过尺寸毫米波铁氧体移相器的工程设计

旋磁波导问题一般是利用驻波展开法导出耦合波方程组再求解。但这种方法由于数值实现比较困难，处理高次模问题有一定的局限性。文中提出利用Galerkin法求解本征模问题，即把波导中的电磁波用矩形波导基本波型函数展开，把波导模式问题进一步转化为矩阵特征值问题。在此基础上计算了过尺寸铁氧体移相器各阶传播模式场型分布，并给出了有关工程设计曲线。     

Ag-coated Long-period Fiber Grating

Based on coupled-mode theory, the eigenvalue equation of five-layered long-period fiber grating （LPFG） sensor with Ag film and gas-sensitive film overlays are firstly studied. The problem of resolving complex eigenvalue equation on five-layered LPFG is analyzed, and the method of resolution is also given. Then the eigenvalue equation of three-layered metal cladding LPFG is analyzed, and the complex transcendental equation is also discussed. The computing result shows that the coupling between the low order EH modes and the core mode is much stronger than that between the low-order HE modes and the core mode.     

能消除“非物理模”的电磁谐振腔的数值方法

本文用矢量偏微分算子理论计算了一种特殊结构电磁谐夺腔的本征问题,计算结果表明,这一方法确实可以消除“非物理模”的影响不需要加任何人为的惩罚因子,直接连续地计算出20个最低的谐振模式,该方法不仅计算快速,节省内存,而且精度很高,是一种很有前景的电磁场数值计算方法。     

Nonparaxial eigenmodes of stable resonators

A method to determine the nonparaxial eigenmodes of stable resonators is presented. The method is based on the perturbation theory of Lax et al. For calculating nonparaxial components of the electric field. A matrix formalism which uses a mode expansion into paraxial Hermite-Gaussian modes is applied to describe the nonparaxial propagation and the phase shift at a parabolic and a spherical mirror. Expressions for these matrices are derived analytically. Multiplying all matrices corresponding to a round trip, a matrix for the resonator is obtained. Eigenmodes of the resonator are numerically found by solving the eigenvalue problem. In the special case of paraxial propagation and parabolic mirror profiles, the standard Hermite-Gaussian modes result analytically. Nonparaxial modes of a given resonator are compared for different mirror profiles. It is found that, in the nonparaxial domain, spherical mirrors do not change the mode profile and the frequencies of the transverse modes, in contrast to parabolic mirrors which aberrate the beam profile and cause frequency shifts     

NETWORK ANALYSIS OF EIGENVALUE PROBLEM FOR MULTILAYER DIELECTRIC WAVEGUIDE CONSISTING OF ARBITRARY NUMBER OF LAYERS

In this paper,the eigenvalue problem of a multilayer dielectric waveguide consisting of arbitrarynumber of layers is solved by the microwave network method.A general program with the function of com-puter graphics has been developed for analyzing the dispersion characteristics and the electromagnetic fielddistributions of an N layer dielectric waveguide.As an example of practical applications,the procedure ofmode conversion and mode separation in dielectric branching waveguides is vividly demonstrated throughanalyzing the field distributions of asymmetric multilayer dielectric structures and the general rules of modeconversion are discussed.     

Waveguide Modes Via an Integral Equation Leading to a Linear Matrix Eigenvalue Problem

A numerical method for determining the modes of a rectanguIar or a circular waveguide strongly perturbed by axial cylindrical conducting objects is presented. The method is based upon an integral equation which leads to a matrix eigenvalue problem by using the Galerkin procedure. Cutoff wavenumbers are simultaneously calculated with very good precision for a number of modes near to the order of the matrix eigenvalue problem. Excellent results are obtained also when the perturbed waveguide section exhibits reentrant parts or edges. Computing time is short and storage requirements are moderate. The method is also applicable for waveguides of arbitrary cross section.     

