Electrodynamical Model of Composite Cylindrical Structure with Laminated Dielectric

The article is devoted to the problem of the natural electromagnetic modes, the regions of their existence and the relationship with all possible types of resonances in the waveguide junction of a cylindrical and radial waveguides with a layered (laminated) filling of the radial waveguide with dielectric material. An electrodynamic model is created on the basis of a rigorous method of modal matching technique, with the separation of the common waveguide coupling region and the representation of the field in it in the form of a superposition of the fields of the partial waveguide eigenmodes. The structure under investigation can be used to measure the electrical parameters of dielectric samples of a cylindrical cross-section. It is shown that the measurements will have a local character, since the spectral characteristics of the junctions are determined mainly by the size of the central coupling region of the waveguides and by the electrical parameters of the dielectric that is in the junction. The problem of edge effects for samples of finite length (partial filling of a radial waveguide with dielectric) is investigated. Taking into account the edge effect enables reducing the error in measuring the permittivity for samples of arbitrary sizes in the investigated structure.     

An Exact Calculation for a T-Junction of Rectangular Waveguides Having Arbitrary Cross Sections

An exact method is developed for the calculation of the electrical performance of the rectangular waveguide T-junction. This method is used to find the equivalent circuit of a rectangular waveguide T-junction in which both cross-sectional dimensions of the side waveguide are different from the cross-sectional dimensions of the through waveguide. The theoretical calculations for a particular T-junction of this type are verified by experimental measurements. In this method the electrical performance is analyzed by using equivalent-circuit concepts applied to waveguide modes to calculate an admittance matrix relating propagating and cutoff waveguide modes to each other. Then the cutoff modes are terminated in their characteristic impedance, and an equivalent admittance matrix of the junction is found relating only the propagating modes in each waveguide to each other. The anlysis is valid when any number of modes can propogate in the waveguides forming the junction. The Inversion of an infinite matrix is required; however, any desired accuracy can be obtained by considering a matrix of finite but sufficient size or equivalently by considering a sufficient number of cutoff modes.     

Field analysis of rectangular waveguide open junction

The problem of a rectangular waveguide open junction is investigated using field theory and the relevant model of two normally intersected, infinite parallel-planes waveguides. Evanescent waveguide modes generated by waveguide wall edges and/or the discontinuity in dielectric are taken into account; an infinite set of equations is derived, where the mode coupling is given by the dielectric slab modes. Proper pole handling is discussed, and a solution for the system is given. Expressions are derived for the reflected, transmitted, and radiated power, which are shown to be sufficiently reliable in the domain of practical interest, regarding the width and the dielectric loading of the gap. The analysis shows that a substantial fraction of the microwave power leaks from the dielectric gap, confirming the absolute necessity of using a choke-flange at the waveguide junction     

Analysis of propagation characteristics of whispering gallery modes in a dielectric disk or a curved rectangular dielectric waveguide

The finite-element method is applied to the analysis of whispering gallery modes in curved optical waveguides. Numerical examples for whispering gallery modes in a dielectric disk with rough boundaries are given. It is demonstrated that the whispering gallery modes and the normal guided modes in a curved rectangular dielectric waveguide are analyzed consistently with this approach, and that the normal guided mode approaches the whispering gallery mode with the increase of waveguide width. The minimum width of the rectangular waveguide needed to support a whispering gallery mode is evaluated.<>     

Field Theory Treatment of H--Plane Waveguide Junction with Triangular Ferrite Post

