Numerical Solution of Dielectric Loaded Waveguides: I-Finite-Element Analysis

A variational expression of the electromagnetic fields in dielectric loaded waveguides is derived. This expression is discretized using the finite-element method and an electromagnetic coupling matrix is derived and evaluated. No restriction is placed on the shapes of the triangular elements or the order of the polynomial approximation. A general finite-element computer program is described and dispersion curves and field plots of some dielectric loaded waveguides are presented.     

A Combined Method for Dielectric Waveguides Using the Finite-Element Technique and the Surface Integral Equations Method

A combined method employing a finite-element technique in the H/sub x/ - H/sub y/ formulation and the surface integral equations method is proposed to treat the propagation characteristics of inhomogeneous waveguides with single or multiple claddings. The significant features of this combined method are that it does not suffer from any kind of spurious modes, which have been troublesome in applying the finite-element technique to waveguides and it is also capable of treating the cutoff frequencies of arbitrarily shaped, inhomogeneous dielectric waveguides with a single cladding, which is perhaps original. Furthermore, the proposed method is convenient in treating propagation constants close to cutoff and in handling coupled waveguides. Numerical results of inhomogeneous elliptical waveguides, diffusion waveguides, and the corresponding directional couplers are presented, including the cutoff frequencies of the elliptical waveguides.     

A scalar variational conformal mapping technique for weakly guiding dielectric waveguides

A novel approach of combining the finite-element method with the conformal mapping technique is proposed for solving the scalar variational formulas for weakly guiding dielectric waveguides. This approach avoids spurious modes and gives satisfactory results even for modes near cutoff, requiring less computer memory and time. Various specific dielectric structures, such as the rectangular guide, channel guide, and rib guide, are considered to estimate the error associated with the scalar formulation relative to the vectorial formulation. The efficiency of this approach is demonstrated with an analysis of a directional coupler whose coupling properties are described by means of numerical results such as propagation constants, field distributions, etc.     

Approximate scalar finite-element analysis of anisotropic optical waveguides

An approximate scalar finite-element program for the analysis of anisotropic optical waveguides with a diagonal permittivity tensor is described. The accuracy of the method has been checked by calculating the eigenmodes of two-dimensional, anisotropic asymmetric slab waveguides. The results obtained for a channel waveguide embedded in LiNbO3 agree well with the results of the earlier vectorial finite-element method.     

非均匀介质填充波导本征值问题的有限元分析

本文讨论了用有限元法求解非均匀介质填充波导本征值问题的具体过程。给出了有关的计算公式和程序。作为例子,对条形介质填充矩形波导主模场结构的分析和色散特性的计算,获得了与解析解十分一致的结果,从而证实了所述程序的可靠性。     

任意块状介质填充矩形波导色散特性的数值分析

本文给出了一个用有限元法计算任意块状介质填充矩形波导的孪生波主模和高次模色散特性的标准程序。使用该程序,对十余种不同结构、不同介质加载矩形波导色散特性的计算,证实了所述程序的可靠性,文中对工字形介质填充波导的有用带宽作了详细的分析。本文所提供的各种色散特性曲线可供分析和设计有关微波元件时参考。     

Fourier decomposition method applied to mapped infinite domains:scalar analysis of dielectric waveguides down to modal cutoff

By transforming the infinite x-y plane onto a unit square and using two-dimensional Fourier series expansions, the modal fields and propagation constants of dielectric waveguides are accurately determined within the scalar (weak-guidance) regime. The new method is reliable down to modal cutoff and gives cutoff V-values directly. Numerical cutoff values for the LP₁₁ modes of square- and rectangular-core waveguides are determined as a function of core aspect ratio, and are found to agree with those obtained by the finite element method to within 0.1%     

基于时域有限差分法填充介质梯形脊波导研究

为了研究填充介质对脊波导截止特性的影响,文章采用FDTD(时域有限差分)法计算了填充介质梯形双脊波导在TE(横电波)模式下的截止特性随几何尺寸的变化,并给出了关系曲线。结果表明,脊间距越小,填充介质的相对介电常数越大,截止波长越长,单模带宽越窄。研究结果丰富了现存填充介质波导数据,有助于填充介质波导的设计和工程应用。     

Approximate Scalar Finite-Element Analysis of Anisotropic Optical Waveguides with Off-Diagonal Elements in a Permittivity Tensor