A simple technique for calculating the propagation dispersion ofmulticonductor transmission lines in multilayer dielectric media

A multiconductor transmission line in a multilayer dielectric medium is complicated and therefore is frequently analyzed by the simple quasi-TEM (transverse electromagnetic) approach. Unlike the full wave eigenvalue approach, the quasi-TEM approach does not give the propagation dispersion characteristics of the line. This work overcomes this problem by first obtaining the solution of each multiconductor mode from the quasi-TEM approach. Then these solutions are used as both basis and testing functions in a variational formulation of the full wave eigenvalue analysis. The result is high accuracy in the dispersive propagation constants of the multiconductor modes. By solving only for high frequency eigenvalues, not for the high frequency eigenvectors, the method is simpler and faster than the conventional full wave dispersion analyses     

Analysis of a parallel resistive plate medium [EM scattering]

A half-space composed of parallel resistive sheets is studied by formulating an eigenvalue problem to find the characteristic modes of the medium. Two equivalent formulations of the eigenvalue problem are presented. The first approach is analytical in nature and provides greater insight into the physical behavior of the material, while the second is numerical and applicable to a wider class of problems. The eigenvalue problem is solved via the Muller method to find the complex modal wavenumbers and field distributions within the resistive sheet medium. The mode-matching procedure is used to study the medium's reflection and absorption properties     

Analysis of Elliptical Thin Ridged Waveguide

Elliptical waveguides and ridged waveguides have found broad applications in many microwave structures. The elliptical waveguide with double infinite thin ridges has been formulated using the mode-matching method. Exact closed-form expressions for eigenvalue problem of all TE and TM modes are presented. Numerical results suggest that the elliptical ridged waveguides have larger bandwidth than that of circular ones.     

Network analysis of eigenvalue problem for multilayer dielectric waveguide consisting of arbitrary number of layers

In this paper, the eigenvalue problem of a multilayer dielectric waveguide consisting of arbitrary number of layers is solved by the microwave network method. A general program with the function of computer graphics has been developed for analyzing the dispersion characteristics and the electromagnetic field distributions of an N layer dielectric waveguide. As examples of practical applications of the program, first, the dispersions and field patterns for the planar waveguides with refractive index of parabolic and exponential profiles are analyzed. Secondly, the procedure of mode conversion and mode separation in dielectric branching waveguides is vividly demonstrated through analyzing the field distributions of asymmetric multilayer dielectric structures and the general rules of mode conversion are discussed. The examples show that the present method possesses the advantages of versatility, rapidity, simplicity and accuracy.     

Eigenvalue Spectrum of Rectangular Waveguide with Two Symmetrically Placed Double Ridges

The eigenvalue spectrum of rectangular waveguide with two symmetrically placed double ridges has been determined by formulating an integral eigenvalue problem and solving by Ritz-Galerkin method. The bandwidth characteristic is found to be adequate for varactor-tuned solid-state microwave oscillator applications requiring ridge structure for resonator. There remains some ambiguity in the designation of trough modes.     

Propagation in Rectangular Waveguide Filled with Skew Uniaxial Dielectric

A solution is given for propagation in rectangular waveguide fully loaded with a uniaxial dielectric, with the C-axis lying anywhere in the transverse plane. This problem arises in the design of particular traveling-wave masers. By application of the Rayleigh-Ritz method to Berk's variational expression, the problem is reduced to a matrix eigenvalue problem, and in a form suitable for direct evaluation on a digital computer. An explicit approximate solution is, however, shown to give accurate results. The analysis can be interpreted directly in terms of mode coupling of the usual rectangular waveguide modes, and the possible extension is indicated to general tensor media and to circular or elliptical waveguide.     

波导本征值问题的有限元分析

本文简要讨论了波导本征值问题的有限元分析方法。给出了一个用有限元法求解波导本征值问题的标准程序。使用该程序可以获得一大类横截面周界由直线及圆弧围成的波导的各个本征值和本征函数。文中通过对十几种不同结构波导本征值问题的求解,证实了该程序的可靠性。     

Selective screening of waveguide modes by a system of two grids with square cells

The problem of selective screening of waveguide modes with the help of a filter consisting of two metal grids with square cells is analyzed. The filter has perfect contacts at conductors’ crosses. The investigation is performed by means of the method of averaged boundary conditions. The general expressions are obtained for the mode reflection and transmission coefficients. Examples of filtering of various modes are presented for the case of a circular waveguide. The method is shown to be especially efficient for extraction of higher order modes. It is noted that, in such filters, grids with very thin conductors are the most promising.     

On the Complete Eigenvalue Solution of Ridged Waveguide

The complete solution of the ridged waveguide eigen-value problem is presented. The solution is obtained by the formulation of an integral eigenvalue equation which is subsequently solved numerically by application of the Ritz-Galerkin method. The significance of the eigenvalue spectrum is discussed and the modes are classified as either hybrid or trough modes. Equations are given for the electric and magnetic fields and a brief discussion of the edge singularity is presented. The theory is illustrated by computing the dominant eigenvalues and characteristic impedances of various unsymmetrical ridged waveguides.     

