Analysis of Elliptical Thin Ridged Waveguide

Elliptical waveguides and ridged waveguides have found broad applications in many microwave structures. The elliptical waveguide with double infinite thin ridges has been formulated using the mode-matching method. Exact closed-form expressions for eigenvalue problem of all TE and TM modes are presented. Numerical results suggest that the elliptical ridged waveguides have larger bandwidth than that of circular ones.     

Modes of a symmetric slab optical waveguide in birefringent media--Part 1: Optical axis not in plane of slab

We derive the eigenvalue equation and the expressions for the field distribution for the TM modes of an anisotropic symmetric slab waveguide; the TE modes are identical to the isotropic case. It is assumed that the field components do not depend on theycoordinate and that thecaxis of the uniaxial crystal lies in thex-zplane. We find that, in spite of the symmetry of the waveguide, even and odd modes do not exist because the phase fronts of the modes are tilted with respect to the waveguide axis. However, the absolute magnitude of the Hycomponent of the field has even or odd symmetry. The interesting case of an anisotropic slab waveguide with the optical axis located in the plane of the slab will be presented in Part II of this paper.     

Scattering at Circular-to-Rectangular Waveguide Junctions

A formally exact solution is given for the problem of scattering at a circular-to-rectangular waveguide junction and at a thick diaphragm, with a centered circular aperture, in a rectangular waveguide. The method uses normal TE and TM mode expansions of the waveguide fields and traditional mode matching of the transverse electric and magnetic fields at the junction boundary. Exact closed-form expressions are obtained for the electric field mode-matching coefficients which couple the TE(TM) modes in the rectangular guide to the TE(TM) and TM(TE) modes in the circular guide. Numerical results are presented for the case of TE/sub 10/ mode propagation in the larger rectangular guide with all other modes cutoff. Convergent numerical results for the equivalent shunt susceptances of such junctions are obtained when about 12 modes (eight TE and four TM) are retained in the circular waveguide or in the circular aperture of the diaphragm. The results are graphically compared with formulas and curves due to the quasi-static theory of Bethe and the variational theory given in the Waveguide Handbook [2].     

Modal Characteristics of Crossed Rectangular Waveguides

The modal solution for the crossed rectangular waveguide is presented. Cutoff frequencies and modal fields are determined by formulating an integral eigenvalue equation which can be solved by application of the Ritz-Galerkin method. Field equations are given for both TE and TM modes. The calculated cutoff frequencies of several lower order modes agree very well with the available experimental results in the literature.     

Transmission Characteristics of Spherical TE and TM Modes in Conical Waveguides (Short Papers)

The transmission properties of spherical TE and TM modes in a perfectly conducting conical waveguide are treated in detail. To start with, an analytically simple and highly accurate digital-computer based iterative algorithm has been employed to evaluate the eigenvalues associated with the spherical TE and TM modes within the guide irrespective of the flare angle (2alpha/sub 0/) of the conical waveguide (theta < 2alpha/sub 0/ < 360/spl deg/). Subsequently, explicit expressions for the attenuation constant, phase constant, phase velocity, and wave impedance are obtained for the spherical modes transmitted within the guide. Accurate eigenvalues obtained numerically are used to study the variation of attenuation constant, phase constant, phase velocity, and wave impedance as a function of the radial distance from the apex with alpha/sub 0/ as a parameter. Measured data on the phase constant of a conical waveguide for the TE/sub 11/ mode have been compared with the analytical results obtained by calculation and an excellent agreement between the two justifies the validity of the analysis presented. Finally, a study of the phase coherence between the dominant spherical TE and TM modes within the guide is presented which may be fruitfully employed in the design of dual-mode conical waveguides.     

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     

Radiation loss coefficients of asymmetric dielectric waveguides with shallow sinusoidal corrugations

Kiselev [10] has solved the boundary equations for an asymmetric slab waveguide with a shallow sinusoidal corrugation, and derived explicit, closed expressions for the TE radiation loss coefficients of various waveguide geometries. For many practical applications in integrated optics, the Rayleigh assumption justifying the boundary-matching procedure and the approximations of linear perturbation analysis employed in this derivation are both satisfied. We have extended this procedure to TM modes and found that the expressions for both TE and TM modes in all of the geometries so treated agree identically with those derived by coupled-mode theory. The dependence of the TM radiation loss coefficient in each waveguide geometry on the grating period, radiation angle, refractive index profile, and mode polarization is illustrated graphically, and compared with its TE counterpart.     

