larger than current FDTD formulations while maintaining an amplification factor equal to one. Example results obtained by this method are presented and compared with analytic solutions     

Application of the FD-TD method to the analysis of circuitsdescribed by the two-dimensional vector wave equation

A class of microwave circuits described by a two-dimensional vector wave equation is defined. It is proposed to refer to them as vector two-dimensional or 2-DV circuits to distinguish them from circuits described by a two-dimensional scalar wave equation (typically referred to as 2-D circuits). It is shown that the 2-DV class contains some planar circuits filled with anisotropic media, two-dimensional waveguide discontinuities, and circular waveguide discontinuities. Calculation of dispersion characteristics of inhomogeneously filled hollow waveguides is an eigenvalue problem belonging to the 2-DV class. Application to the finite-difference-time-domain (FDTD) method to the analysis of 2-DV circuits is described. Examples show the efficiency of the method for several types of circuit     

矢量波函数空间的电磁矢量恰当射影

提出了一种简化电磁场问题求解的新方法，将电磁场矢量的无旋场部分和无散场部分各自应用一个满足二阶方程的标量函数表示出来，然后由此分析了电磁场矢量在矢量波函数空间的恰当射影问题，并给出用一个标量格林函数构造的无散电磁场并矢格林函数。     

基于矢量波函数空间算子理论的波导系统有限元分析

该文介绍了一种能够消除非物理模的波导系统的有限元分析方法,从矢量波函数空间的偏微分算子理论出发,推导出具有简洁而自洽数学形式的完备的电磁波基本方程组,将电场矢量用两个标量函数表示,并用有限元法对这两个标量函数进行数值求解,从而得到了波导系统的有关参数,文中以加载膜片波导和E面矩形波导阶梯为例说明了这一分析及计算过程。     

抛物线坐标系非傍轴矢量光束的解及聚焦特性

为了求解柱坐标系下非傍轴矢量波动方程,得到光束的电场解析表达式,基于轴对称情况下沿角向偏振的电场,将非傍轴近似情况下的矢量波动方程进行了抛物线坐标的转化,利用分离变量法进行了相应求解,并给出了相应的数值计算。结果表明,非傍轴近似情况下,矢量波动方程的解能描述一种光束的电场,该场的解析表达式与合流超几何函数以及梅杰函数的解有关;光束的光强分布与第1类零阶贝塞尔模式光束类似;光束在近光轴处的光强表现为无限大并且沿边缘方向急剧衰减;在焦平面上沿着径向方向光强急剧减小。所得结果对于探究非傍轴近似情况下矢量光束的传输特性有一定的意义。     

A weak form of the conjugate gradient FFT method fortwo-dimensional TE scattering problems

The problem of two-dimensional scattering of a transversal electric polarized wave, by a dielectric object is formulated in terms of a hypersingular integral equation, in which a grad-div operator acts on a vector potential. The vector potential is a spatial convolution of the free-space Green's function and the contrast source over the domain of interest. A weak form of the integral equation for the unknown electric flux density is obtained by testing it with rooftop functions. The vector potential is expanded in a sequence of the rooftop functions and the grad-div operator is integrated analytically over the dielectric object domain only. The method shows excellent numerical performance     

求解电磁场并矢格林函数的新方法

本文提出了求解电磁场边值问题的新方法:把矢量波方程的边值问题化为对应的标量波方程的边值问题加上两个附加的矢量微分运算的问题。用这种方法可以很方便地求解所有现在用并矢格林函数的本征展开法所能求得的各种并矢格林函数。可以求解用现有的方法很难求解的比较复杂系统的并矢格林函数。文中给出了加载的谐振腔的并矢格林函数就是其中的一例。     

A NEW METHOD FOR SOLVING DYADIC GREEN''''S FUNCTION OF ELECTROMAGNETIC FIELD

A new method for solving electromagnetic field boundary value problem is given.Byusing this method,the boundary value problem of the vector wave equation can be transformedinto the independent boundary value problem of scalar wave equations and the two additionalvector differential operations.All the dyadic Green's functions got by eigenfunction expansionof the dyadic Green's function can be got by this method easily and some of the dyadic Green'sfunctions for complex systems which are very difficult to get by the ordinary method have beengot by this new method.The dyadic Green's function for a dielectric loaded cavity is one of thegiven examples.     

