Magnetic Field

With the help of the orthogonality requirement H_l^$\pm$ = 1/($\eta_{0}^{}$k_l) k^$\pm$_l x E^$\pm$_l the magnetic field phasors H_l⁺ and H_l^- are easily calculated from the electric ones. From (C.1) we obtain similar to (C.5) for the z-dependent part of the lateral magnetic field components

$$\begin{alignedat}{2}H_{l,x}(z) &=\textstyle \frac{1}{\eta_0k_l}\l... ..._0k_l}\left(-k_{l,z}E^-_{l,x}-k_xE^-_{l,z}\right)e^{-jk_{l,z}z}.\end{alignedat}$$

The vertical amplitudes E^$\pm$_{l, z} can readily be eliminated with the help of (C.4) resulting in

$$H_{l,x}(z) =\!\textstyle \left(-\frac{k_xk_y}{\eta_0k_lk_{l,z}}E^+_{l,x} -\f... ...E^-_{l,x} +\frac{k_y^2+k_{l,z}^2}{\eta_0k_lk_{l,z}} E^-_y\right) e^{-jk_{l,z}z}$$

$$H_{l,y}(z) =\!\textstyle \left(+\frac{k_x^2+k_{l,z}^2}{\eta_0k_lk_{l,z}} E^+... ...z}} E^-_{l,x} -\frac{k_xk_y}{\eta_0k_lk_{l,z}} E^-_{l,y}\right) e^{-jk_{l,z}z}.$$ (C.5)