Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

The integral equation method for the H-polarization case looks
sligh-tly nlore complicated. This is related to the fact that even
for three-dimensional structures Maxiqell's equations l.oo?c simp1.e
when formulated for - E, whereas in the 2-formulation additional gra-
dien'ts of the conductivity arise:
The pertinent equa.tion for H-polarization is (3.5) , i. e.
with the usual splitting
1
div (- gradB) = iwpoH
u
and the additional definitions
the equations for the normal and anomalous part are
and
d l d
-(--- H ) = iwll H , H (o) = H~
dz an dz n o n n ,
1 --
div(pll gradHal = iwpoHa - div(pa gradH)
This equation corresponds to (3.41) for the E-polarization case.
Green's function appropriate to (3.51) is defined as
Physically G can be interpreted as the magnetic field due to an
11
infinite straight line of oscillating magnetic dipoles along the
x-axis.
(3.48)
Multiply (3.51) by Gn and (3.52) by IIa, subtract and integrate over
the whole space. Then