A hybrid projection method for analysis of waveguide arrays with protruding dielectric elements: 2D problems

A method is proposed for the analysis of an array of parallel-plate waveguides with protruding longitudinally inhomogeneous dielectric elements. The method consists in expansion of the transverse electric (for the case of E polarization) or magnetic (for the case of H polarization) field in the domain containing the dielectric elements in terms of transverse functions of the Floquet channel. This expansion contains unknown variable coefficients. Projection of the Helmholtz equation for the aforementioned fields onto the transverse functions and application of a 1D finite-element method along the longitudinal coordinate in combination with projective matching of the fields in the waveguide apertures and at the boundary with free space reduces the problem to solution of a system of linear algebraic equations. The results of calculation of the reflection coefficient and the radiation pattern of an array element are presented. These results characterize both the efficiency of the proposed method and the possibility of formation of sector element patterns in the studied arrays.     

Analysis of waveguide antenna arrays with protruding dielectricelements

The two-dimensional problem of radiation of TE and TM waves from a waveguide array with protruding smooth dielectric elements of arbitrary shape is considered, and solution algorithms are suggested. The algorithms are based on applying the method of auxiliary sources for the representation of electromagnetic fields outside and inside the protrusions in combination with the method of integral equations for the electric field at the waveguide aperture. The point matching of the field tangential components on the protrusion-to-free-space boundary and at the waveguide aperture is used to reduce the problem to a system of linear algebraic equations for the amplitudes of the auxiliary filamentary currents and of the waveguide aperture electric field, which is assumed to be piecewise constant. The amplitudes obtained from the solution of the system are used for computing the array reflection coefficient and element pattern, which are shown in some cases to be significantly dependent on the protrusion shape. Examples of arrays with flat-topped element patterns resulting from array geometry numerical optimization are also presented     

Analysis of 1D periodic dielectric structures using a hybrid projection method

A method is proposed for analysis of longitudinally inhomogeneous 1D periodic dielectric structures located on a homogeneous magnetodielectric layer. According to the method, in the case of the E (H) polarization, the transverse electric (magnetic) field in the region containing the elements of the structure is expanded over transverse functions of Floquet harmonics with unknown variable coefficients. Projection of the Helmholtz equations for the aforementioned fields onto the transverse functions, application of the 1D method of finite elements for the longitudinal coordinate, and use of projection matching of the fields on the boundaries of partial regions reduce the problem to numerically solvable systems of linear algebraic equations. The results of comparison demonstrating the efficiency of the method, the results of optimization of rectangular and triangular elements of a lossless dielectric structure designed for matching to free space, and the reflection coefficients for absorbing periodic structures based on recently developed wideband polyurethane-foam materials with a superdispersed carbonic filler are presented and discussed.     

Mode matching analysis of the dielectric waveguide 3-D discontinuity problem

In this paper, the dielectric waveguide 3-D discontinuity problem is investigated by the method which combines the multimode network theory with the rigorous mode matching procedure both in the transverse cross section and in the longitudinal direction. Good agreement has been found between the numerical results and the experimental data in the literature, and the effectiveness and accuracy of the present method are justified. Some numerical results are given to establish useful guidelines for the design of dielectric waveguide components in the millimeter and optical wave integrated circuits.     

A hybrid dielectric slab-beam waveguide for the sub-millimeter waveregion

A hybrid dielectric-slab-beam waveguide is suggested which should be well suited as a transmission medium for the design of planar quasi-optical integrated circuits and devices operating in the millimeter- and sub-millimeter-wave regions. The guide consists of a grounded dielectric slab in which a sequence of equally spaced cylindrical lenses is fabricated. The center line of the slab guide is the axis of the lenses. The structure uses two distinct waveguiding principles in conjunction to guide electromagnetic waves. In the direction normal to the slab surface, the guided fields behave as surface waves of the slab guide; their energy is largely confined to the interior of the dielectric and they are guided by total reflection at the slab surface. In the lateral direction the waves behave as Gauss-Hermite-beam modes that are guided by the lenses, which periodically reconstitute their cross sectional phase distribution, resulting in a wave beam that is iterated with the lens spacing. The guided fields are in effect TE and TM modes. The analysis of the new guiding structure is analyzed, the mode spectrum is calculated, and the iteration loss due to the finite size of the lenses is estimated     

