= Complex refractive index
{title2=$N=n+i\kappa$}
For a plane wave proportional to $e^{i(N\omega z/c-\omega t)}$, the <complex refractive index> separates phase propagation from attenuation. In a nonmagnetic medium $N^2=\epsilon_r$, so $n^2-\kappa^2=\epsilon_r'$ and $2n\kappa=\epsilon_r''$. The passive branch has $\kappa\geq0$. If $\kappa\ll n$ and $\epsilon_r'>0$, then $n\simeq\sqrt{\epsilon_r'}$ and $\kappa\simeq\epsilon_r''/(2\sqrt{\epsilon_r'})$. These signs assume the $e^{-i\omega t}$ convention for the <complex permittivity>.
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