An approximate scalar finite-element program for the analysis of anisotropic optical waveguides having a permittivity tensor with nonzero off-diagonal elements is described. In this approach, the nonphysical spurious solutions which are included in the solutions of the earlier vectorial finite-element method in an axial-components formulation do not appear. Numericaf examples On an anisotropic dielectric rectangular wave-guide composed of a uniaxial medium are given. Our results for the waveguide whose optic axis lies in the plane ( xy-plane) normal to the direction (z-axis) of propagation agree well with the results of the vectorial wave analysis using the variational method. We also demonstrate the application of this approach by analyzing the anisotropic dielectric rectangular waveguide whose optic axis lies in the xz - or yz -plane.     

A Variational Analysis of Dielectric Waveguides by the Conformal Mapping Technique

The variational formulation together with the finite-element method is a well-established technique for the solution of a dielectric waveguide. One common difficulty is the handling of the problem with the infinite extent of the electromagnetic fields in the transverse plane. In this paper, the conformal mapping technique is employed to improve the modeling of the region exterior to the guides; hence it may give more accurate results for the modes near the cutoff region. Also included are the numercal results for rectangular, strip, and channel waveguides to demonstrate the applications of the proposed technique.     

Numerical modeling of generalized millimeter-wave transmission media with finite element and transmission line matrix methods

In this paper, a general finite element method as well as a graded-mesh TLM procedure for determining the dispersion characteristics, field distribution, pseudo-impedance and losses of generalized millimeter-wave transmission media are described. These methods cover arbitrary cross-sections and account for realistic features (finite metallization thickness, substrate mounting grooves etc.) that are often neglected in theoretical analysis. Dispersion characteristics and characteristic impedances obtained for dielectrically loaded ridged wave-guides compare well with the available data. Conductor and dielectric losses are also computed for these structures. A modified finline structure called “ridged finline” is also analysed. The main advantages of this structure are its large monomode bandwidth and reduced dispersion. The cutoff frequencies of bilateral finlines in circular waveguides are also computed.     

A modified finite-element method for dielectric waveguides using anasymptotically correct approximation on infinite elements

A modified finite-element method for the propagation analysis of such dielectric waveguides as optical fibers and integrated optical waveguides is presented. Possible applications include nondissipative structures of arbitrary anisotropic media with, in some cases, inhomogeneous exterior regions. The method is based on the full vectorial finite-element formulation, which is known to be without spurious solutions. With this formulation all appropriate boundary and interelement conditions on both tangential and normal components are a priori satisfied. For the unbounded, exterior region a novel type of asymptotically correct approximation on infinite elements is proposed that simultaneously, for each mode and frequency, locally adapts the rate of radial decay to the transversal wavenumbers. The linearity of the original finite-element method has been retained by using β/k₀ as a parameter, which results in a sparse generalized eigenvalue problem. Numerical examples including both optical fibers and integrated optical waveguides, isotropic as well as anisotropic, have been analyzed to confirm the validity of the method. The observed correspondence with analytical solutions has been excellent. For some examples a special near-field wavenumber has been added to preserve a high accuracy close to cutoff     

Approximation Technique for Dielectric Loaded Waveguides

An algebraic procedure is described which yields approximate values for the cutoff frequencies and propagation constants of dielectric-loaded waveguides. The procedure is demonstrated for a waveguide completely filled with an anisotropic dielectric and for waveguides partially filled with isotropic dielectrics. For the latter case results are tabulated for five types of waveguide loading. The symmetrically loaded waveguide is used to show the accuracy which may be expected. This procedure is shown to be identical with the Rayleigh-Ritz variational method but with the advantage that it provides a systematic approach to improve the accuracy and to handle a multitude of waveguide geometries.     

