Numerical Solution of Coupling Between Two Collinear Parallel-Plate Waveguides

The problem of coupling between two collinear parallel-plate waveguides is investigated numerically using moment methods. The exciting mode in the waveguide is assumed as the incident field, and the integral equation for the induced current is expressed in terms of the reflected, transmitted, and evanescent currents on the waveguides. The integral equation is then solved numerically by a point-matching method and the reflection and the transmission coefficients and the radiated fields are obtained. To examine the accuracy of the results, the special case of a semi-infinite exciting waveguide coupled to a finite coupled waveguide is also considered and is solved numerically by treating the singularities of the induced currents using a transformation method. For a TE/sub 0,1/ excitation of the exciting waveguide, the results of both numerical methods are compared with the analytical results obtained previously using the Wiener-Hopf technique, and are found to be in good agreement. The methods are then used to study the effect of the coupled waveguide on the radiation field.     

Coupling Between Two Collinear Parallel-Plate Waveguides of Unequal Widths

The problem of coupling between two collinear parallel-plate waveguides of unequal widths is investigated using the moment methods. The exciting mode of the waveguide is assumed as the incident field and an integral equation for the induced currents is expressed in terms of the reflected, the transmitted, and the evanescent currents on the walls of the waveguides. This integral equation is solved numerically and the results for the reflections and the transmission coefficients and the radiated field are obtained. The effect of varying the coupled waveguide width and the separation distance of the waveguides is investigated.     

Mutual coupling between two circular waveguides

The problem of coupling between two circular waveguides is solved using the Wiener-Hopf technique. Expressions for the radiated, reflected, and the transmitted fields are obtained and are expressed by three terms. The first term in these expressions represents the solution for an open ended circular waveguide, while the other two are due to the interaction between the two waveguides. It is shown that, the radiated, reflected, and the transmitted fields can also be found from the reflection coefficient of an open ended circular waveguide and an evaluation of a semi-infinite integral involving the fourier transformed Green's function of the Weiner-Hopf equation. Exact solutions are used to generate the approximate solution of the ray theory of diffraction. This is achieved by expanding the exact solution and using the modified diffraction coefficient of Lee in conjunction with a spherical wave-factor.     

A Planar transversal junction of two planar waveguides

A rigorous analytic method is used to solve the wave-propagation problem for a planar transversal junction of two planar waveguides. The problem is reduced to an iteratively solved system of integral equations of the second kind. Dependences of the transmission and reflection coefficients of guided waves, radiation patterns, and the power of the radiation field on the ratios of the waveguide thicknesses and the waveguide permittivities are obtained.     

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.     

Analysis of a phase mismatched three waveguide coupler with an optical amplifier

A novel optical amplifier is proposed and analyzed. This device consists of three parallel waveguides and each has a slightly different propagation constant, that is, each waveguide is slightly phase mismatched and couplings among these waveguides are weak. Two adjacent waveguides are passive and the third one is active and all end facets of waveguides are antireflection coated, so that optical feedback can be eliminated and the active waveguide is a traveling wave type amplifier. Because of a phase mismatched configuration, this device can be used to tap optical signals without much power reduction in optical transmission lines. Signals coming into the device are weakly coupled to the active waveguide via the passive waveguide in between and they are amplified through the active waveguide. Characteristics of this device are studied and parameters which are required to design the device are also given as an example.     

Analysis of mode conversion in waveguide transition sections with surface impedance boundaries applied to VLF radio propagation

First- and second-order correction terms are derived for the reflection and transmission scattering coefficients for a step-type transition between two uniform waveguides with surface impedance boundaries. This analysis yields rigorous expressions for the differential transmission and reflection coefficients defined for an infinitesimal step transition. These coefficients are essential in the derivation of the coupled differential equations for the wave amplitudes in a transition section of gradually varying height.     

Influence of gap between laser and optical waveguide

In the letter, an approximate analysis is developed for calculating the reflection and transmission coefficients at the junction discontinuity between two planar dielectric waveguides when there is a dielectric gap between them. The analysis is applied to the junction between a heterojunction laser and a planar optical waveguide with an airgap, and results are presented showing the variation of the reflection and transmission coefficients with the gapwidth.     