This paper presents an exact field theory treatment for the H-plane waveguide junction with three-sided ferrite prism. The treatment is general, being independent of the geometrical symmetry of the junction, the number of ports, and the location of the ferrite post inside the junction. The solution of the wave equations in the ferrite post and in the surrounding region is written in the form of an infinite summation of cylindrical modes. The fields at the ferrite-air interface are matched using the point-matching technique. This results in two amplitudes for the cylindrical modes describing the fields in the air region in the form of a matrix. The fields at the arbitrary boundary between the air region and the waveguides are also matched using the point-matching technique. This results in a finite system of nonhomogeneous equations in the field amplitudes. The three-port waveguide junction circulator with central triangular ferrite post is analyzed using this technique. Two specific arrangements are considered. In the first arrangement, the points of the triangles are in the centers of the waveguides, and in the second, the sides of the triangles are in the centers of the waveguides. The method used in this paper can also be applied to study the effect of the ferrite-post geometry on the circulator performance in order to seek the best possible circulator structure. Excellent agreement has been found between published experimental measurements and the numerical results obtained by this technique in the case of a waveguide junction circulator with cylindrical ferrite post.     

General Field Theory Treatment of H-Plane Waveguide Junction Circulators

In this paper an exact field theory treatment for the waveguide junction circulators is presented. The treatment is general, being dependent on neither the geometrical symmetry of the junction nor the number of ports. The electromagnetic fields in the joining waveguides are written in the form of infinite summation of waveguide modes. The solutions of the wave equations in the ferrite rod and in the surrounding air are obtained in the form of infinite summation of cylindrical modes. The fields at the ferrite air interface and at an imaginary boundary chosen arbitrarily between the air region and the waveguides are then matched. This process leads to an infinite system of nonhomogeneous equations in the field amplitudes. Three types of waveguide junction circulators using this technique are analyzed: the simple ferrite-rod Y junction, the simple ferrite-rod T junction, and the latching Y junction. Point-matching techniques are used to get numerical results for the field distributions and the circulator characteristics. Excellent agreement has been found between the published experimental measurements and the numerical results obtained by this technique.     

An integral equation analysis of an infinite array of rectangulardielectric waveguides

An integral equation analysis is applied to the study of the propagation characteristics of an infinite array of dielectric waveguides. The geometry under study is assumed to be rectangular. To find the Green's function of the structure, the Floquet theorem is applied such that the mutual coupling between dielectric waveguide elements is effectively included in the analysis. The effect of the coupling on the propagation characteristics of a dielectric waveguide is studied by varying the size of the Floquet cell. The validity of this analysis to simulate the case of an open dielectric waveguide is confirmed by a comparison with previous results, this in spite of the fact that radiation and leaky wave modes are not accounted for. The complex modes due to the periodicity of the structure are found and their properties are described. The analysis presented, with minor modification, can deal with the problems of dielectric image lines, or dielectric-loaded metallic waveguides     

Characteristics of coupling between parallel-plate waveguides with and without dielectric plugs

An analysis is presented of the coupling between parallel-plate waveguides excited in TE modes. Integro-differential equations are formulated for finite arrays of such waveguides with arbitrary widths and spacings. The waveguides, moreover, may be loaded with dielectric plugs having different dielectric constants and thicknesses. Solutions to these equations are effected by the method of moments. Extensive numerical data are obtained for the coupling between two waveguides, and their characteristics are examined in detail. The results show that in unloaded situations the coupling diminishes monotonically with increasings/lambda, wheresis the separation between the waveguides andlambdais the wavelength. At a given frequency, moreover, the coupling for largesdecreases asymptotically ass^{-3/2}. By contrast, an asymptotic dependence ofs^{-3/2}was uncovered earlier for TM-mode coupling. It is found that substantially different coupling behavior may result when the waveguides are loaded by dielectric plugs because of the excitation by the aperture discontinuity of higher order modes, which propagate inside the dielectric but are attenuated in the unloaded waveguide region. Of particular interest is the observation, under suitable conditions, of resonance characteristics in the coupling as functions of both the frequency and the thickness of the dielectric plug. These resonances are found to occur when the impedances of a certain higher order mode satisfy the transverse resonance condition, and thus are the manifestation of the resonances of such modes inside the cavity formed by the dielectric plug.     

