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The T.M. Field
For the T.M. degrees of freedom the source and the electromagnetic
field are also derived from a solution to the same inhomogeneous
scalar wave Eq.(5). However, the difference
from the T.E. case is that the four-vector components of the source and
the vector potential lie in the Lorentz -plane. Thus, instead
of Eqs.(9) and (10), one has the T.M. source
|
(11) |
and the T.M. vector potential
|
(12) |
All the corresponding T.M. field components are derived from the
scalar :
|
(13) |
These components are guaranteed to satisfy all the Maxwell field equations
with the T.M. source, Eq.(11), whenever
satisfies the inhomogeneous scalar wave equation, Eq.(5).
Ulrich Gerlach
2001-10-09