= Evanescent transverse electric mode in a rectangular waveguide
{title2=$\kappa^2=(\pi/a)^2-\epsilon_r\omega^2/c^2$}
Below the lowest <waveguide cutoff frequency>, the axial wave number of the $\mathrm{TE}_{10}$ mode is $i\kappa$, with $\kappa>0$. For a real peak scale $E_0$ and time convention $e^{-i\omega t}$, $E_y=E_0\sin(\pi x/a)e^{-\kappa z}$, $B_x=-i\kappa E_y/\omega$ and $B_z=-iE_0(\pi/a)\cos(\pi x/a)e^{-\kappa z}/\omega$. The <electric field> and <magnetic field> are in quadrature. A single decaying mode in a lossless semi-infinite guide consequently has zero time-averaged <Poynting vector>, although its instantaneous field stores <energy>.
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