Integral equation analysis for first order vector correction ofarbitrary profiles

The author's semianalytical method of analysis for arbitrary weakly guiding circular and noncircular profiles based on the scalar wave equation is extended and developed to encompass the analysis of the first order vector correction for the zeroth order modes of the scalar wave equation. The method presented implements no approximations in the analysis of the first order correction and retains all the properties of the semianalytical method of analysis previously presented, thus resulting in a method of analysis possessing extremely high accuracy (<10^-5%)     

Complex frequency shifted-perfectly matched layer for the finite-element time-domain method

We present a new formulation to implement the complex frequency shifted-perfectly matched layer (CFS-PML) for boundary truncation in three-dimensional vector finite-element time-domain method applied to the vector wave equation. It is shown that the proposed method is highly absorptive to evanescent modes, when computing the wave interaction of elongated structures or sharp corners, and can improve the performance of the boundary truncation, significantly. The impact of the CFS-PML parameters on the reflection error is investigated and optimal choices of these parameters are derived.     

Two-dimensional rectangular lattice distributed feedback lasers: Acoupled-mode analysis of TE guided modes

Two-dimensional rectangular lattice distributed feedback lasers in a waveguide geometry are described by a coupled-mode analysis of a scalar wave equation derived from a vector field for TE guided modes. A detailed analysis is provided for a two-dimensional grating which allows the method of separation of variables for the scalar wave equation so that the threshold conditions are described by those of two orthogonal one-dimensional gratings. We present the correct definitions of threshold gain and detuning of the two-dimensional distributed feedback laser, and also the optimum design conditions for the minimization of the threshold gain. It is found that there is an optimum structural angle for the given area and periods of the two-dimensional grating     

Radiation patterns of higher azimuthal order spatial modes from aconcentric-circle-grating waveguide cavity using the volume-currentmethod

We calculate the surface-emitted scattered radiation from a concentric-circle-grating waveguide cavity. The full vector form of the scattered radiation is calculated using the volume-current method, where the index perturbation caused by the grating is represented as an induced-current driving term in the free-space wave equation for the scattered field. We show intensity patterns and field vector plots for a range of azimuthal modes besides the previously reported fundamental mode, and we find excellent agreement with the observed emission patterns and field polarization from concentric-circle-grating surface-emitting semiconductor lasers     

Spurious modes in finite-element methods

This paper describes the problem of spurious modes that appear with finite-element solutions of the vector wave equation. It explains that this problem is caused by inconsistent approximations of the static solutions to the wave equation. Tangential-vector finite elements are described that enforce the tangential continuity of the vector field, but leave the normal component discontinuous. It is shown that tangential elements provide consistent approximations of the static solutions to wave problems, and that spurious modes are not produced by this type of finite element. Applications of the theory presented include problems from microwave and antenna design, and from electromagnetic compatibility     

A new method for solving Dyadic Green’s Function of electromagnetic field

A new method for solving electromagnetic field boundary value problem is given. By using this method, the boundary value problem of the vector wave equation can be transformed into the independent boundary value problem of scalar wave equations and the two additional vector differential operations. All the dyadic Green’s functions got by eigenfunction expansion of the dyadic Green’s function can be got by this method easily and some of the dyadic Green’s functions for complex systems which are very difficult to get by the ordinary method have been got by this new method. The dyadic Green’s function for a dielectric loaded cavity is one of the given examples. This project is supported by the National science Fundation of China     

