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27 we thus obtain in both directions three different subregions. First we assume that we have discretisation points inside and on the surface of the metal. However, the discretised components on these points should be removed in our calculations. Therefore, we reduce the total number of discretisation points to that outside the metal. Let us ◦ ◦ , Nx2 assume that in our example the number Nx◦ of ◦ columns consists of Nx1 ◦ and Nx3 columns in the three subregions 1, 2, 3 in x-direction, respectively.

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.

As can be seen, by decreasing the discretisation distance (hx ) we approach the analytic value. As a second example, we examine the propagation of two eigenmodes in a slab waveguide in Fig. 11. The interference can be seen clearly. Finally, the normalisation in eq. 38) is not mandatory. g. without the factor β we obtained a different expression for the wave admittance/impedance. Now the following formula can be used for this case as well. 2 Introducing 26 Analysis of Electromagnetic Fields and Waves Fig.

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