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Substituting (2.65) into (2.67), we get
sin (
−
E
1
)cos (
−
E
1
)
≥
0
.
H
1
H
1
H
1
−
E
1
) is nonneg-
ative by definition. Thus, the condition (2.67) is satisfied when sin (
Since
E
1
and
H
1
are limited by
±
/4, it is evident that cos (
0,
that is, when orientation of the magnetic and electric polarization ellipses meets the
condition
H
1
−
E
1
)
≥
≤
≤
+
.
(2
.
68)
E
1
H
1
E
1
Let us consider properties of normalized eigenfields
e
1
,
h
1
and
e
2
,
h
2
.
According to (2.64)
e
ym
e
xm
=
E
ym
E
xm
=
P
e
m
=
P
E
m
,
(2
.
69)
h
ym
h
xm
=
H
ym
H
xm
=
P
h
m
=
P
H
m
,
m
=
1
,
2
.
Vectors
e
m
,
h
m
have the same polarization ratios as initial eigenfield vectors
E
τ
m
,
.
Hence all parameters characterizing polarization of the electric and
magnetic eigenfields can be calculated from
P
e
m
,
H
τ
m
P
h
m
.
What we have to stress is that vectors
e
1
and
e
2
as well as vectors
h
1
and
h
2
are
orthonormal:
e
m
·
e
n
=
mn
,
h
m
·
h
n
=
mn
,
(2
.
70)
where
1
m
=
n
mn
=
0
m
=
n
.
We represent normalized eigenfields
e
1
,
e
2
and
h
1
,
h
2
by matrices
e
1
x
h
1
x
e
2
x
h
2
x
=
,
=
.
[
U
e
]
[
U
h
]
(2
71)
e
1
y
e
2
y
h
1
y
h
2
y
forming orthonormal basises in the spaces of electric and magnetic fields. The con-
jugate matrices are
e
1
x
e
1
y
e
2
x
e
2
y
h
1
x
h
1
y
[
U
e
]
=
,
[
U
h
]
=
.
(2
.
72)
h
2
x
h
2
y
By virtue of (2.70)