Analytical calculation of resonances in tapered double-port TEM waveguides

This contribution presents an analytical method for the calculation of resonances of higher order modes valid for tapered double-port TEM waveguides with constant characteristic impedance. Because these resonances determine the usable bandwidth of the waveguide, their precise knowledge is essential. The accuracy of the proposed method has been proven using TEM waveguides with either rectangular or circular cross section.     

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.     

Energy loss in a planar waveguide caused by a high refracting andabsorbing overlay

An explanation of the mode behavior in dielectric waveguides with an absorbing, high-refractive-index cladding is given. By considering the total waveguiding system as two separate waveguides, it is possible to attribute the behavior of the complex refractive index of the guided modes to the mixing of the modes of both waveguides. For systems with absorption, so-called quasi-leaky waves are observed in the total system for finite thicknesses of the overlay. For absorptionless systems these leaky waves are found only for infinite thicknesses of the overlay. The occurrence and behavior of these quasi-leaky waves versus the increasing overlay thickness are interpreted. A method for calculating the coupling efficiency of modes at the junction unclad waveguide-clad waveguide, taking into consideration waveguides with absorption, is presented. An experimental method for measuring the absorption coefficient for the guided modes in the cladded waveguide and the coupling losses at the unclad-clad waveguide junction was developed. The measured values are in a good agreement with the theoretical calculations     

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.     

Resonance phenomena in a junction of cylindrical and rectangular waveguides

The electrodynamic and numerical analyses of resonance phenomena in a junction of cylindrical and rectangular waveguides with a magnetodielectric are performed. The applicability of such a junction for nondestructive measurements of the parameters of magnetodielectric specimens of cylindrical and rectangular cross sections is demonstrated.     

Dielectric-waveguide discontinuities

The discontinuity between two planar dielectric waveguides is examined on the basis of an integral-equation formulation. The aperture field is approximated by a finite set of discrete modes, characteristic of the region Z<0. Results are presented for the launching efficiency and reflection at the junction between a solid-state heterojunction laser and an optical waveguide.     

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。     

波导介质不连续性问题的FEM/PML方法分析

将完全匹配层(PML)与矢量有限元方法(FEM)相结合对波导介质不连续性问题进行分析。利用PML对计算区域进行截断，大大节省了FEM分析问题的内存消耗。对波导的单介质块加载问题的S参数进行了分析计算，数值结果与文献结果一致。在此基础上，计算了多介质块加载波导的散射参数。数值结果证实了应用FEM／PML方法对波导介质不连续性问题进行分析的正确性与有效性。     

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.     

Boundary elements and analytic expansions applied to H-planewaveguide junctions

We propose a method to calculate field distribution and S-parameters in a planar n-port junction with rectangular waveguides. We use boundary elements on metallic walls, combined with modal expansion in waveguides and analytic representations for the field in dielectric samples or ferrites. Our approach uses fewer nodal points than either the finite-element or the boundary-element method. It is applicable to an H-plane junction with quite arbitrary geometry. The junction may contain several homogeneous or piecewise homogeneous circular cylindrical dielectric samples or ferrites, or samples with more general shape if a simple analyticity condition is met     

Analysis of a general coaxial-line/radial-line region junction

A general analysis of a coaxial-line/radial-line region junction is presented for the case in which the center conductor is sheathed in a dielectric and extends the full width between two parallel metal plates. Expressions for the current distribution and the admittance of the junction are presented. Two example environments are considered, a rectangular waveguide and a base entrant cylindrical cavity, although the technique can be used for other environments. Comparison of theoretical and experimental results for these two cases shows the theory to be very accurate     

Why are accurate computations of mode fields in rectangulardielectric waveguides difficult?

The electric field of the modes of rectangular dielectric waveguides is known to diverge in the corners of the waveguide. An accurate numerical computation of the vector mode fields for a sample waveguide exhibits clear signs of this divergence. The divergence makes the design of rapidly converging numerical algorithms for vector mode field computations difficult