High‐Performance Ambipolar Polymers Based on Electron‐Withdrawing Group Substituted Bay‐Annulated Indigo

For donor–acceptor conjugated polymers, it is an effective strategy to improve their electron mobilities by introducing electron‐withdrawing groups (EWGs, such as F, Cl, or CF₃) into the polymer backbone. However, the introduction of different EWGs always requires a different synthetic approach, leading to additional arduous work. Here, an effective two‐step method is developed to obtain EWG substituted bay‐annulated indigo (BAI) units. This method is effective to introduce various EWGs (F, Cl, or CF₃) into BAI at different substituted positions. Based on this method, EWG substituted BAI acceptors, including 2FBAI, 2ClBAI, and 2CF₃BAI, are reported for the first time. Furthermore, four polymers of PBAI‐V, P2FBAI‐V, P2ClBAI‐V, and P4OBAI‐V are developed. All the polymers show ambipolar transport properties. Particularly, P2ClBAI‐V exhibits remarkable hole and electron mobilities of 4.04 and 1.46 cm² V^?1 s^?1, respectively. These mobilities are among the highest values for BAI‐based polymers.     

Coupled mode analysis of a finline

A theoretical analysis of a unilateral finline loaded with arbitrary inhomogeneous lossy dielectric material is presented. The rigorous coupled-mode approach is used. The electromagnetic field in the line is expressed in terms of the modes of a ridged waveguide, and the problem is transformed to a matrix eigenvalue equation. Approximate expressions are derived for investigating the properties of the fundamental mode in finlines loaded with dielectric slabs. Dispersion characteristics, the characteristic impedance, and the attenuation due to dielectric losses and the finite conductivity of the metal coating are computed for various line configurations. The numerical results are compared to data obtained by means of the spectral-domain method, proving the validity and usefulness of the proposed approach     

Analysis of dielectric-loaded cavities using an orthonormal-basis method

An orthonormal-basis method to analyze dielectric-loaded cavities is proposed. Resonant frequencies and fields are obtained by solving an eigenvalue problem in which the modes of an auxiliary problem define the orthonormal-basis that is used to expand the fields of the original problem. The merit of our approach is to take advantage of some mathematical properties to develop a computationally efficient and versatile method. The accuracy of the method is demonstrated by comparing our results with other results available in the literature.     

Brewster Angle Effect on Performances of a New Millimeter Wave Omni-Directional Antenna Gloved with a Dielectric Shell

A new millimeter-wave omni-directional antenna consisting of circular rod corrugations gloved with a dielectric shell operating in the TM₀₁ mode is investigated. As an eigenvalue problem, the antenna is analyzed with the rigorous mode matching method. The radiation characteristics of the antenna are calculated for different parameters with a particular attention directed to the Brewster angle effect on the performances of the antenna. A comparison of the radiation characteristics is made between the antennas with and without dielectric shell. It is found that the introduction of the dielectric shell will change the location where the leakage constant α reduced to zero. The effectiveness and reliability of the present analysis are verified by the calculated results given in the literature. Therefore, some useful guidelines for the design of the antenna are thereby suggested.     

A General High-Order Finite-Element Analysis Program Waveguide

A very general computer program for determining sets of propagating modes and cutoff frequencies of arbitrarily shaped waveguides is described. The program uses a new method of analysis based on approximate extremization of a functional whose Euler equation is the scalar Helmholtz equation, subject to homogeneous boundary conditions. Subdividing the guide cross section into triangular regions and assuming the solution to be representable by a polynomial in each region, the variational problem is approximated by a matrix eigenvalue problem, which is solved by Householder tridiagonalization and Sturm sequences. For reasonably simple convex polygonal guide shapes, the dominant eigenfrequencies are obtained to 5-6 significant figures; for nonconvex or complicated shapes, the accuracy may fall to 3 significant figures. Use of the program is illustrated by calculating the propagating modes of a class of degenerate mode guides of current interest, for which experimental data are available. Numerical studies of convergence rate and discretization error are also described. It is believed that the new program produces waveguide analyses of higher accuracy than any general program previously available.