Scattering of Surface Waves on Transverse Discontinuities in Symmetrical Three-Layer Dielectric Waveguides

This paper presents a rigorous Wiener-Hopf solution to the problem of transverse discontinuities in a symmetrical three-layer dielectric waveguide excited by the dominant TE mode. Fourier transformation and the proper boundary conditions provide the Wiener-Hopf equation for the Fourier components of the scattered fields at the interface between the free space and the dielectric waveguide. A formal solution to this equation is derived by conventional factorization methods, and an iterative method is proposed to calculate the reflected, transmitted, and radiated fields numerically.     

Cutoff Frequencies of Eccentric Waveguides

This paper discusses the uniform cylindrical waveguide formed by placing one conductor inside a conducting tube. Because of the complexity of the guide's cross section, the numerical technique of the point-matching method is adopted to solve the boundary-value problem. The formulations are carried out for the case when each of the conductors has an arbitrary cross section and also for the case when one of the conductors has a circular cross section. The coaxial waveguide modes, in which the field components have angular variations, split into odd and even modes when the center conductor begins to shift axis to form the uniform eccentric waveguide. However, only even modes in the eccentric guide correspond to the coaxial modes with no angular variations. The dependence of the cutoff frequency on the eccentricity of the guide is determined numerically for even and odd TE and TM modes. Experimental results verify the theoretical calculations for TE modes.     

Delay Equalization by Tapered Cutoff Waveguides

When a wave packet propagates in a guided mode subject to cutoff at a definite frequency, dispersion is always present. To restore the shapes of the wave packets at the receiving end, a proper delay equalization must be applied. Waves propagating in a waveguide tapered to cutoff dimensions are reflected mostly in a region where the dimensions are at cutoff. Accordingly waves of higher frequencies will penetrate deeper into the tapered guide and thereby introduce more delay than those of lower frequencies. A profile of a tapered waveguide is obtained for the case of linear delay on the hypothetical assumption that a wave is totally reflected only at the plane of cutoff dimensions. The problem of finding a proper profile is similar in nature to the inverse scattering problem in quantum mechanics. The complex input reflection coefficient introduced by a tapered cutoff waveguide is invariably unity in its magnitude for all frequencies below cutoff and has different phases for different frequencies. Presently available theory for computing the complex reflection coefficient is valid only when its magnitude is smaller than unity. A theoretical method to calculate with accuracy the phase of such unity reflection coefficient is presented. The linking section between the standard waveguide and the tapered cutoff waveguide is designed on the basis of a high-pass filter that introduces no appreciable perturbation to the prescribed delay characteristic. The excellent agreement between the theoretical results and measured data suggests that microwave delay equalizers can be designed "on paper" with "measurement" accuracy without even going to the laboratory. Accordingly the claim can be made that any reasonable amount of delay of simple shape within certain bandwidth limits can be equalized by the present approach.     

Composite Dielectric Waveguides

Composite dielectric waveguides, or a class of dielectric waveguides made of a few dielectric materials, are described. A composite circular dielectric waveguide (CCDW) is treated with the the point-matching method. Computed values of the propagation constant of the CCDW are compared with those of the homogeneous circular dielectric waveguides (HCDW). Microwave experiments carried out to comfirm the theory are discribed.     

Planar Spiral in Three-Layer Dielectric with Screen

The excitation of a planar spiral placed in the three-layer dielectric medium in non-symmetric regime have been analysed using the integral representation method. Numerical computations of the patterns, polarization and power characteristics have been carried out for various geometrical and physical parameters. A great influence of the system geometry and dielectric permittivity of the layers on radiated field characteristics has been shown.     

Bends in Nonradiative Dielectric Waveguides

An experimental study was made of bends in the nonradiative dielectric waveguide (NRD-guide) at 50 GHz. The main cause of the bending losses was found to be due to the reflection at the transitions between the straight and curved waveguides rather than due to the radiation. The width of the dielectric strip was experimentally optimized in order to reduce the reflection, and a bend with a curvature radius as small as one guide wavelength could be realized. The experimental results are examined theoretically. The theory implies that the NRD-guide has a favorable tendency to suppress not only the radiation but also the reflection at the curved sections. It is also shown that the field maximum moves outwards or inwards from the mean path of the curved guide according to whether the dielectric strip is wider or narrower than a certain critical width. This critical width can be adopted as a design criterion for a low loss, very sharp NRD-guide bend.     

