Full vectorial finite-element-based imaginary distance beampropagation solution of complex modes in optical waveguides

In this paper, we address accurate computation of complex propagation constants and field distributions of different modes, in general, lossless and lossy optical dielectric waveguides. Using the vector finite-element formulation of the beam propagation method combined with the imaginary distance propagation technique, sequence of both the guided and leaky modes can be accurately calculated. To show the versatility and numerical precision of the proposed technique, we compute the modes of three different three-dimensional (3-D) waveguide structures and compare the results against those of other, different, vector formulations. Further, we present the design of a higher order mode filtering device, based on a 3-D leaky mode optical waveguide     

Electromagnetic coupling of coplanar waveguides and microstriplines to highly lossy dielectric media

The spectral-domain technique is utilized to analyze the coupling characteristics of coplanar waveguides and microstrip lines coupled with multilayer lossy dielectric media. Numerical results illustrating the dispersion characteristics of coplanar and microstrip lines, as well as the various electric field components coupled to highly lossy dielectric media, are presented. It is shown that the presence of a superstrate of lossless dielectric between the coplanar waveguide and the lossy medium plays a key role in setting up an axial electric field component that facilitates leaky-wave-type coupling to the lossy medium. The thickness of the superstrate relative to the gap width in the coplanar waveguide is important in controlling the magnitude of this axial electric field component. The coupling characteristics of the microstrip and coplanar lines are compared, and results generally show improved coupling if coplanar waveguides are utilized. Values of the attenuation constant α are higher for coplanar waveguide than for microstrip line, and for both structures α decreases with frequency     

Multilayer waveguides: efficient numerical analysis of generalstructures

An efficient numerical method for accurately determining the real and/or complex propagation constants of guided modes and leaky waves in general multilayer waveguides is presented. The method is applicable to any lossless and/or lossy (dielectric, semiconductor, metallic) waveguide structure. The method is based on the argument principle theorem and is capable of extracting all of the zeros of any analytic function in the complex plane. It is applied to solving the multilayer waveguide dispersion equation derived from the well known thin-film transfer matrix theory. Excellent agreement is found with seven previously published results and with results from two limiting cases where the propagating constants can be obtained analytically     

A multipole analysis of a dielectric loaded coaxial rectangularwaveguide

A multipole analysis of a coaxial rectangular waveguide whose inner conductor is circular is made in order to determine the TE and TM modes of the system. The analysis is based on using multipole (dipole, quadrupole etc.) electric and magnetic current sources to generate field solutions in the waveguide. These solutions are used to match the electromagnetic boundary condition in a homogeneous coaxial rectangular waveguide and to determine the TE and TM eigenvalues of the waveguide system. Eigenvalue results are compared with results of the generalized spectral domain method and to eigenvalue results for a ridged waveguide. Propagation in a coaxial rectangular waveguide is also studied when the coaxial rectangular waveguide is loaded with lossy inhomogeneous dielectric material. A variational formula is used to relate the TEM, TE, and TM modes of an empty coaxial rectangular waveguide to the propagation in the loaded inhomogeneous dielectric waveguide     

Modal attenuation in multilayered coated waveguides

Propagation and attenuation constants of low-order normal modes in a circular waveguide lined with lossy coating layers are calculated using a generalized dispersion equation. It is found that the use of multilayered coating can significantly enhance modal attenuations over a broader frequency range compared to that for a single-layer coated structure. For a cylinder with radius a=2λ, the attenuation constants for the dominant modes are shown to increase by 20 dB per a by adding a lossless padding layer to a lossy magnetic coating. Application of this result in radar cross-section (RCS) reduction is discussed     

Series solutions to the arbitrary profile 1-D waveguide andquantum-well problems

The 1D waveguide of arbitrary dielectric profile is solved for TE and TM modes by a method based on series solutions. It is a guess-propagate-iterate scheme. The profile is approximated by small segments of either constant or linearly changing dielectric constant. The method is accurate, generally significantly faster than other methods, and can cope with modes near cutoff; and with lossy, or gain-guided modes. Series solutions are also given to solve the 1D Schrodinger equation     

An asymmetric discrete-time approach for the design and analysis ofperiodic waveguide gratings

