= TE wave equation in a stratified magnetodielectric
{c}
{title2=$E_{y,xx}+E_{y,zz}-\frac{\mu'}\mu E_{y,z}+\omega^2\mu\varepsilon E_y=0$}
With permittivity and permeability depending only on $z$ and time dependence $e^{i\omega t}$, a <transverse electric polarization> $\mathbf E=\widehat{\mathbf y}E_y(x,z)$ obeys the displayed equation. <Maxwell's equations> give $H_x=E_{y,z}/(i\omega\mu)$ and $H_z=-E_{y,x}/(i\omega\mu)$. The latter satisfies $H_{z,xx}+H_{z,zz}+(\mu'/\mu)H_{z,z}+[\omega^2\mu\varepsilon+(\log\mu)'']H_z=0$. At normal incidence $H_z=0$; the nonzero magnetic component is $H_x$.
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