Transient analysis of distortion and coupling in lossy coupledmicrostrips

The transient response of lossy coupled microstrips is studied using the spectral-domain approach (SDA) to rigorously compute the dielectric losses. The dielectric loss coefficient is computed using the SDA with a complex dielectric constant, and results are compared with those obtained by the formula advanced by M.V. Schneider (1969) using a finite-difference approximation for the partial derivative. Transient coupling is formulated in the frequency domain by an even/odd mode approach, showing how differences in either the modal loss coefficients or modal propagation constants can be responsible for coupling between lines. Results for pulse distortion on a semiconductor substrate are presented, showing how losses reduce the signal amplitude without significantly distorting the shape     

Numerical method for investigating the propagation of surface waves on dissipative guides

A finite-element method is developed to investigate surface waveguides of complicated shapes in the presence of dissipative materials. The complex propagation constants for axially symmetric TM surface-wave modes on a conducting wire and on a lossy dielectric rod are determined. The results are compared with analytical results and in the case of the dielectric rod, the calculation is extended beyond the limits of accuracy of the perturbation method.     

Effect of Loss and Frequency Dispersion on the Performance of Microstrip Directional Couplers and Coupled Line Filters (Short Papers)

The effect of ohmic and dielectric losses, conductor thickness, and frequency dispersion on the performance of edge-coupled microstrip directional couplers and interdigital filters have been determined in this short paper. The odd- and even-mode attenuation constants due to ohmic losses in the conductor have been calculated using Wheeler's inductance formula. The theoretical results for the characteristic impedance and propagation constants are in good agreement with the experimental results of Napoli and Hughes. Among the parameters that can be calculated from this theory are the isolation, directivity, and coupling coefficients of lossy directional couplers and the midband insertion loss of interdigital filters.     

Self-Adjoint Vector Variational Formulation for Lossy Anisotropic Dielectric Waveguide

This paper presents the derivation of a new self-adjoint variational formula for complex propagation constant in a lossy anisotropic dielectric waveguide, in terms of the magnetic field and real frequency. The ability to include loss and anisotropy (into the permittivity tensor) while preserving the self-adjointness of the system is achieved by using the less common real-type inner product. When used as a basis of Rayleigh-Ritz or finite-element methods, the formula leads to the canonical eigenvalue eqnation of the form Ax= gamma/sup 2/Bx.     

FDFD full-wave analysis and modeling of dielectric and metalliclosses of CPW short circuits

A finite-difference method in the frequency domain (FDFD) is used to analyze the influence of lossy materials on the scattering behavior of CPW short ends. Not only dielectric losses but also realistic metallic losses are taken into account for the first time in an FDFD method. Both, the numerical results for the three-dimensional structure and the complex propagation constants of the homogeneous waveguide are presented. These are compared with those yielded by an analytical method and shown to be of good agreement. Finally, a simple model is presented, which describes the CPW short end with good accuracy     

Full vectorial finite element formalism for lossy anisotropicwaveguides

An efficient computer-aided solution procedure based on the finite-element method is developed for solving general waveguiding structures containing lossy, anisotropic materials. In this procedure a formulation in terms of the transverse magnetic field component is adopted and the eigenvalue of the final matrix equation corresponds to the propagation constant itself. Thus one avoids the unnecessary iterations which arise when using complex frequencies. To demonstrate the strength of the presented method, numerical results are shown for a rectangular waveguide filled with lossy anisotropic dielectric with off-diagonal elements in a permittivity tensor and compared with those obtained by the telegrapher equation method. The results are in excellent agreement both for phase and for attenuation     

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.     

A moment method solution for TMz and TEzwaves illuminating two-dimensional objects above a lossy half space

A moment method (MM) solution for analyzing the electromagnetic shielding and scattering properties of two-dimensional (2-D) objects over a lossy half space is presented. The materials of the objects can be metal, dielectric, or magnetic. Also, the lossy half space is included to simulate the effects of the earth ground or any flat homogeneous lossy surface. An MM based on a volume formulation and a special Green's function in the spectral domain is developed. Both TM _z and TE_z waves incident upon 2-D metal or lossy material structures are demonstrated for the shielding effects of those bodies in the presence of the lossy ground. Besides, the echo widths of a composite object either in free space or above the lossy half space are determined by using the MM. Some of the results are compared with those by other methods, and good agreements are obtained. The MM solution can be used to study the shielding and scattering problems for cylindrical structures located over a lossy ground     

Full-wave analysis of dielectric frequency-selective surfaces using a vectorial modal method

A novel vectorial modal method is presented for studying guidance and scattering of frequency-selective structures based on lossy all-dielectric multilayered waveguide gratings for both TE and TM polarizations. The wave equation for the transverse magnetic field is written in terms of a linear differential operator satisfying an eigenvalue equation. The definition of an auxiliary problem whose eigenvectors satisfy an orthogonality relationship allows for a matrix representation of the eigenvalue equation. Our proposed technique has been applied to the study of lossy all-dielectric periodic guiding media with periodicity in one dimension. This method yields the propagation constants and field distributions in such media. The reflection and transmission coefficients of a single layer under a plane-wave excitation can be obtained by imposing the boundary conditions. Study of the scattering parameters of the whole multilayered structure is accomplished by the cascade connection of components as characterized by their scattering parameters. Results obtained with this method for the propagation characteristics of a one-dimensional periodic dielectric medium are compared with those presented by other authors, and results for the scattering of several dielectric frequency-selective surfaces (DFSS) are compared with both theoretical and experimental results presented in the literature, finding a very good agreement. A symmetrical band-stop filter with a single waveguide grating is also demonstrated theoretically.     

