Matrix theory approach to complex waves (in shielded lossless guides)

Complex Root Finding Algorithm Based on Delaunay Triangulation

“…The last example concerns a complex wave propagation problem in a circular waveguide of radius b, coaxially loaded (lossless dielectric with permittivity ε r ) with a cylinder of radius a [Mrozowski and Mazur 1992;Mrozowski 1997]. To ensure continuity of the fields at the boundary, the following determinant function must be equal to zero:…”

On the Independence of the Excitation of Complex Modes in Isotropic Structures

“…Moreover, we observe that the eigenvectors of a complex mode and its conjugate counterpart are linearly independent (13). The relevant orthogonality relation applicable to the paraskew Hermitian matrix in (11) is (15) Substituting into (15) the various transformations outlined in (12) to (14), the following useful orthogonality relations are obtained:…”

“…The theoretical aspects of complex modes have been investigated by several authors, including T. Tamir [10], A. S. Omar and K. F. Schunemann [11], M. Mrozowski and J. Mazur [12] and T. F. Jablonski [6]. The physical constraints which determine whether a given structure can support these modes are outlined in the short list of references above.…”

Complex Surface Wave Modes of Plasma Column Loaded Closed Cylindrical Waveguide

“…This was shown in the dielectric loaded cylindrical waveguide [21,22], the twolayer circular shielded waveguides with different permittivity or permeability [23], the shielded rectangular dielectric image [24,25] and the rod waveguides [26], the planar transmission lines [27], the shielded suspended coupled microstrip line [28], the nonreciprocal finline [29], the suspended ferrite loaded strip lines [30], and the multilayered parallel plate waveguide with ferrite layers [31]. Some studies purpose to give a theoretical proof of the existence of complex wave modes [32] or the co-existence of complex and backward wave modes [19,33] for different waveguide structures. These studies base on the matrix equivalent of the waveguide structures and derive the theoretical proof using the fundamental properties of equivalent matrix.…”

“…The existence of complex and backward wave modes was proved for the general case of only inhomogeneous or only anisotropic filled waveguides with arbitrarily shaped cross sections [19]. The necessary condition for existence of complex waves was given in [32] and it is also shown that complex waves may exist in slightly perturbed homogenous guides. In later studies, the necessary and sufficient conditions for the existence of backward waves in metallic waveguides filled the media which do not include coupling between transverse and longitudinal fields (simultaneously inhomogeneous and anisotropic) were given in [34] and the proof that whenever there is a frequency region of a backward wave then there exists an adjacent region with a complex propagation constant was presented in [33].…”