A partial variational approach for arbitrary discontinuities inplanar dielectric waveguides

A novel approach for analyzing arbitrary discontinuities in planar dielectric waveguides is proposed that uses the finite-element method along with the frontal solution technique. On the basis of the partial variational principle (PVP), the fields interior and exterior to the discontinuity finite-element region can be treated independently and eventually can be coupled. The interior fields are expanded by the finite-element nodal values and the corresponding local bases, while the exterior ones are handled by an approach combining modal expansion and Green's function. In numerical computation, the continuous spectra of the waveguide modes are discretized by the Laguerre expansion method. To check the correctness of the present analysis, two numerical results are compared to those of other methods. The scattering characteristics of several linearly tapered discontinuities, such as transformers and feed structures, are analyzed and compared to those having step junctions     

Numerical analysis of dispersion characteristics of rectangular waveguides filled with arbitrary block-shaped dielectrics

The dispersion characteristics of rectangular waveguides filled with arbitrary block-shaped dielectrics are calculated by the method of finite element. A generalized program is given for the hybrid dominant and higher order modes. More than ten different rectangular waveguides loaded with various dielectric distributions have been investigated, and the results verify the reliability of the program. In particular, the useful bandwidth of the waveguide filled with I-shaped dielectric is analyzed in detail. The dispersion curves given in this paper are useful for analyzing and designing related microwave components of current interest.     

An efficient finite-element formulation without spurious modes foranisotropic waveguides

A numerically efficient finite-element formulation is presented for the analysis of lossless, inhomogeneously loaded, anisotropic waveguides of arbitrary shape. The electromagnetic field is described either by the three components of a magnetic vector potential and an electric scalar potential or by the three components of an electric vector potential and a magnetic scalar potential. The uniqueness of the potentials is ensured by the incorporation of the Coulomb gauge and by proper boundary conditions. Owing to the implementation of the solenoidality condition for the vector potential even in the case of zero wavenumber, no spurious modes appear. Variation expressions suited to the finite-element method are formulated in terms of the potentials. Standard finite-element techniques are employed for the numerical solution, leading to a generalized eigenvalue problem with symmetric, sparse matrices. This is solved by means of the bisection method with the sparsity of the matrices fully utilized. Dielectric- and ferrite-loaded waveguides with closed and open boundaries and including both isotropic and anisotropic materials are presented as examples     

Numerical analysis of arbitrarily shaped discontinuities betweenplanar dielectric waveguides with different thicknesses

An approach that combines the finite-element and boundary-element methods is applied to the analysis of arbitrarily shaped discontinuities between planar dielectric waveguides with different thicknesses. The fields interior and exterior to the region enclosing the discontinuities are treated by the finite-element method and the boundary-element method, respectively. The waveguide regions connected to the discontinuities are handled by analytical solutions. In this approach, scattering characteristics of the discontinuities can be accurately evaluated, and far-field radiation patterns can be easily calculated. To show the validity and usefulness of this approach, the scattering characteristics of a step, a staircase transformer, and a tapered transformer are analyzed. Also, a simple equivalent network approach is introduced for estimating the reflection and transmission characteristics of planar dielectric waveguide discontinuities, and the effectiveness of this simple approach is confirmed by comparing the numerical results with those of the approach that combines the finite-element and boundary-element methods     

Finite-element analysis of leaky waveguide antennas

A finite-element method is described for the analysis of leaky modes of open uniform waveguides with arbitrary cross-section. The field is represented by a hybrid element in the infinite exterior region, and by conventional triangular elements inside and near the waveguide. Results are presented for channel waveguide, slotted square guide and slotted circular waveguide.     

The Solution of Inhomogeneous Waveguide Problems Using a Transmission-Line Matrix

A method of applying the transmission-line matrix method to inhomogeneous waveguide structures is described. The technique uses open-circuit stubs of variable characteristic impedance at each node in the matrix, thereby providing an analog for a dielectric. LSE and LSM modes in rectangular waveguides, and problems involving a step of dielectric are solved. Results are given in terms of the cutoff frequency and field pattern for continuous waveguides, and the waveguide input impedance for scattering problems.     

Finite-Element Analysis of Overmoded Waveguide Using Silvester's Algorithm (Short Paper)

A general, high-order finite-element waveguide analysis program originated by Silvester [1], [2] has been used to analyze overmoded waveguides. The algorithm approximates arbitrarily shaped waveguides by triangular subsections and solves the Hehnholtz equation subject to homogeneous Dirichlet or Neumann boundary conditions to obtain the eigenvalues (cutoff wavelengths) and the eigenvectors (scalar potentials). During these investigations of arbitrarily shaped overmoded waveguides, a computer program error was identified. This error resulted in incorrect higher-order mode potential functions. As this algorithms has been rather widely disseminated, it is the purpose of this communication to inform users of a correction which yields the correct higher-order-mode potential functions.