Application of Davidenko's Method to a Lossy Nonlinear Waveguide

Davidenko's method is implemented for determining the complex propagation constants (Modal index and attenuation coefficient) of nonlinear TE waves guided by an asymmetrical lossy nonlinear dielectric wave-guide. The waveguide structure has a generalized nonlinear substrate with a permittivity of the form ? ～ | E |^δand an absorbing cover making the propagation constant to be complex. Davidenko's method shows to be a fast and accurate analysis in finding the complex propagation constants. The effects of initial condition parameter on the propagation characteristics are investigated, analyzed and discussed.     

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。     

Negative Refraction Without Negative Index

Refraction of a microwave plane wave by a wedge with exact characterization of and is evaluated by a ray approach. Snell's Law is used for the lossless wedge, while exact formulations are used for the propagation constants and angle in the lossy wedge. The heavily lossy wedge produces negative refraction. Data are given on the loss factor that allows Snell refraction to be exactly reversed by lossy refraction, and the internal angle in the lossy wedge.     

抛物方程法在森林环境电波传播特性预测中的应用

为提高大区域森林环境电波传播特性预测的准确性,研究抛物方程（PE）法在森林环境电波传播特性预测中的应用,提出了基于抛物方程的森林模型。该模型采用PE法实现准确快速求解,考虑森林在垂直方向上的非均匀性,引入森林分层模型,将森林分为树冠、树干两个均匀有耗介质层,并根据森林区域的特性参数确定各有耗介质层的等效介电常数,相比于传统将森林等效为一个给定介电常数的均匀有耗介质层,能够更准确地描述森林对电波传播的影响。将其应用于三种常见绿叶林的电波传播特性预测中,仿真结果表明,该模型能够反映不同区域、不同植被种类的森林对电波传播的影响差异,有效预测大区域森林环境电波传播特性。     

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     

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.     

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     

Mode confinement and gain in junction lasers

For a three layer dielectric sandwich, the center dielectric region must have a dielectric constant higher than the outer regions and some finite thickness for a wave to be "bound" to the center region. We have calculated the transverse propagation constants for even TE modes when the dielectric sandwich is unsymmetrical. The resultant field distributions are used to derive a formula for the gain of a junction laser of the formalpha = frac{alpha_{1} + Palpha_{3}/nR + falpha_{2}}{g}, where the αn's are the attenuation (or gain) constants associated with the various regions of the junction structure. Curves ofP/nR,f, andgas a function of active region thickness are given from which the condition for laser oscillation or the net gain or loss per unit length of a given device may be found.     

Scattering by thin dielectric strips

A plane wave incident on a thin dielectric strip with infinite length is considered, letting the incident electric field vector be parallel with the edges of the strip. The field is expanded in the dielectric region as the sum of three plane waves (the forced wave and two surface waves). Thex-axis andy-axis propagation constants are known for each wave, and Galerkin's method is employed to determine the amplitudes of these waves. Finally, the far-zone scattered field is determined by considering the polarization currents radiating in free space. Numerical data are presented to illustrate the scattering properties of lossless and lossy dielectric strips as a function of the angle of incidence and the width of the strip. The calculations show excellent agreement with an earlier moment method using pulse bases and point matching.     

Investigation into the Effect of Dielectric Loss on RF Characteristics of Helical SWS

A general theory has been developed to account for the effect of the dielectric loss of discrete rods on the performance characteristics of an actual helical slow wave structure (SWS). The effect of the lossy dielectric rods has been studied on various propagation parameters, namely, phase propagation constant, interaction impedance and attenuation constant at different operating frequency. It is clearly shown that the influence of dielectric loss on RF characteristics is much larger at the millimeter frequency band than that at the microwave frequency band, especially on interaction impedance and attenuation constant. The general theory developed here has been further confirmed by comparing the results with those obtained elsewhere for some special cases.     

Refractive index approximations from linear perturbation theory forplanar MQW waveguides

The mode powers and propagation constants for planar multilayer waveguides formed with multiple quantum well (MQW) materials and with the MQW layers replaced by a single uniform layer are compared. By considering linear perturbations of the solutions of the wave equation, the optimal choice of average for the dielectric constant of the substituted single layer is determined. For the case of TE modes, minimal error in the propagation constant is predicted if a weighted average of the dielectric constants of the MQW materials is used. For the case of TM modes, using a weighted average of the reciprocal of the dielectric constants is predicted to yield the minimum error. Numerical results confirm these predictions