Propagation in the Open Cylindrical Guide of Arbitrary Cross Section With the Use of Field Matching Method

Global Complex Roots and Poles Finding Algorithm Based on Phase Analysis for Propagation and Radiation Problems

“…For all the edges in C (k) the phase change is |∆Q p | ≤ 1 and the condition ( 5) is fulfilled. An example of DCAP (single root in z (1) = 1, double root in z (2) = i, triple root in z (3) = −1 and singularity in z (4) = −i) is presented in Figure 1. For each of the four candidate regions, the function argument varies along the contour taking the values from the four quadrants.…”

“…Since the quadrant difference along a single edge is |∆Q p | ≤ 1, the discretization of the boundary is sufficient to evaluate the total phase change over the region boundary. By summing all the increases in the quadrants along the contour in the counterclockwise direction, one obtains the values 4, 8, 12 and −4 for regions containing z (1) , z (2) , z (3) and z (4) , respectively. Since the increase in the quadrant numbers along the edge represents the changes in the function argument of π/2, the parameter q is equal to 1, 2 , 3 and −1, respectively (single root, double root, triple root and singularity):…”

“…In many cases the evaluation of these parameters boils down to finding a complex root of a more or less complicated function. Even in the case of a simple technique, as mode matching or field matching [1], the roots cannot be found analytically. For more sophisticated structures and methods the function can be expressed in the numerical form (spectral domain approach, discrete methods, nonlinear matrix eigenvalue problem) [2], [3].…”

Semi-Analytical Methods for the Electromagnetic Propagation Analysis of Inhomogeneous Anisotropic Waveguides of Arbitrary Cross-Section by Using Cylindrical Harmonics

“…Figure 5. 22 Transversal E φ field pattern for the first (a) second (b) and third (c) cases of deformities in cross-section of the noncircular tunnel. Figure 5.23 Geometry of coaxial waveguide filled with two elliptical dielectric layers.…”

“…In addition, some methods are in a middle ground between analytical and brute-force approaches, where a series expansion in terms of special functions are employed to match the boundary conditions in cylinders with cross-sections that does not deviate a lot from circles or ellipsis. These semi-analytical methods will be denote herein was point-matching methods (PMMs) 1 , and have been used with success of the years for the analysis of non-circular hollow waveguides [9,17,18], scattering by dielectric cylinders [19][20][21], and others wave-guided-devices [22,23].…”