7.2.3 The Model of the Nonsymmetric Waveguide
For the strength for the main field mode, for nonsymmetric waveguide (ε 3 6 ¼ ε 1 and
therefore a 0 6 ¼ 0), we obtain the following formula:
E Y0 y
ð Þ ¼
E 00 exp a 0 y=l
ð
Þ
ch y=l
ð Þ
½
Š
S 01 þjS 02
:
ð7:26Þ
The expression (Eq. 7.26) we normalize on E 00 and take the logarithm, taking into
account Eq. (7.27), and as a result, we have:
ln E Y0 y
ð Þ=E 00
½
Š¼
a 0 y=l
ð
ÞÀS 01 ln ch y=l
ð Þ
½
Š
2 þ S 02 ln ch y=l
ð Þ
½
Š
f
g
2
h
i
n
o 1=2
 exp j arctan
S 02 ln ch y=l
ð Þ
½
Š
a 0 y=l
ð
ÞÀS 01 ln ch y=l
ð Þ
½
Š
½
Þ :
ð7:27Þ
Thus, the expression (Eq. 7.27) can be presented as:
ln E Y0 =E 00
ð
Þ¼E LN00 y
ð Þ Á exp jΦ LN y
ð Þ
½
Š ,
ð7:28Þ
Here in Eq. (7.28) we use the expression for the normalized amplitude mentioned
in Eq. (7.28):
-1.5
E
0 (y)
-1.0
-0.5
1.0
1.0
0.5
-0.5
-1.0
-1.5
-2.0
0.5
0.5
a)
b)
transverse offset y
transverse offset y
1.0
1.5
-1.5
Φ (y), radian
-1.0
-0.5
0.5
y
1.0
1.5
Fig. 7.8 Functions of the
amplitude E 0 ( y) (a) and the
phase Φ( y) (b) of the field
strength in the near zone
versus the transverse offset
y for S 0 ¼ S 01 + jS 02 at
S 01 ¼ 2, S 02 ¼ 2
382
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .