TABLE OF CONTENTS We consider wave guides. The frequency ? is given; the eigenvalue problem then determines the permissible (axial) wave numbers k. Depending on the boundary conditions one distinguishes between fields of different types:
TM, transverse magnetic: B z, = 0 everywhere (hence the terminology) and E z surface = 0,
TE, transverse electric: E z, = 0 everywhere (hence the terminology) and ? B z/ ? n surface = 0,
TEM, transverse electric-magnetic: B z, = 0 = E z, everywhere.
We consider first the case of TEM fields.
In these cases we obtain from Eqs. (14.20) and (14.21) the equations
These equations have the trivial solution
Hence for a nontrivial solution we have in general
Equations (14.20) and (14.21) imply 0 E ?, B ?, = 0, i.e. E ?, B ? remain undetermined. For this reason we now write the TEM fields
According to Eqs. (14.31) we now have (with ? ? 2 = ? ?):
i.e. E TEM, B TEM are solutions of the two-dimensional Laplace equation. Before we investigate these equations we show that
This is not trivial, because so far we established the transversality of electromagnetic radiation only for the case of an unlimited medium.
From
we get
For E, B ? E TEM, B TEM, i.e. B z
