Mode Matching Method for Anisotropic Guides

Abstract

The mode matching technique is employed frequently in formulating discontinuity problems in isotropic waveguides. An example of this procedure appears in the work of Hurd and Gruenberg who have solved the problem of a bifurcated waveguide. They derive two doubly infinite sets of equations by using the continuity of the interface electrical and magnetic fields, respectively. The final equation for the large waveguide mode coefficients is obtained by subsequent elimination of the unknown mode coefficients of the smaller guides from the first two sets. A key step in this two‐step method of formulation involves the Fourier analysis of the fields using orthogonal mode functions as the basis. In the anisotropic version of the same problem, which is considered in this paper, it is observed that the conventional procedure does not lead to a convenient form. This is a consequence of the fact that the anisotropic guide modes are no longer orthogonal. It is shown that by using biorthogonality relationships introduced by Bresler and others, it is possible to derive a set of equations in the desirable form for the anisotropic case as well. An interesting observation about the procedure is that the matching of interface tangential electric and magnetic fields is carried out in a simultaneous manner, and hence, the final equations are obtained in a one‐step process as opposed to the two‐step procedure conventionally followed in the isotropic case. The paper discusses the solution of the infinite set of equations appropriate to the anisotropic case and compares it with the Wiener‐Hopf solution derived elsewhere.

Commission 6: Progress in Radio Waves and Transmission of Information: 1. Radio Waves

“…Some basic aspects have received attention [Tai, 1967;Berger and Griemsmann, 1967], but most contributions have dealt with applications of the theory. These include guided waves in an isotropic and anisotropic environment [Du and Compton, 1966;Gruenberg and Daly, 1967;Berger and Griemsmann, 1968;Kong and Cheng, 1968a], scattering from moving targets and boundaries [Lee and Lo, 1967a;Lee and Mittra, 1967b;Kong and Cheng, 1968b;Tsandoulos, 1968;Restrick, 1968], waves in moving plasmas [Unz, 1968] Applications of partial coherence theory continue to be explored in radio astronomy [Ko, 1967;Swenson and Mathur, 1968] and for radiation and diffraction [Mitchell, 1966;Schell, 1967;Shore, 1968]. Of special interest are the effects of partial coherence on wavefront reconstruction [Lurie, 1966;Reynolds and DeVelis, 1967], the use of holographic methods for determining the coherence properties of fields [Lurie, 1968], and the use of partially coherent illumination for radar ranging [Poirier, 1968].…”

Cold plasma-induced effects on electromagnetic wave scattering in waveguides: a mode-matching analysis

“…To analyze the scattering of electromagnetic waves in cold plasma-filled waveguides, different numerical techniques have been applied [25][26][27][28][29][30][31][32][33][34][35]. The mode-matching technique is often applicable in solving discontinuity problems in isotropic waveguides [36]. This technique has been applied to write a high-frequency structure to analyze the program for the resonator of gyro-devices [37].…”

Wiener-Hopf Analysis of Planar Canonical Structures Loaded With Longitudinally Magnetized Plasma Biased Normally to the Extra-Ordinary Wave Propagation

“…The quantities A p (λ), B p (λ) and C p (λ) involved in the above equations are arbitrary spectral functions to be estimated by enforcing the appropriate boundary conditions. The incident extra-ordinary TEM wave propagating in the parallel-plane region toward the positive z-direction is given by Johansen, [21] as well as Mittra and Lee [36], in the spatial domain as:…”

“…In contrary u p defined in Equation (5b) does not introduce any singularity, since it appears as a function u p coth(pu p ) → 1/p when u p → 0. Returning to Q c (λ) the u 0 branch cut singularity is transformed to a pole in Equation (36), since: (37) where…”