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6.2.2 Second Maxwell Equation

In an exactly analogous way the components of the second Maxwell equation are first written explicitly:

$\displaystyle \begin{aligned}\frac{\partial E_z(\mathbf{x})}{\partial y} - \fra...
...c{\partial E_x(\mathbf{x})}{\partial y}\right] &= H_z(\mathbf{x}),\end{aligned}$    

and then transformed into the frequency domain. This yields two coupled ODEs for the lateral electric field coefficients Ex, nm(z) and Ey, nm(z) as well as one analytical expression for the vertical magnetic field coefficients Hz, nm(z):

$\displaystyle \begin{aligned}\frac{d E_{y,nm}(z)}{d z} &= -j\omega\mu_0H_{x,nm}...
...{1}{\omega\mu_0}\Big[k_{x,n}E_{y,nm}(z) - k_{y,m}E_{x,nm}(z)\Big].\end{aligned}$    

Heinrich Kirchauer, Institute for Microelectronics, TU Vienna