An Analysis of a Hybrid-Mode in a Twisted Rectangular Waveguide

Analytic expressions of electromagnetic fields for the dominant hybrid-mode in a twisted rectangular waveguide are obtained. The fields exactly satisfy the boundary conditions on the guide walls in a helicoidal shape. By expanding these expressions for the fields in terms of the eigenfunctions of a straight waveguide, the hybrid-mode is found to be composed of a fundamental TE/sub 10/ -mode component, accompanied with TE/sub 01/, TM/sub 21/,TE/sub 21/, and TE/sub 03/ modes, as successive higher order components. The result of the modal power calculation reveals that there exists a frequency at which the transmitting power carried in the cross-polarized TE/sub 01/-mode component just vanishes. As a limiting case of the twisted waveguide, fields in a twisted strip line are discussed also, and the existence of a propeller-like equiphase surface is shown.     

非线性衬底平板光波导TE模的图解法

本文推导出了以衬底光功率流为参数的非线性衬底光波导TE模的本征值方程,且采用简单的图解法求解。     

Simple Approximate Expressions for Higher Order Mode Cutoff and Resonant Frequencies in TEM Cells

Simple approximate expressions for determining the cutoff frequencies of the first few higher order modes and the associated resonant frequencies in transverse electromagnetic (TEM) cells are presented. Both symmetric (seven TE and two TM modes) and asymmetric (three TE modes) cells are discussed.     

对称单负材料平面波导的波导模

基于经典电磁理论建立了芯层为单负材料的对称三层平板波导的导波方程,采用图解法研究了该波导中的TE和TM波导模,分析了TE波导模和TM波导模会受波导参数μ1/μ2和R的影响,给出TE模和TM模解的横向场分布图.结果显示,在单负材料的对称三层平板波导中只存在慢波导模,TE慢波模只能在磁负材料中传播,TM慢波模只能在电负材料...     

含单负材料对称三层平板波导的模式特性

由电磁场的波动方程和边界条件建立了单负材料作为芯层的对称三层平板波导的模式本征方程,用图解法研究其色散特性。研究发现,单负介质波导不支持快波的传播,只支持表面波的传播。在负磁材料平板波导中只存在TE表面模,不存在TM表面模。分析了在负磁材料平板波导中TE模受磁导率的比值-μ2／μ1和波导参数的影响,给出了横向场分布图。在-μ2/μ1〈1时,偶对称只有TE0表面模存在,奇对称只有TE1表面模存在,高阶模式并不存在,且两种模式都没有低频截止;-μ2/μ1〉1时,TE1表面模始终不出现;TE0模的存在与否和波导参数有关,在一定条件下TE0模可出现双模并存。给出的结果可望对表面波器件的设计提供理论基础。     

Propagation Properties of a Planar Dielectric Waveguide with Periodic Metallic Strips

A dielectric waveguide with periodic metallic strips suitable for millimeter-wave and submillimeter-wave integrated circuits is analyzed by a rigorous formulation. The accuracy of the solution of our analysis can be systematically improved by increasing the size of the matrix associated with the eigenvalue equation. Stopband properties are numerically presented as a function of the spacing and width of metallic strips and dielectric profile. It is found that there is a difference in the stopband properties of TM and TE modes. Experimental results for the band reject filter are also presented to verify the validity of our analysis.     

On the Theory and Application of the Dielectric Post Resonator (Short Papers)

This short paper deals with the modes of the dielectric post resonator when epsilon/sub r/ is large. The normalized frequency F/sub 0/ = (pi D/lambda/sub 0/) /spl radic/ as a function of D/L is discussed. The simple approximate expressions for the resonant frequencies of the lower order modes are given. The properties of the TE/sub 011/, mode are discussed in detail from the point of view of its application to the measurement of the complex permittivity of microwave dielectrics. Curves and expressions for fast and simple determination of the maximum measurement errors are given.     

