132 3. FINITE FERRITE SAMPLES
Mode clinging onto the bottom surface x D d=2 and propagating toward the positive
Oy:
‰.x/ D ‰
0
0e
e
jk
y
y
e
jk
z
sinh
Œ
˛
i
.
x d=2
/
sinh
.
˛
i
d
/
j
˛
i
d=2>>1
‰
0
0e
e
jk
y
y
e
jk
z
e
˛
i
.
xd=2
/
e
˛
i
d
‰
0
0e
e
jk
y
y
e
jk
z
e
˛
i
.
xCd=2
/
for
j
x
j
d=2: (3.164b)
A graphic representation of the above case is shown in Figure 3.23. It is important to note
that non-reciprocal MSSW modes follow the right-hand rule, circulating around the positive z-
direction, along which the DC bias and saturation magnetization are assumed; in other words,
align your right thumb along the static DC biasing field and turn your hand clokwise to show
the direction of the circulating MSSW field. Another important feature of these MSSW modes
is their circular (or elliptic) polarization [41].
K = + k
y
Z
Y
K = - k
y
+d/2
-d/2
Figure 3.23: Graphic representation of the two non-reciprocal MSSW modes for the limiting
case when ˛
i
d >> 1 [41].
3.23.3 POLARIZATION OF MAGNETOSTATIC WAVES
It is likely that circularly or elliptically polarized waves exist in ferrites due to the 90
ı
phase dif-
ference between the diagonal and off-diagonal elements of the permeability tensor. In turn, this
circular polarization appears directly in the RF magnetic field components that are transverse to
DC magnetization. In the present case, this would occur in h
x
and h
y
since the DC bias is along
the z-axis. Recall that the RF magnetic field
N
h is expressed in terms of the magnetic potential
i
as
N
h D r‰
i
. Now, a question appears about the modes for which the differentiation causes
a 90
ı
(namely, an additional j ) phase difference between h
x
and h
y
.
Concerning volume magnetostatic modes (MSBVW in longitudinal bias), the differen-
tiation shifts both h
x
and h
y
by 90
ı
. is happens because the former has an exponential e
jk
y
y
dependence, while the latter has a sinusoidal one, which is also equivalent to e
˙jk
x
x
. In con-
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