Systematic and efficient root finder for computing the modal spectrum of planar layered waveguides

Abstract

An efficient and systematic strategy to find the propagation constants of real, complex, and leaky modes of covered and uncovered planar multilayered isotropic/uniaxial waveguides is presented. This strategy first builds up a pole-free characteristic function and then makes use of a root-searching scheme based on an integral nature method to search for its zeros. For uncovered waveguides, the branch points of the characteristic function can be removed by introducing the upper half-space vertical wavenumber as the working variable. Examples of the efficiency, reliability, and robustness of the presented technique are given for both covered and uncovered waveguides, which sets up this technique as a very convenient CAD tool. The method is also applied to study a new and interesting problem: the evolution of the modes of a grounded dielectric waveguide when increasing the permittivity of the upper semi-infinite medium.

Application of Total Least Squares to the Derivation of Closed-Form Green's Functions for Planar Layered Media

“…The values of these poles and residues have been computed for the particular spectral-domain Green's function of Fig. 6 by means of an appropriate numerical algorithm [44], and the results are shown in Table I Table I(B) within six significant figures. The real part of the residues at the aforementioned poles also coincide within four significant figures.…”

“…Looking at (28), (29), (32), (33), (36), and (37), it can be observed that the functions denoted in this paper by (i.e., , and ) are all linear combinations of functions of the type (44) where…”

Solving the cutoff wave numbers in partially filled rectangular waveguides by the Cauchy integral method

“…Recently, the method based on the Cauchy integral has become more popular to solve these sets of equations [11,12]. It has the property that is valid for any complex transcendental equation, and additionally it needs no previous information or seed.…”

“…It has been employed more recently on planar circuits by Y. Long [15][16][17], for microstrip lines by Mesa et al [11], for microstrip antennas [18], and also for circular-waveguide resolution [19].…”

Solving the Cut-Off Wave Numbers in Partially filled Rectangular Waveguides with Ferrite by the Cauchy Integral Method

“…Additionally, it does not need any previous information or seed. The method has been employed recently on planar circuits [10][11][12], for microstrip lines [13], for microstrip antennae [14], and also for the rectangular [15] and circular [16] waveguides resolution.…”