The method of lines for the analysis of dielectric waveguide bends

The analysis of a wide class of waveguide bends using the method of lines is suggested. The discretization is performed in radial direction. The cross section of the waveguide may consist of many inhomogeneous layers. Loss can be taken into account by using complex permittivities. The radiation loss is calculated by the use of absorbing boundary conditions. The presented algorithm is verified by the analysis of a rib waveguide bend. The results are in good agreement with those published in the literature     

一种波导裂缝阵列天线设计方法

结合等效电路法和有源导纳法,将设计波导裂缝阵列天线的Elliott方程改写为两个方程组进行求解,利用归一化电导迭代求解两个方程组,得到裂缝参数,避免了直接求解二元非线性方程而产生的大量无用解。互耦系数gmm的计算采用Taylor级数展开式近似。用等效电路法与本文方法分别设计了64元驻波线阵,仿真结果表明,本文方法降到了天线副瓣。     

Design of slot arrays in waveguide partially filled with dielectric slab

The Elliot procedure for the design of a waveguide slot array is extended to the case of partially filled radiating waveguides. The dielectric slab lies on the top of the radiating waveguide, i.e. on the slotted wall. The proposed solution prevents some of the most common drawbacks of waveguide slot arrays. Results are validated against a commercial FEM software.     

High-accuracy finite-difference equations for dielectric waveguide analysis II: dielectric corners

For part I see ibid., p. 1210, 2002. We present a discussion of the behavior of the electric and magnetic fields satisfying the two-dimensional Helmholtz equation for waveguides in the vicinity of a dielectric corner. Although certain components of the electric field have long been known to be infinite at the corner, it is shown that all components of the magnetic field are finite, and that finite-difference equations may be derived for these fields that satisfy correct boundary conditions at the corner. These finite-difference equations have been combined with those derived in the previous paper to form a full-vector waveguide solution algorithm of unprecedented accuracy. This algorithm is employed to provide highly accurate solutions for the fundamental modes of a previously studied standard rib waveguide structure.     

Vector analysis of optical dielectric waveguide bends usingfinite-difference method

A full-vectorial analysis of optical dielectric waveguide bends using the finite-difference method has been developed. The formulation was based on the transverse electric field components, E_r and E_z. To set up the boundary conditions at each dielectric interface, the continuity of E_&thetas;, H_&thetas;, and the tangential component of the electric field, and the discontinuity of the normal component of the electric field were satisfied. The finite-difference scheme was modified to satisfy these boundary conditions. The results of the analysis using the current method is compared with previous results. The optimal offset for 90° bends was obtained, and the losses for these optimal bend structures are also presented     

Generalized moment method analysis of planar reactively loadedrectangular waveguide arrays

A combined modal expansion and moment method is applied for analyzing finite planar arrays of rectangular waveguides in an infinite ground plane including reactively loaded waveguide elements. The analysis, which is based on the moment method for solving the aperture problem, in combination with the modal analysis for the reactively loaded waveguide cavities or feeding waveguides, extends the network formulation of single apertures to multiple waveguide arrays including reactively loaded elements. Two orthogonally polarized sets of basic functions are utilized to model the expansion into the complete set of eigenmodes is used to formulate the waveguide cavity problem. The theory is applied to a finite planar array of arbitrarily spaced rectangular waveguides, where reactive loads are realized by placing sliding electrical conductors at specified distances in each of the unfed waveguides. Numerical design examples show that beamforming, beamsteering, and the improvement of the crosspolarization behavior is possible by a suitable choice of the geometrical parameters. The theory is verified by results available from the literature as well as newly performed experimental measurements     

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.     

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.     

