Hybrid modes on anisotropic dielectric rods

The boundary value problem for wave propagation on a cylindrical anisotropic rod has been solved for hybrid modes, i.e., those having angular dependence. Solutions for the rod radius, normalized by the free space wavelength, as a function of the phase velocity, are presented for various values of the transverse and longitudinal dielectric constants. When the rod is terminated by conducting end plates, a highQmicrowave resonator results. The electric and magnetic energies stored in the rod have been calculated, as has the cavityQ. Experimental resonant frequencies for various modes in anX-band cavity using a ruby laser rod are compared with theory.     

介质波导阵列的横向传播特性分析

根据已提出的有关二维周期介质严格分析理论，针对介质波导阵列进行了大量的数值计算。对介质波导阵列中波的横向传播作了详细分析。首先，在给定纵向波矢量(k)的情况下，分析了在不同工作频率时的横向波矢量间布里渊区色散特性，对空间谐波的相互作用情况也进行了研究。其次，在给定工作频率的情况下，分析了不同纵向波矢量和不同调制系数时的横向波矢量间布里渊区色散特性。由于空间谐波的相互作用随纵向波数或调制系数的增大而增强，导致阻带能明显地表现出来，从而使介质波导阵列的横向传播特性能较为全面地得到分析。     

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.     

Broadside coupled strip inset dielectric guide and its directionalcoupler application

A theoretical and numerical method is presented for the analysis of broadside-coupled strip inset dielectric guide. The method of analysis is based on an integral equation formulation and Galerkin's procedure. Besides propagation constants for two fundamental and higher order modes, the characteristic impedances for the two fundamental modes are calculated using the total propagating power and the longitudinal strip currents. The propagation characteristics of the two fundamental modes are then used to compute 4-port circuit parameters that are essential for accurate analysis and design of coupled line circuits. The effects of various structural parameters on the S-parameters are investigated and it is found that this broadside coupled strip IDG structure is useful for the realization of the directional couplers. Examples of strong and weak directional couplers are given. Furthermore, the propagation constants and S-parameters of coaxially excited coupled strips are measured, and are in good agreement with the theoretical analysis     

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.     

Propagation Constants of Circular Cylindrical Waveguides Containing Ferrites

The paper describes some results of a theoretical and experimental investigation of the propagation behavior of circular cylindrical wave guides containing longitudinally magnetized ferrite rods. As long as no concentration of the RF-magnetic field in the ferrite occurs, theoretical expressions for the propagation constants can be given by applying first-order perturbation method. Faraday rotation measurements have been made between 5000 and 7600-mcs using commercially available ferrites. Reasonable agreement between theoretical and experimental results has been found for a thin axial ferrite rod in an air-filled guide in both cases of saturated and nonsaturated ferrites. Energy concentration in the ferrite determines the propagation behavior in the partially filled waveguide. This effect can be enhanced by surrounding the ferrite rod with a dielectric tube. For a given rod diameter and permittivity of the tube there is an optimum outer diameter of the tube for which the Faraday rotation becomes maximum.     

Complex modes in shielded suspended coupled microstrip lines

The existence of complex modes in electrically shielded suspended coupled microstrip lines has been studied extensively, and the results are presented. A rigorous full-wave spectral-domain approach (SDA) with a newly proposed and tested set of basis functions can efficiently and accurately determine the propagation characteristics of the dominant, higher-order, and complex modes for planar or quasi-planar transmission lines. These basis functions are validated by comparing the convergence study of field solutions with those obtained by various sets of preconditioned bases and by the unconditioned subdomain ones. Excellent agreement is obtained for the propagation constants and the normalized complex longitudinal and transverse current distributions on conducting strips for the strongly coupled microstrip lines. For all the particular case studies discussed, it is shown that the complex modes may exist in all the shielded suspended coupled microstrip lines, even when the substrate dielectric constant is low. Theoretical results for the fundamental, higher-order, evanescent, and complex modes are presented for suspended coupled microstrip lines     

Guided Waves in Inhomogeneous Focusing Media Part I: Formulation, Solution for Quadratic Inhomogeneity

