Information Technology Reference
In-Depth Information
Note that
|
E
| =
0 for the linear polarization, and
|
E
| =
1 for the circular
polarization. What is the sense of the sign of
E
? Let us define the angle velocity of
the field rotation:
dt
arctan
E
y
(
t
)
d
|
E
x
||
E
y
|
E
=
E
x
(
t
)
=
sin
)
.
2
cos
2
(
2
cos
2
(
E
y
|
E
x
|
t
−
x
)
+|
E
y
|
t
−
E
This makes clear that the electric vector rotates clockwise if sin
>
0, that is,
E
<
0, that is, for
for
E
<
0.
With (2.14), we can present simple formulae for normalized semi-axes of polar-
ization ellipse:
E
>
0, and counterclockwise if sin
a
E
a
E
+
1
1
b
E
=
=
1
E
=
cos
,
E
tan
2
+
b
E
a
E
1
+
(2
.
15)
b
E
a
E
+
1
tan
E
b
E
=
=
1
E
=
sin
E
.
tan
2
+
a
E
b
E
1
+
It is obvious that the polarization state of the electric field is completely deter-
mined by its polarization ratio. The complex quantity
P
E
=
E
e
i
E
tan
characterizes
E
x
|
,
E
y
and
E
E
the entire class of electric fields with different
|
x
,
y
, but with
E
y
/
|
E
E
y
x
and hence with the same elliptic
the same tan
=
E
x
|
,
=
−
parameters
E
which define the orientation and shape of the polarization ellipse.
According to (2.13), (2.14)
,
E
E
cos
E
tan 2
E
=
tan 2
−
/
2
≤
E
≤
/
2
(2
.
16)
E
sin
E
E
=
tan
E
sin 2
E
=
sin 2
−
1
≤ ≤
1
−
/
4
≤
E
≤
/
4
.
Converting these relationships, we get
E
E
cos 2
=
cos 2
E
cos 2
0
≤
≤
/
2
E
(2
.
17)
E
E
tan
=
tan 2
E
csc 2
−
<
≤
.
E
Similar formulae are available for the polarization ellipse of the magnetic field
(Fig. 2.1b).
The angle
H
between the major axis of the magnetic ellipse and the
x
-axis can
be determined from the equation
2Re
P
H
H
cos
H
tan 2
=
2
=
tan 2
(2
.
18)
H
1
− |
P
H
|