Approximate 3D model of electromagnetic modes in waveguide cross-shaped junctions with dielectric filling

Athree-dimensional electrodynamic model of hybrid electromagnetic modes in a waveguide junction of cylindrical and rectangular waveguides with dielectric filling of a cylindrical waveguide is proposed in this study. To solve the vector problem, the mode matching technique (MMT) is applied with the separation of the common waveguide junction region and the representation of the field in this region in the form of superposition of the fields of the partial eigenwaves of waveguides. Classification of eigenmodes is carried out: intrinsic resonances of junction based on transcendental modes and resonances of a waveguide-dielectric type. The investigated structure can be used for measuring the electrical parameters of dielectric samples of both cylindrical and rectangular cross-section shape. Since the spectral characteristics of the junction are determined mainly by the size of the central coupling region of the waveguides and the electrical parameters of the dielectric in the junction, the measurements are of a local nature.     

A novel design method for electromagnetic bandgap based waveguide filters with periodic dielectric loading

An extremely rapid, versatile prototyping methodology is developed for waveguide filters with periodic dielectric loading which enables direct dimensional synthesis of the unit cell starting from given design objectives. A prototype filter has been designed using a low dielectric constant material and built for the purposes of testing the feasibility of the proposed approach. Our numerical results are compared with an independent commercial software package and also with experimental measurements. Simulation results are also presented for a filter loaded high dielectric constant material. In both cases the results are in excellent agreement with the theory and demonstrate the validity and the applicability of the proposed method.     

复杂多层介质电磁分析的几何建模及剖分技术

三维复杂介质结构高精度的几何建模和高质量的离散网格数据文件是应用体积分方程矩量法(VIE-MoM)分析其电磁问题的重要前提.借助商用CAD建模软件,针对复杂多层非均匀介质结构的特点,采取了一种由面到体的几何建模思路快速地建立其三维实体几何模型,有效地解决了非均匀介质突变表面上四面体网格的匹配问题,从而实现对实体模型的快速网格离散,获取高质量的四面体网格数据文件.对双层半球壳、双层直锥形、正切卵形天线罩等几种多层介质结构的建模和网格剖分实例表明,采用本文所述方法,在不同形状的介质交界面上都能够实现优良的网格匹配效果,可为VIE-MoM计算复杂多层介质电磁问题提供高质量的网格数据文件.     

A hybrid finite element method for 3-D scattering using nodal andedge elements

A hybrid finite element method for three-dimensional scattering is presented and numerical examples shown. This approach, which couples finite element discretization with the method of moments, is particularly well suited for monostatic radar cross section calculations. The method is based on a scalar and vector potential formulation of Maxwell's equations, the use of nodal elements, and a highly efficient body of revolution implementation of the method of moments. Combined nodal and edge elements are employed to accurately model fields around corners and edges. A curvature-based sampling criterion is derived and shown to ensure accurate answers for highly curved scatterers. Numerical results and Cray computer timings are compared with published results for an edge element code using radiation boundary conditions     

High-accuracy finite-difference equations for dielectric waveguide analysis I: uniform regions and dielectric interfaces

A methodology is presented that allows the derivation of low-truncation-error finite-difference representations or the two-dimensional Helmholtz equation, specific to waveguide analysis. This methodology is derived from the formal infinite series solution involving Bessel functions and sines and cosines. The resulting finite-difference equations are valid everywhere except at dielectric corners, and are highly accurate (from fourth to sixth order, depending on the type of grid employed). None the less, they utilize only a nine-point stencil, and thus lead to only minor increases in numerical effort compared with the standard Crank-Nicolson equations.     

小型波导缝隙天线阵的改进设计方法研究

利用传输线理论构造负载阻抗的近似计算公式,采用数值逼近法直接计算阵列中的缝隙归一化导纳,从而可以在Elliott波导缝隙天线阵设计过程中避免使用感应电动势法和矩量法,进而可以提高设计速度.最后采用该方法设计了工作频率为9.375GHz的缝隙阵结构参数,仿真结果表明改进设计方法比较有效.     

一种抑制波导窄边缝隙阵列天线交叉极化的方法

为了抑制波导窄边缝隙阵列天线交叉极化电平,采用一种在波导外壁开非倾斜缝隙、在波导内壁开倾斜缝隙的方法。利用电磁仿真软件HFSS进行仿真,得到孤立缝隙与阵中单个缝隙的电导函数。设计了一个47单元X波段波导窄边缝隙均匀直线阵列,与常规缝隙阵列相比,天线交叉极化电平降低了6.8 dB。