A discrete-time approach is introduced for the analysis of periodic waveguide gratings with gain (or loss) extending concepts developed for transfer matrix and Gel'fand-Levitan-Marchenko (GLM) inverse scattering techniques. The periodic waveguide grating with gain (or loss) is modeled as a lossy layered dielectric that allows for a digital signal processing (DSP) formulation of the forward and inverse scattering problem. It is shown that the DSP forward scattering formulation as an asymmetric two-component wave system is equivalent to the impedance matching matrix method. A numerical example is presented to emphasize this result. The DSP formulation is an exact discrete design, not just an approximation to a continuous design, and includes all multiple reflections, transmission scattering losses, and absorption effects. A comparison of the continuous GLM, discrete GLM, and discrete Krein inverse problem formulations for a medium with gain (or loss) is presented. The discrete lossy formulations generalize previous lossless results and are found from two different types of reflection data. Since slab gratings are discrete (not continuous) structures, the integral equations used to describe the continuous inverse problem are shown to become matrix equations. Thus, our result enables fast algorithms to be used to solve the inverse problem. A fast algorithm is presented allowing for the complete reconstruction of the grating parameters from its two-sided response in a recursive (slab by slab) fashion     

A simple method for calculating the reflection coefficient ofopen-ended waveguides

This paper presents a simple but effective method for the analysis of open-ended waveguides. The method begins with the introduction of a large waveguide to approximate the half-space. In order to avoid the convergence problem lossy dielectric is assumed to homogeneously fill the large waveguide. After obtaining a number of convergent data for different values of the loss tangent an extrapolation technique is employed to calculate the solution to the original problem-a waveguide terminated by an infinite conducting range and radiating into a lossless or low-loss half-space. Numerical results are given to show the validity of the proposed method. The behavior of the effect of the loss tangent on the size of the large waveguide and on the final results are also examined     

An absorber tip diffraction coefficient

The UTD corner diffraction solution for a perfectly conducting corner is empirically modified for the case of a dielectric corner. The dielectric may be lossless or lossy, but is assumed to be homogeneous. This modified solution is used to calculate the bistatic scattering from the tip of a dielectric pyramid. Sample calculations display some features of the scattering from a single lossy dielectric pyramid. To verify the solution, calculations are compared with backscatter measurements of a single pyramid that is cut from a homogeneous lossless dielectric (polyethylene). Calculations are then compared with measurements for the more pertinent case of bistatic scattering from a wall of pyramidal radar absorbing material     

A Lossy Dielectric-Ring Loaded Waveguide With Suppressed Periodicity for Gyro-TWTs Applications

A dielectric-loaded (DL) waveguide is an attractive possibility for interaction circuits with high-power sources in the millimeter-wave regime down to tenths of millimeters, particularly for gyrotron-traveling-wave-tube amplifiers (gyro-TWTs). We present results on a systematic investigation of the influence of the periodically loaded lossy dielectric on the propagation characteristics of the operating modes, which reveals that a complex mode in the periodic system can be mapped to a corresponding mode in an empty waveguide or a uniform DL waveguide. Dielectric losses not only induce modal transitions between different modes with similar field structures and close phase velocities in the uniform system but also unify the discrete mode spectrum into a continuous spectrum in the periodic system. Since the lossy dielectric functions as a power sink, the higher order Bloch harmonic components arising from the structural periodicity are suppressed, and the mode spectrum of the lossy periodic system degenerates into that of an empty waveguide. This alleviates the potential danger of spurious oscillations induced by the higher order harmonic components, making the periodic lossy DL waveguide promising in a high-power millimeter-wave gyro-TWT.     

Modal Transition and Reduction in a Lossy Dielectric-Coated Waveguide for Gyrotron-Traveling-Wave Tube Amplifier Applications

A metal cylindrical waveguide coated with an inside layer of lossy dielectric which affects the propagation characteristics of a guided electromagnetic mode is investigated for gyrotron-traveling-wave tube (gyro-TWT) amplifier applications. This paper reveals a series of novel phenomena. The dispersion curve of a higher order mode has a turning point during its evolvement from the fast wave region to the slow wave region. An electromagnetic mode in the lossy dielectric-coated waveguide exhibits a transverse partial-standing-wave distribution. The dielectric loss induces modal transition which results in the dispersion curves of a pair of nearby modes crossing each other and interchanging mode structures. Modal reduction caused by strong dielectric loss merges a pair of nearby modes into one. In this one merged mode, the dielectric-coated waveguide is equivalent to a conventional cylindrical waveguide with imperfect conducting wall. This improved understanding of lossy dielectric-coated metal cylindrical waveguide is of value and usefulness for application toward gyro-TWTs capable of high-power and wide bandwidth.     