Mode Coupling Between Surface Wave Transmission Lines

The eigenvalue equation describing the mode coupling between two Goubau surface wave lines is derived utilizing the point matching method for solutions of boundary value problems. Excellent agreement is obtained between theoretical and experimental results. A method for obtaining the hybrid wavenumbers of coupled surface wave lines is proposed for a finite set of TE and TM modes.     

Diffraction of a general surface wave mode by a surface reactance discontinuity

The scattering of a general hybrid surface wave mode at a reactance discontinuity, on a cylindrical surface waveguide, is considered both theoretically and experimentally. The theory leads to coupled Wiener-Hopf equations, which are solved approximately by assuming the hybrid modes to be mainly TE or TM. The theoretical expressions obtained are evaluated numerically for the symmetrical and dipole modes and compared with experimental results with which substantial agreement is obtained.     

The Amplitude of Longitudinal Characteristic Modes in Dielectric Waveguide Array

It's not adequate to just obtain eigenvalue for solving eigenvalue problem. Since the eigenvalues associated with longitudinal characteristic modes in dielectric waveguide array (DWA) has been studied, the paper concentrates on the corresponding eigenvector, namely, the amplitude of these characteristic modes. Through numerical study of the amplitude of longitudinal guided TE and TM modes in DWA, space harmonic (SH) coupling and energy conversion effect have been discovered. The paper not only contribute to deep understand the mechanism of SH interaction, but also do good to analyze the resonance, radiation problem in DWA.     

Directional couplers made of nonidentical asymmetric slabs. Part II: Grating-assisted couplers

In this second part of the paper we discuss TE and TM mode directional couplers made of nonsynchronous, nonidentical asymmetric slab waveguides. Coupling is accomplished with the help of a diffraction grating that is placed on either of the two guides on the side facing the opposite slab. The grating couples the compound modes of the complete slab structure to each other. However, since the two slabs are nonsynchronous, the compound modes resemble closely the modes of each slab in isolation. We also provide approximate expressions that result from approximating the compound modes with the modes of the individual slabs. The accuracy of these approximations is estimated by comparison with the exact results.     

Propagation of TE Modes in Dielectric Loaded Waveguides

The propagation of TE/sub no/ modes in rectangular wave-guides that contain two dielectric slabs parallel to the narrow wall and extending over the full height of the guide is investigated. Waveguide and dielectric are assumed to be lossless and infinitely long. Apart from these restrictions, the dielectric slabs may have arbitrary thickness, position, and dielectric constant. The analysis is restricted to TE/sub no/ modes with the E-field parallel to the narrow guidewall. The guide containing only one dielectric slab is covered by this analysis. The even modes n = 2, 4, 6, . . . of the guide with two slabs correspond to the odd modes n' = n/2 = 1, 2, 3, . . . of the guide with one slab half the width of the guide with two slabs. For six relative dielectric constants (/spl epsilon/= 2.25, 4.00, 9.00, 12.25, 16.00, 25.00) the cutoff frequencies for TE 10, 20, 30, 40, 60 modes and the normalized propagation constants for TE 10 and TE 20 modes between their respective cutoff frequencies and a frequency slightly above the second- and fourth-order mode cutoff frequency for the empty guide, respectively, have been computed for a large range of slab thicknesses and slab positions. Selected results are presented graphically. These results are discussed. The parametric dependence of field distributions, of normalized characteristic impedances, of the ratio of cutoff frequencies (fractional bandwidth), and of the ratio of magnetic field components (ellipticity) are illustrated.     

高次谐波太赫兹回旋管的多模工作研究

为了发展大功率、实用性强的太赫兹辐射源,文中对太赫兹回旋管中多个二次谐波工作模式的注波互作用进行了理论和实验研究,分析不同参数下多个二次谐波工作模式单模振荡的条件.实验研究结果表明,在二次谐波工作状态下,通过调节工作磁场、电流等参数,在单管中实现了四个不同频率0.391、0.404、0.416、0.423 THz,千瓦级以上输出功率的太赫兹波辐射.