Eigenmodes of coaxial quad-ridged waveguides. Theory

The electrodynamics eigenmodes boundary problems’ solutions for the eigenmodes of coaxial quad-ridged waveguides are presented. These solutions have been obtained by integral equations technique utilizing the proposed system of orthogonal basis functions, which take correctly into account singular behavior of the field at the ridges’ edges. The formulas obtained provide possibilities to calculate cutoff wave numbers and electric and magnetic fields distributions for TEM, TE and TM modes in the presence of the ridges either on the inner or on the outer conducting cylinder. Analysis of the dependence of numerical solutions convergence for cutoff wave numbers on the number of basis functions and partial modes has been carried out. It has been shown that for calculation of cutoff wave numbers with residual error less than 0.1% it is enough to utilize the 7 proposed orthogonal basis functions and the 21 partial modes.     

Eigenmodes of sectoral coaxial ridged waveguides

The results of numerical investigation of sectoral coaxial ridged waveguides eigenmodes of two configurations (with a ridge on inner or outer wall) for different cross-section dimensions are presented. In particular, dependences of cutoff wave numbers on geometrical dimensions ratios for first four modes are investigated, electric field components distributions for these modes have been obtained and the optimization of sectoral coaxial ridged waveguides has been carried out to provide maximal single-mode operation frequency band. Two optimal configurations of waveguides with single-mode operation bandwidth ratio 5.6:1 are obtained. It is shown that smaller cross-section dimensions at the fixed single-mode operation frequency band has the waveguide with the ridge at the inner round wall. The size of the gap between the ridge and the round wall of optimal waveguide is identical for both configurations and is determined by the required ratio of cutoff frequencies of two lower TE modes. Calculations are conducted utilizing the mathematical model obtained in [1] by the integral equation technique with the correct account of singular behavior of the field at the ridge.     

Eigenmodes of a periodic array of coupled waveguides

General properties of eigenmodes in periodic arrays of coupled waveguides are considered. The Floquet channel model is used to analyze arrays operating in the quasi-periodic mode. Relationships for the orthogonality of different types of eigenmodes are obtained on the basis of the Lorentz lemma and the active power theorem. The problem of excitation of array eigenmodes by given currents is solved. The relation between two representations of the array field, by means of the eigenmode expansion and in the form of the Fourier integral, is shown by the example of an array of coupled slot lines.     

Propagation in two circular coaxial waveguides

Two variants of the circular waveguide loaded with a coaxial dielectric rod are discussed. The first has conducting hoops around the rod, the second has conducting discs across the rod, the planes of the closely spaced hoops or discs being normal to the waveguide axis. The characteristic equations for the two systems are given, and a consistent mode notation is suggested.     

Mutual coupling in arrays of coaxial waveguides and horns

A solution is presented for the mutual coupling between the modes of different-sized circular coaxial aperture arrays, which are used as direct radiators and feed antennas. This solution is expressed in terms of integral transforms and the mutual admittances for the cross coupling between all three mode types, TE, TM, and TEM, are obtained. The accuracy of this new integral formulation is demonstrated by comparing computed results with measured data for a three-element test array. Excellent agreement is obtained between theory and experiment for both coupling coefficients and radiation patterns. Results are also presented for a coaxial feed array for the Lovell radio telescope.     

Propagation and radiation properties of corrugated cylindrical coaxial waveguides

A theoretical study is given for the behavior of cylindrical coaxial waveguides having reactive (corrugated) surfaces. After a general analysis assuming independent values for the surface reactances, the propagation and radiation properties for specific surfaces are considered. These include the case where 1) both surfaces are smooth-walled; 2) one surface is smooth-walled with the other corrugated; and 3) both surfaces are corrugated such that they have equal values for the surface reactance.     

Microwave waveguides in EBG structures formed from coaxial cylinders

Infinite 2D periodic EBG structures from coaxial metal cylinders placed in a planar waveguide are investigated. Short-circuited and open-circuited metal cylinders forming, respectively, short-circuited and open-circuited sections of coaxial transmission lines are considered. It is shown that, by varying the lengths of these coaxial lines, it is possible to create defects in EBG structures that form regular waveguides. The eigenmodes of such waveguides are studied. It is shown that the EBG structures formed from coaxial metal cylinders can be used as the base for the development of multifunction microwave devices.     

Evanescent and complex solutions in two circular coaxial waveguides

Evanescent and complex solutions for two variants of the circular waveguide loaded with a coaxial dielectric rod, that with conducting hoops around the rod and that with conducting discs across the rod are given. A previously given notation for the propagating solutions for the two systems is re-examined.     

Radiation characteristics of coaxial waveguides as a small primary feed

The radiation patterns of coaxial waveguides with a TE11 exciting mode are computed numerically. It is shown that by a proper selection of the coaxial aperture dimensions the symmetry of the copolar patterns can be improved considerably. Coaxial radiators can therefore be designed as a useful small primary feed for paraboloid reflector antennas.     