Dielectric Loaded Elliptical Waveguides

Wave propagation in a metallic elliptic waveguide loaded with a dielectric rod or a dielectric lining is investigated theoretically. The mode spectrum for both slow and fast hybrid modes is obtained by numerical solution of the characteristic equations. Correspondence is established between the modes of the loaded and unloaded elliptical waveguides. Typical field plots for /sub e/HE/sub 01/ and /sub 0/EH/sub 01/ modes are presented. Power flow, power loss, and attenuation are obtained using a perturbation method.     

Low Loss Dielectric Waveguides

The history of dielectric waveguides begins back in 1910 with the publication of a theoretical paper by Hondros and Debye, who gave a mathematical treatment of transverse magnetic mode propagation in lossless dielectric guide. In the 1930's Southworth began experimental work on these modes while Carson, Mead, and Schelkunoff developed a general theory which showed the existence of TE, TM, and hybrid HE modes. During World War II, dielectric rod antennas came into use. However, dielectric waveguides as transmission lines were considered impractical at that time when the shortest wavelengths in use were several centimeters long. The size of dielectric required at these long wavelengths, and the problems of support, radiation, and crosstalk, appeared to be serious drawbacks to the practical utilization of these guides. Furthermore, there was no great need for dielectric guides, since dominant-mode metallic guides had sufficiently low loss while flexibility could readily be obtained by corrugated guides or by coaxial lines.     

Mode Conversion in Tapered Waveguides At and Near Cutoff

The coupling coefficient between the TE/sub 11/ mode and the TM/sub 11/ mode in tapered circular waveguides is derived, and at cutoff frequency it tends to approach an infinity of the order of 0/sup -1/4/. It is surprising to discover that the corresponding coupling coefficient between the TE/sub 10/ mode and the TM/sub 12/ mode in tapered rectangular waveguides approaches instead a zero of the order of 0/sup 1/4/ at cutoff frequency. Accordingly, for the modes concerned, the choice of using circular or square waveguides as tapers for transition at and near cutoff frequency is significant in reducing mode conversion level. At and near cutoff frequency a "synthesized" square taper is better in that it is shorter than a "synthesized" circular taper for the same mode conversion levels. On the other hand, for frequencies far away from cutoff the choice is insignificant. Design procedures for "synthesized" waveguide tapers at and near cutoff are presented, and the results of measurements are in agreement with the theoretical calculations.     

Modes and Cutoff Frequencies of Crossed Rectangular Waveguides

One complete solution is presented for determining the electromagnetic field of a generalized crossed rectangular waveguide. The method adopted is that of partial regions. Cutoff frequencies of symmetrical crossed waveguides are presented as an example. The results, even for low-order approximations, correspond well with the only experimental results available in the literature.     

Dielectric Resonator in a Waveguide Below Cutoff

A structure is considered consisting of a waveguide 2 below cutoff, connected to waveguides above cutoff, 1 and 3, by means of suitable junctions. A dielectric resonator is introduced in waveguide 2. Its effect on the transmission curve of the structure is evaluated in the limit epsilon/sub r/spl rarr/spl infin/. Theoretical results are compared with experiment.     

The Cutoff Wavelengths of Composite Waveguides (Correspondence)

When electromagnetic waves propagate in waveguides of nonsimple cross section, no exact solution can be obtained by the conventional method of solving the wave equation by separation of variables. In such cases approximations are available such as perturbation methods, variational methods, etc.     