This work is a theoretical study of waves in a circular-cylindrical radially inhomogeneous guiding medium. A vector theory based upon Maxwell's equatious is used to derive linear homogeneous fourth-order equations satisfied by the longitudinal electric and magnetic field components for a medium in which the permittivity decreases monotonically from the propagation axis. The percentage change of permittivity from the guide axis to some radius a is assumed small. For modes with propagation constants approximately equal to the wave number at guide center, all field components are shown to satisfy second-order differential equations. In particular, all transverse field components are proportional to a single scalar function. In a Iossless system with no containing boundary, a new class of polynomial-Gaussian solutions describes the longitudinal fields for the case of a quadratically decreasing permittivity, while the transverse fields are Gaussian-Laguerre. Mode patterns, propagation constants, and orthogonality relations are given. It is shown analytically that the modes tend to TE or TM as the mode order increases. Moreover, the transverse fields become dominant at large wave numbers, and the fields become tightly bound to the guide axis as the wave number and/or inhomogeneity increases. Studies of more general permittivity variations and wall effects will be reported shortly.     

Surface wave along a ferrite rod magnetized below saturation

Surface waves supported by a ferrite rod, magnetized longitudinally near and below saturation, are studied experimentally using the surface wave resonator technique. Two types of slow waves are found to exist. Their propagation constants depend on the dc magnetic field and rod size. They are interpreted as theHE_{11}mode positive and negative circularly polarized surface waves. For pure circularly polarized waves, a magnetized ferrite is considered as a dielectric with nontensor permeability. A calculation of the propagation constant of these circularly polarized surface waves, based on the dielectric analogy, is made. The agreement between calculation and measurement is close.     

Propagation of ELF waves below an inhomogeneous anisotropic ionosphere

The ionospheric anisotropy is considered with horizontal magnetic field either for transverse (East-West or West-East) or for longitudinal (South-North) propagation. For transverse propagation in a vertically stratified medium the differential equations of the various field components are uncoupled and a closed form solution is given for identical exponential height variation of the components of tensor conductivity. For arbitrary height variation of the tensor conductivity numerical solutions are obtained after expressing the surface impedance below the ionosphere in terms of a Riccati-type differential equation. The West-East direction of propagation exhibits a lower attenuation constant than the East-West direction forf < 1000cps. This is contrary to the expectations based on a model of a homogeneous anisotropic ionosphere. For longitudinal propagation the differential equations of the various field components are coupled, with the coupling being particularly strong above theDregion. The differential equations are simplified by assuming no coupling in the lower ionosphere and strong coupling above a pre-selected altitudey_{1}. For exponential height variation of the tensor conductivity components the closed form solution differs negligibly from the isotropic case. For arbitrary height varition of the tensor conductivity numerical solutions are obtained similarly as for the transverse propagation. Over most of the frequency range the attenuation figures for South-North propagation are intermediate between the corresponding figures for West-East and East-West propagation.     

Analysis of curvature losses of whispering gallery modes in anoptical dielectric disk by the finite-element method

The finite-element method is applied to the analysis of curvature losses of whispering gallery modes in an optical dielectric disk. Numerical examples on the dielectric disks with various side shapes are given. We also demonstrate that when the curvature radius of the disk is large enough, the difference between the propagation constants obtained by considering and by ignoring the curvature loss is very small     

Composite Dielectric Waveguides with Two Elliptic-Cylinder Boundaries

It is shown that the propagation constants of composite dielectric waveguides with two different elliptic-cylinder boundaries, such as the recent single-polarization optical fibers, are computable by the point-matching method. Numerical results are shown for various combinations of the dielectric constants.     

Electromagnetic wave propagation in multilayer dielectric periodicstructures

The propagation characteristics in multilayer dielectric periodic structures, that extends a previous analysis by introducing additional dielectric layers, is presented. It is applied to propagating electromagnetic modes along the longitudinal and transverse directions of the structure's periodicity. The use of Floquet's theorem reduces the analysis to a single cell of the propagating fields for both, TE and TM polarizations. Results showing the effect of varying the layers thickness and electric permittivity on the propagation constant and on the field distributions within each cell are presented as well as the band structure associated with the periodic structure     

Analysis of the coupling of two non-parallel dielectric rod waveguides

In this paper the coupling between two closely spaced single mode dielectric rod waveguides is investigated when the corresponding propagation axes are not in the same plane. An approximate analysis is presented by assuming only first order interaction between the guided waves. For a given incident HE₁₁ mode (in one of the rod waveguides) the coupled wave amplitudes are computed in the other waveguide for both propagation directions. Numerical results are presented for several coupling geometries.     