The Green's Dyadic for Radiation in a Bounded Simple Moving Medium

The studies here show that the wave equation for electromagnetic wave propagation in an isotropic and uniformly moving medium is solvable by the separation method in four coordinate systems. Solutions in the form of complete sets of eigenfunctions are possible for problems where boundary surfaces are presented. A Green's dyadic for finite or semi-infinite domain problems involving sources in the moving medium has been formulated through vector operation on the eigenfunction solutions of the homogeneous wave equation. The case of electromagnetic waves excited by a current loop, immersed in a moving medium, and confined by a circular cylindrical waveguide, was examined. The electric and magnetic field intensities in such a waveguide were compared with those obtained through a different approach. The Green's dyadic for electromagnetic waves in an infinite domain moving medium was shown to be obtainable from the finite domain Green's dyadic through a limiting process.     

Diffraction by a perfectly conducting semi-infinite screen in an anisotropic plasma

The scattering of a plane electromagnetic wave by a perfectly conducting semi-infinite screen embedded in a homogeneous plasma is investigated. A uniform magnetic field is assumed to be impressed externally in a direction parallel to the edge of the half plane. The plasma is idealized to be a dielectric characterized by a tensor dielectric constant. The direction of the incident wave is assumed to be in a plane perpendicular to that of the screen. This vector problem is separable into two equivalent scalar problems for which either the electric or the magnetic vector is parallel to the edge of the half plane. It is found that for the case of theEmode, the magnetic vector parallel to the edge of the half plane satisfies a simple wave equation and a new type of impedance boundary condition on the screen. This problem is formulated in terms of an integral equation which specifies the current induced on the screen. The integral equation is of the Wiener-Hopf type and is solved by the usual function-theoretic methods. For a given orientation of the external magnetic field, a surface wave is found to exist along the screen but on one side only. The characteristics of this surface wave are determined.     

用场量迭代法分析三维介质目标的电磁散射

本文用场量迭代方法对三维电场积分方程进行数值求解,得到了给定电磁波照射下介质体内的场分布,并由此求得介质体外的散射场.从本文给出的几个算例看出,得到的解能较快收敛,并且避免了矩阵求逆运算,具有运算简便与速度快等优点。本文给出的薄板形介质的计算结果与现有文献的实验结果和计算结果进行了比较.证实了本文方法的正确性。     

A fast combined field volume integral equation solution to EM scattering by 3-D dielectric objects of arbitrary permittivity and permeability

A fast solution to the combined field volume integral equation (CFVIE) for electromagnetic scattering by large three-dimensional dielectric bodies of arbitrary permittivity and permeability is presented. The CFVIE is formulated in the region of the scatterers by expressing the total fields as the sum of the incident wave and the radiated wave due to both the electric and magnetic polarization currents. The resultant integral equation is solved using the method of moments (MoM). Then the precorrected fast Fourier transform (P-FFT) method is applied to reduce the memory requirement and accelerate the matrix-vector multiplication in the MoM solution. In the implementation of the P-FFT method, two sets of projection operators are constructed respectively for the projections of the electric sources and magnetic sources. In addition, two sets of interpolation operators are also applied respectively for the computation of the vector/scalar potentials and the curl of the vector potentials in the support of the testing functions. The resultant method has a memory requirement of O(N) and a computational complexity of O(NlogN) respectively, where N denotes the number of unknowns.     

Stability issues in vector electric field propagation

Demonstrates that although standard paraxial and wide-angle vector field propagation techniques lead to divergences for sufficiently small grid-point spacings and large refractive index differences, stability may be restored through either certain Pade approximates to the propagation operator or suitable boundary conditions. The authors also introduce a novel alternating directional implicit method applicable to less divergent discretizations of the vector wave equation     

Field representations in uniaxial bianisotropic medium bycylindrical vector wave functions

Field representations are presented in a uniaxial bianisotropic material region. The results reveal that the solution of a source-free vector wave equation is the sum-integral form of the circular cylindrical vector wave functions in isotropic media. The application of the proposed theory to scattering is considered