高斯光束在介质波导中的传播

本文考虑轴对称高斯型激光束在均匀介质及类透镜介质中的传播问题。本文采用作者以前所导出的正确方程,计及光束的衍射效应,求出了方程的解析解。在此基础上,讨论了激光束的宽度和波阵面问题。在均匀介质中,激光束将单调变粗;在类透镜介质中,激光束的宽度是z正弦函数,粗细交替出现。     

Propagation of Cladded Inhomogeneous Dielectric Waveguides

An approximate theory on the propagation of modes in an arbitrarily inhomogeneous optical waveguide embedded in a homogeneous medium is presented. Simple formulas are given, whereby the propagation constants can be determined assuming that the analytic solution is known in the absence of cladding. The results obtained applying the theory to a truncated parabolic-index profile are shown to be in good agreement with those obtained by the rigorous analysis. The theory is also applied to the propagation of TE and TM waves in truncated near-parabolic-index media.     

Coupling Characteristics of Nonradiative Dielectric Waveguides

An analytical method is presented for predicting coupling characteristics of dielectric strips in the nonradiative dielectric waveguide. Starting with an approximate but very accurate expression for the coupling coefficient between parallel dielectric strips, the scattering coefficients for nonuniform coupling structures are derived in simple closed-form expressions by taking the effect of the field deformation at the curved sections into account. The coupling coefficient of the nonradiative dielectric waveguide is found to be so large compared to those of other dielectric waveguides that complete power transfer can be attained with coupled polystyrene bends having a curvature radius as small as 20 mm at 50 GHz. The theory was verified experimentally for various coupling structures. As an application toward millimeter-wave integrated circuits, 0-dB couplers, quadrature hybrid couplers, and an in-phase power divider were constructed based on the present analysis. A comparison of theory and experimental data of these fabricated coupling circuits suggests that the effect of the nondegenerate modes in the straight and curved guides must be included in the analysis to further improve the theory.     

Approximation Technique for Dielectric Loaded Waveguides

An algebraic procedure is described which yields approximate values for the cutoff frequencies and propagation constants of dielectric-loaded waveguides. The procedure is demonstrated for a waveguide completely filled with an anisotropic dielectric and for waveguides partially filled with isotropic dielectrics. For the latter case results are tabulated for five types of waveguide loading. The symmetrically loaded waveguide is used to show the accuracy which may be expected. This procedure is shown to be identical with the Rayleigh-Ritz variational method but with the advantage that it provides a systematic approach to improve the accuracy and to handle a multitude of waveguide geometries.     

Analysis of Circular Chiral Dielectric Waveguides

The general eigenequations and the field expressions for circular waveguides containing chiral material in both the core and the cladding are given in a simple formulation. The results indicate that there are two types of field distribution which is related to the operating wavelength and chiral admittance. When the chiral admittance is larger than a critical value, the fields of one kind of circularly polarized wave in the core become exponentially-like damping in the transverse direction. Based on the eigenequations, the characteristics of a circular waveguide with chiral medium filled in the core are investigated. The relation between the cutoff frequency and the chiral admittance, the dispersion curves for some modes with different angular mode number and the transverse distribution of fields are presented. Some features different from the ordinary circular waveguide are resulted.     

Wave Scattering in Nonuniform Waveguides with Large Flare Angles and Near Cutoff

A set of coupled first-order differential equations for the wave amplitudes in nonuniform waveguides is developed. The coupling coefficients are regarded as differentiaI transmission and reflection scattering coefficients between two adjacent elementary radial waveguide sections. The analysis is an extension of an earlier quasi-optical solution. This set of coupled equations is compared with the familiar generalized telegraphist's equations which may be derived by considering the nonuniform waveguide to consist of elementary rectangular waveguide sections. The equations for the wave amplitudes derived in this paper are less coupled than the commonly used telegraphist's equations, and they may also be applied to waveguides with large flare angles and in regions at which the waveguide modes are at their respective cutoff cross sections.     

Coupled-Mode Theory of Two Nonparallel Dielectric Waveguides

A general theory for treating the coupling between two nonparallel dielectric waveguides is developed using the coupled-mode assumption. This theory is used to analyze directional couplers consisting of two circularly curved, single-mode dielectric slab waveguides. By assuming continuous coupling between the two waveguides rather than only between adjacent segments on the two waveguides, the present theory avoids the awkwardness of having to specify in a somewhat arbitrary manner the separation between these segments, as is the case for existing theories reported in the literature. It is shown that this over-simplification results often in an overestimate of the power transfer in a directional coupler by 10-20 percent, compared to this theory.