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Additional resources for Analysis of Electromagnetic Fields and Waves: The Method of Lines (RSP)
We obtain from eq. 105) = ru ru Exs Z21 Z22 jSxm 0 Z rl Z rl 21 22 The superscript r means ‘reduced’ in connection with the ﬁrst step. 106) is an indirect eigenvalue system. The elements (Zijrl )lk of the system matrix contain the normalised propagation constant (εre = (kz /k0 )2 ). The eigenvalue εre must be varied until the determinant of this system matrix vanishes. The current vector [Stym , jStxm ]t is afterwards determined as an eigenvector. If εre and the current vector are evaluated, the ﬁeld vector [−jEtys , Etxs ]t can be calculated with eq.
17). 22) and obtain the result in the equation on the right side. The GTL equations have the advantage of allowing us to immediately obtain the wave equation for the transverse electrical ﬁelds. Further, we see that we start with the wave equation for the magnetic or the electric ﬁeld and obtain the same expressions later on. By using GTL equations we can very easily take into account anisotropic material as well. Furthermore, the modal matrices obtained from GTL equations lead to simpler analysis equations.
The permittivity of the layers might be either a continuous or stepwise function of the lateral coordinate, and the layers may diﬀer in width. 28 Analysis of Electromagnetic Fields and Waves z B A MMPL1030 Fig. 13 General cross-section of a multilayered waveguide (Reproduced by permission of Elsevier) Metallic strips are embedded at diﬀerent interfaces. The metallisations are either inﬁnitely thin or of ﬁnite thickness. Lossy materials are modelled by complex permittivities. Therefore, lossy strips are modelled as inhomogeneous layers with the thickness of the metallisation.