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TE Waves

$\displaystyle E_z$ $\textstyle =$ $\displaystyle 0$ (10.64)
$\displaystyle \frac{\partial B_z}{\partial n}\vert _S$ $\textstyle =$ $\displaystyle 0$ (10.65)

The electric field is strictly transverse, but the magnetic field in the $z$-direction can be nonzero. Doing exactly the same algebra on the same two equations as we used in the TM case, we get instead:
\mbox{\boldmath$H$}_\perp =
\pm \frac{k}{\mu\omega}(\hat{\mbox{\boldmath$z$}}\times \mbox{\boldmath$E$}_\perp )
\end{displaymath} (10.66)

along with
\mbox{\boldmath$B$}_\perp = \frac{\pm ik}{(\mu\epsilon\omega^2 - k^2)}\mbox{\boldmath$\nabla$}_\perp
\end{displaymath} (10.67)

where $\psi(x,y) e^{ikz} = B_z$ and
\left(\nabla_\perp^2 + (\mu\epsilon\omega^2 - k^2)\right)\psi = 0
\end{displaymath} (10.68)

and the boundary conditions for a TE wave:
\frac{\partial \psi}{\partial n}\vert _S = 0
\end{displaymath} (10.69)

Robert G. Brown 2007-12-28