6.2.3 Elimination of the Vertical Field Components

Both vertical field components E_{z, nm}(z) and H_{z, nm}(z) are analytically related to the lateral ones. Hence they can be eliminated in (6.15) and (6.18) and we end up at an ODE system comprising only the Fourier coefficients of the lateral field components:

 

$$\begin{aligned}\frac{d E_{x,nm}(z)}{d z} &= +j\omega\mu_0 H_{y,nm... ...1}{\omega\mu_0} \Big[k_{x,n}E_{y,nm}(z) - k_{y,m}E_{x,nm}(z)\Big].\end{aligned}$$