有耗介质导波结构的高次杂交四边形边缘元分析

本文提出了一种高次杂交四边形边缘元方法。讨论了这种高次杂交边缘元的有限元空间构造，给出了其形函数的显形表达式。这种方法不仅消除了伪解而且能直接求解传播常数，从而无需迭代便能分析有耗介质导波结构的传输特性。对矩形导和条形介质填充波导本征模传播常数的计算表明这种高次杂交边缘元的计算精度比低次杂交边缘元要高出一个量级。     

Tunable low-reflection waveguide termination

A low-reflection sliding load in WG11A is described. The load is constructed from sections of lossless and lossy dielectric which completely fill the waveguide cross-section and which can be moved longitudinally in the guide with respect to each other. The reflection coefficient can be set to zero to within 0.0002.     

A parallel-plate waveguide model of lossy microstrip lines

An improved semi-analytical model of a lossy microstrip transmission line is proposed. The model is based on the theory of the fundamental transverse magnetic mode of a lossy parallel-plate waveguide whose dielectric medium is assigned the effective permittivity of the respective lossless microstrip line. The complex propagation constant of the fundamental mode is computed by imposing the Leontovitch boundary condition at the upper and lower plates whose impedances take into account the thickness of the conductors and the current crowding effect. The dielectric loss is computed by perturbation formulas. The proposed model features high accuracy and computational efficiency at frequencies up to 100 GHz.     

E面部分填充介质矩形波导的导体损耗

本文推导了E面部分填充介质矩形波导的导体损耗的计算公式,给出了Ka波段标准波导中对称填充结构的衰减常数随填充厚度、介电常数及工作频率的一系列变化曲线,由此得出在一定填充厚度范围内衰减常数小于未填充波导的值等若干有用结论.作为一应用实例,计算了一只Ka波段三节E面带通滤波器的频率响应特性,所得插入损耗的理论值与测量结果符合较好.     

Finite-difference analysis of cyclic H-plane waveguide three-port circulators with an arbitrary-shape lossy ferrite post

A finite difference method (FDM) with an analytical truncation boundary condition is developed for the analysis of cyclic H-plane waveguide three-port circulators with an arbitrary shape ferrite post. The method is based on scalar wave equations and the analytical field distribution in the rectangular waveguides. A general boundary field equation for an arbitrarily shaped ferrite or dielectric interface is derived. To verify the validity of the present method, the eigenvalue phases of the cyclic three-port empty junctions and the characteristics of H-plane waveguide Y-junction circulators with lossless, lossy cylindrical, composite and triangular ferrite post are calculated. Good agreements with previously published experimental and theoretical results have been achieved. The performance of a Y-junction circulator with a hexagonal ferrite post and the characteristics of a cyclic three-port circulator with a ferrite rod are also investigated.     

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     

Numerical analysis of H-plane waveguide junctions bycombination of finite and boundary elements

A numerical method is formulated for the analysis of H-plane waveguide junctions with arbitrary cross sections. The junctions are loaded with arbitrarily shaped dielectric or ferrite. The method is a combination of the finite-element method and the boundary-element method, and is applied to the regions with and without dielectric or ferrite, respectively. To show the validity and usefulness of the method, a lossy dielectric post and a ferrite slab in a rectangular waveguide are investigated in detail, and the computed results are compared with earlier theoretical and experimental results     

Finite element formulation for lossy waveguides

An efficient computer-aided solution procedure based on the finite-element method is developed for solving general waveguiding structures composed of lossy materials. In this procedure, a formulation in terms of the transverse magnetic-field components is adopted and the eigenvalue of the final matrix equation corresponds to the propagation constant itself. Thus, it is possible to avoid the unnecessary iteration using complex frequencies. To demonstrate the strength of the presented method, numerical results for a rectangular waveguide filled with lossy dielectric are presented and compared with exact solutions. As more advanced applications of the presented method, a shielded image line composed of a lossy anisotropic material and a lossy dielectric-loaded waveguide with impedance walls are analyzed and evaluated