122
Dropping terms that contain products of derivatives of j and derivatives of the current as
well as products of the current and second derivatives of £ (i.e. terms that are designated
by an overbrace) equation (D.7) is rearranged as
I [fccos0(p U2) + u/E/j + 2 [fccos(p E/2) + u/l/] ^ +Wi4
+ [~fc2 cos2 B(p U2) + k2p + u/2 a2 2u/fccos0l/j ^ i(k cos 0)vUV
+1 [Vy (w k cos 8 U) (Jfc cos 6U)yV k cos 0E/V] ^ } e*'(/ k COi 9
+ [P(ae,^fcCO,<,l)) +2. [K(w-ifccosE7)] = g)
It is easily shown that
kcos0{p U2) +- k cos OU
it is also easily shown that
or a2 = 2o>k cos 0U (k cos BUy
From equation D.2 it is apparent that for a constant o
(k cos 6)y = -a v
Thus equation (D.8), becomes
{ [
+2iVa ^-ei(fkca,9dz^ + |p
where a i(kcos 6)vUV£ term has been dropped.
At this point a phase shift is introduced
v.
= 0
(D.9)
(DIO)
(D-11)
(D.12)
(D.13)
^ A'e*(f icof dx-f k co 6 dz)
(D.14)