Propagation characteristics of dielectric-rod-loaded waveguides

A general technique for calculating the propagation characteristics of a waveguide with arbitrary cross-sectional shape loaded with a circular dielectric rod is presented. The waveguide fields, which are represented as a sum of functions satisfying the homogeneous Helmholtz equation and the boundary conditions at the rod surface, are point-matched at the surface of the waveguide. Numerical examples of a rod centered in a square guide and off center in a circular guide are given, and results for a rod centered in a rectangular cavity are compared with measured data     

Full-wave analysis of coupled perfectly conducting wires in amultilayered medium

A full-wave analysis of coupled perfectly conducting cylindrical wires in a multilayered dielectric medium is presented. The analysis is based on a Fourier series expansion of the unknown surface currents on each wire and on an integral equation for the longitudinal field on the wires. The calculations are not restricted to the propagation constants of the different modes, but explicit results are presented for the impedances associated with each wire and each eigenmode as a function of frequency. Propagation constants, longitudinal currents on the wires, and impedances lead to a complete equivalent circuit for the structures being considered     

The fundamental electromagnetic wave of a single-wire line in a weakly absorbing medium

An approximate dispersion equation valid over a wide frequency range is obtained from the dispersion equation for the symmetric E ₀₀ wave (the Sommerfeld wave) propagating along a finite-conductance metal wire embedded in a lossy dielectric. The boundaries of this frequency range are determined. A technique is developed for solution of the obtained approximate dispersion equation in the frequency band where the pronounced skin effect is observed. The ratio of the wire radius to the thickness of the skin layer is assumed to be no less than 10. This technique is applied to calculate the longitudinal and transverse propagation constants for 1.0-and 2.5-mm-radii copper wires over the frequency range 0.5 MHz to 1000 GHz.     

Waves and Evanescent Fields in Rectangular Waveguides Filled with a Transversely Inhomogeneous Dielectric

A numerical-calculation method for rectangular waveguides containing a transversely inhomogeneous dielectric is presented. The method is not restricted to the cutoff case or to special inhomogeneities. The relative permittivity of the dielectric can be an arbitrary function of the cross-sectional coordinates. The electric-and magnetic-field strengths, the dispersion characteristics of the propagating modes, and the attenuation constants of the evanescent modes result from the solution of a matrix eigenvalue problem with typically 8000 matrix elements. Propagating and evanescent modes in a waveguide containing a longitudinal semicircular dielectric rod are calculated as examples. The accuracy of the calculation method is confirmed by measurements and by calculating a special example with an exactly known solution. The error of the field intensities is typically 5 percent; the error of the dispersion characteristics and of the attenuation constants is typically 0.5 percent.     

The dispersion characteristics of shielded microstrip lines on magnetized ferrite and anisotropic dielectric substrates

The dispersion characteristics of the dominant mode in shielded microstrip lines on magnetized ferrite and anisotropic dielectric substrates have been obtained. The solution is obtained by applying the transverse equivalent transmission line in the spectral domain and Galerkin's method. Numerical results for the frequency-dependent propagation constants are presented which could be used in designing directional couplers and isolators.     

Radiation from cylindrical leaky waves

Formulas are derived for the far-infrared radiation pattern of cylindrical leaky waves propagating on a planar surface. The formulas can be used to predict the radiation pattern of a general class of leaky-wave antennas, consisting of a finite-size source which excites a radially propagating leaky wave on some planar surface. Leaky-wave antennas consisting of antenna elements embedded in dielectric layers (microstrip elements) fall into this category. Using the equivalence principle, formulas are derived for both transverse electric (TE) and transverse magnetic (TM) leaky waves with arbitrary propagation constants. The formulas allow for radiation from cylindrical apertures of arbitrary size, so that the effect of truncating the supporting planar surface with an absorbing material can be determined. Particular attention is devoted to the case of a leaky wave for which the real and imaginary parts of the complex propagation constant are equal, since this type of wave has been shown to be responsible for broadside radiation in certain leaky-wave antennas comprised of dielectric layers