is derived from two functions and, , scalars on the 2-D Lorentz plane and the 2-D-Euclidean plane respectively. They are, however, not independent. Charge conservation demands the relation

The T.E.M. four-vector potential

has the same form, but only the difference is determined by the field equations. Indeed, the T.E.M. field components are derived from this difference:

are satisfied. The last equation is, of course, simply the conservation of charge equation. Furthermore, it is evident that the T.E.M. field propagates strictly along the -axis, the direction of the Pointing vector.