Reflection and transmission at an abrupt change in cross-section of a rectangular waveguide in the E and H plane

For a symmetric cross-sectional enlargement of a rectangular waveguide, the reflection and transmission coefficients of the H10 mode are calculated. At low frequencies, they agree well with the values for the H11 mode at an axial-symmetric junction of two circular waveguides. An axial offset of the two rectangular waveguides has a small influence on these coefficients.     

Moment method solution of double step discontinuities in waveguides

The problem of scattering of a double step waveguide discontinuity is investigated. Two coupled sets of equations in terms of the unknown magnetic current sheets on the apertures are obtained and solved for the electric field distribution using the moment method. The scattering matrix coefficients describing reflection, transmission, and mode conversions at a symmetric double step waveguide discontinuity are obtained and presented graphically for specific junctions.     

A computation of the reflection and transmission coefficients for dielectric coated waveguides

A previously developed variational technique for finding the approximate solution to the electromagnetic field inside waveguides of varying shapes and containing non-uniform dielectric and magnetic materials is applied to the specific case of an axisymmetric waveguide containing three layers of different dielectric materials. The magnetic permeability is taken equal to unity. The method enables the problem to be reduced to a two point boundary value problem for a pair of second order, linear, ordinary differential equations. The values of the reflection and transmission coefficients obtained by this method are in good agreement with those derived from solving the partial differential equations for the field.     

Scattering and radiation from a slitted parallel-plate withrectangular grooves: TE-wave

TE-wave scattering and radiation from a slitted parallel-plate waveguide with rectangular grooves is considered. The Fourier transform and the mode matching are used to represent the scattered field in terms of the continuous and discrete modes. The simultaneous equations for the discrete modal coefficients are obtained by matching the boundary conditions. The fast-converging series solutions are presented to evaluate the far-zone radiation, reflection, and transmission coefficients. The numerical computations illustrate the angular behavior of far-zone radiation in terms of the slit size, groove size, and operating frequency. The antenna radiation pattern of the slitted parallel-plate is measured and compared with theory     

A Complete Solution of the Inductive Iris with TE/sub k0/ Incidence in Rectangular Waveguide

A TE/sub k0/ wave incident on an inductive metal iris in a rectangular waveguide excites a reflected and a transmitted wave in the TE/sub k0/ mode. The reflection and transmission coefficients describing these waves are computed. In addition to the incident mode, a number of other modes are excited by the discontinuity. The amount of coupIing to these other modes, given by coupling coefficients, is determined using the variational technique. The method developed makes it possible to find the coupling to any desired mode without first finding the coupling to any other mode or group of modes. The analysis shows under what conditions certain modes can be suppressed or eliminated. The method should be applicable to other problems of interest where modes other than the incident one are excited. Since the reflection, transmission, and coupling coefficients are known, the total field at any point in the waveguide can be computed. As an example, the total field at the discontinuity when the TE/sub 10/ mode is incident is calculated. The result closely resembles the expected result (of zero electric field over the metal iris).     

Accurate analysis and modeling of laminated multilayered 3-D optical waveguides

The theoretical investigation of waveguides having nonuniform cross-sections is an attractive and challenging problem which deserves serious interest. In this paper, we present a novel analysis of laminated multilayered three-dimensional waveguide, based on two modes: 1) a new coupled transmission line approach that considers the sloping of the layers along the longitudinal direction and 2) a transmission line matrix integral equation (TLMIE) modeling that complete and extends the investigation of the field propagation. In method 1), we neglect radiation modes and their EM coupling. All physical effects instead are accounted for by the full-wave TLMIE method. By using TLMIE, we validate the EM analysis and calculate TE/TM losses, arising from radiation modes.     

Coupled-waveguide exchange-Bragg resonator filters: coupled-modeanalysis with loss and gain

Novel resonator filters made of two closely coupled asymmetric waveguides with phase-shifted exchange-Bragg grating, are investigated. Coupled-mode theory based on the normal modes is used to examine the effects of loss and gain on the filter spectral responses. The filter exhibits a total transmission at central wavelength and a rejection to the adjacent waveguide with high extinction ratio for other signals in the absence of loss and gain. Material loss reduces the transmitted power level and increases the filter bandwidth. With a certain amount of optical gain, good transmission can still be maintained in the presence of material loss. Proper control of the optical gain can lead to the amplification of both the transmitted and reflected powers at the central wavelength     

Surface wave scattering from a notch in a dielectric-covered groundplane: TE-mode analysis

026The problem of TE mode surface wave scattering from a rectangular notch in a dielectric-covered ground plane is considered. A Fourier-transform technique is used to express the scattered field in the spectral domain in terms of parallel-plate waveguide modes. The boundary conditions are enforced on the ground plane and the notch aperture to obtain simultaneous equations for the transmitted field inside the notch. The simultaneous equations are solved to obtain a solution in a fast convergent series, thus facilitating the numerical computation. The transmission, reflection, and scattering coefficients are found to oscillate as the notch width increases especially when the notch depth is comparable to and larger than one wavelength. A limited number of computations show that the reflected power loss is less than 2% when the notch width is less than one wavelength     

Modal analysis of waveguide antennas with arbitrary cross sections

An approach is given to analyze the modal coupling of open-ended waveguides with arbitrary cross sections located in a conducting screen. The presented theory enables the determination of reflection characteristics of a single waveguide, as well as the analysis of mutual coupling between elements in waveguide antenna arrays. The field inside each waveguide is expressed as a sum of the transverse-electric and transverse-magnetic modes and expressions for the mutual admittances of modes excited at the aperture are obtained using a direct integration method. From these expressions, the mode reflection and conversion coefficients are determined. Computed and measured results are presented. Furthermore, this approach has been used to design a new type of horn antenna with high return loss and equal radiation patterns in the two principle planes     

Coupling phenomena in concentric multi-applicator phased arrayhyperthermia systems

The coupling between the waveguide applicators of a four-element phased array hyperthermia system irradiating a three-layered cylindrical tissue model of circular cross section is analyzed theoretically. The fields inside the tissue layers are expressed in terms of cylindrical vector wave functions satisfying the corresponding wave equations, while the fields inside each waveguide are expanded in terms of guided and evanescent normal modes. Then, by implementing the appropriate boundary conditions, a system of four coupled integral equations is derived in terms of the unknown electric field distributions on the open waveguide apertures. This system is solved by expanding the unknown electric field on each aperture into waveguide normal modes and by applying a Galerkin's procedure. The self reflection coefficient and the mutual coupling coefficients are then determined and numerical results for a four-element phased array hyperthermia system are computed and presented for different waveguide applicator sizes and settings     

Reflection and transmission of guided electromagnetic waves at anair-chiral interface and at a chiral slab in a parallel-plate waveguide

Recently, the concept of chirowaveguides, which exhibit some novel and interesting properties due to electromagnetic chirality, was introduced and studied elsewhere. In this paper, the authors analyze theoretically another problem associated with chirowaveguides, namely, the problem of reflection and transmission of guided waves at an air-chiral interface and at a chiral slab located transversely in a parallel-plate waveguide. The notable features and the role of chirality of the medium on the reflected and transmitted guided waves are discussed, and physical insights into these results are provided. It is found that since the guided modes inside the chiral region of the waveguide are hybrid, in order to satisfy the boundary conditions at interfaces, the reflected and transmitted guided modes in the air regions of the waveguides need to be of TE and TM modes. The motivation behind this study is the potential applications of this problem to the design of novel measurement techniques for determining material parameters of chiral composites     

Perturbation analysis and modeling of curved microstrip bends

The curved microstrip bend consisting of a microstrip ring segment between two microstrip lines is analyzed for its transmission properties. The microstrip lines are modeled by equivalent ideal magnetic wall waveguides for which the electromagnetic field solutions are known. The field solutions in the microstrip ring segment are derived by using a perturbation analysis of a modified (magnetic wall) curved waveguide model. Other techniques have been formulated to evaluate the fields inside curved metallic waveguides. These include the use of an equivalent nonuniformly loaded straight waveguide and rectangular and annular model analysis. The perturbation solution for the fields in the equivalent curved waveguide model presented is readily adaptable to the mode-matching procedure, and is used to calculate the properties of the curved microstrip bend discontinuities. The frequency-dependent reflection and transmission coefficients of curved microstrip bends are determined and compared with those of the right-angle and chamfered right-angle microstrip bends