Mode coupling in coaxial waveguides with varying-radius center andouter conductors

The mode conversion process in a coaxial waveguide with varying-radius center and outer conductors is shown to be described by a system of first-order differential equations-the coupled mode equations. The nondiagonal coefficients of this system are called the coupling coefficients. In this paper, we derive the explicit expressions for the coupling coefficients in a varying-radius coaxial waveguide and discuss some of their important features. These coefficients can be used in determining model conversion in a coaxial cavity with slowly varying walls or designing and analyzing coaxial waveguide tapers and mode converters. Some experimental results of the coupling coefficients for the case of azimuthally symmetric modes, TE_0n modes, are also given     

Numerical modeling of axisymmetric coaxial waveguidediscontinuities

Techniques for determining field behavior in the presence of coaxial-to-coaxial discontinuities are presented for axisymmetric geometries. A bilinear functional is formulated from which field solutions are obtained by way of the finite element method. An absorbing boundary condition is applied at the input and output port boundaries to reduce the size and complexity of the problem. An additional approach, mode matching, is outlined and presented as verification of finite element results. Two geometries are investigated, for which numerical results are presented. A comparative evaluation of the two techniques is included     

Higher order mode impedances and cut-off frequencies of overmoded coaxial waveguides

Using both theoretical and experimental methods the critical geometrical ratios for effective higher order mode superposition in coaxial waveguides are identified for SDMA beam forming antenna applications. Higher order mode impedances are also important in the design of such antennas and a closed form expression for the power-voltage definition of impedance is derived together with estimates for the voltage-current and power-current forms. An industry standard finite element solver is used to confirm the accuracy of these formulations for a 60?mm radius overmoded coaxial waveguide. In the second part of the paper, the mode chart is used to design a coaxially fed, overmoded air-spaced coaxial waveguide “T” junction supporting the TEM, TE ₁₁ and TE ₂₁ modes. A Green's function based model of the input impedance of this junction establishes that the power-voltage characteristic impedance occurs naturally in calculations requiring absolute impedance values. Finally, this input impedance model, which includes higher order and evanescent mode propagation, is demonstrated to agree well with experimental data for this junction.     

Linear analysis of cyclotron-cherenkov and cherenkov instabilities in dielectric-loaded coaxial waveguides

We present, based on the cold fluid theory, linear analysis of the Cherenkov and cyclotron-Cherenkov instabilities which are driven when a linear electron beam is injected into a dielectric-loaded waveguide immersed in an axial magnetic field. In the analysis we consider azimuthally symmetric TM_0n modes. We derive dispersion relations for three types of waveguide, and compare computationally obtained linear growth rates of both instabilities. For the type A, which consists of a metallic cylinder with dielectric liner on its inner surface, the growth rate of the Cherenkov instability is larger than that of the cyclotron-Cherenkov instability. For the type B, which consists of a dielectric core and an outer metallic cylinder, both growth rates are comparable. And for the type C, which consists of a metallic core with dielectric liner on its surface and an outer metallic cylinder, the growth rate of the latter instability is higher than that of the former instability. Finally, for the type C, obtained are dependences of the oscillation frequency and the growth rates of both instabilities on the following parameters: the beam energy, the beam current, the axial magnetic field, the dielectric constant, and the thickness of the dielectric.     

Eigenmodes of multiwaveguide structures

Finite periodic structures for multichannel waveguiding are analyzed by self-consistent field matching at the interfaces and matrix formalism for lateral propagation. The characteristic eigenvalue equation for a symmetric system with N coupled slab waveguides is shown to be of the same functional form as that of a single-slab waveguide. The eigenmodes of the system are exactly calculated and compared to the approximate results of coupled mode theory. Basic features of multiwaveguide structures not derivable from the coupled-mode theory (CMT) are uncovered by rigorous formulation and solutions. More complicated structures are solved, and ways of mode shaping and mode filtering are suggested     

Numerical analysis of nonlinear bistable optical waveguides

Numerical solutions illustrating the onset of bistability and hysteresis are presented for the symmetrical step index, asymmetrical step index, and asymmetrical diffused slab nonlinear optical waveguides. Two different numerical techniques have been used independently-a finite-element method and a variational method. Both methods produce numerically stable solutions, and agreement between them is good for both increasing and decreasing total power from below or above the threshold power. The results are compared with analytical solutions for these structures. The onset and the end of the physically unstable solutions regime coincides with the two power thresholds for the increasing and decreasing powers     

Numerical solution of lossy waveguides: t.l.m. computer program

The transmission-line-matrix method is a time-domain numerical method for solving wave problems. The method uses a mesh of transmission lines to represent a propagation space, and the losses in the space are accounted for by making the transmission lines lossy. Lossy boundaries are simulated by imperfect boundary reflections on the transmission lines. A FORTRAN program implementing this technique is presented.     

Numerical analysis of three-parallel embedded optical waveguides

Three parallel embedded dielectric waveguides are investigated numerically. The mode-matching method that matches the boundary conditions in the sense of least squares is applied to this problem, using the hybrid-modal representation. Precise numerical results for the dispersion relations and field distributions are presented for the lowest three modes near the cutoff. The frequency range in which only the three modes can propagate and the differences in their propagation constants are discussed at length, in order to highlight the available frequency range and the coupling length of the configuration with respect to its use as a directional coupler     

Numerical analysis of dielectric-rod waveguides with deepcorrugation

Dielectric-rod waveguides with deep surface corrugation is analyzed by using the finite-difference time-domain method. In order to mitigate the load in numerical calculation and to analyze a wide region, the method is formulated in two-dimensional form. It is shown that disks located in a line function as a waveguide of low loss in a frequency region. The procedure of deciding the propagation constant from the analyzed field is presented. The complex propagation constant is obtained and the dependence of the amount of radiation on the corrugation amplitude is discussed