Here we consider only the action of the laser noises assuming that detected laser
noises significantly exceed the own PD noises and reduced to the NA input. For
simplicity, we suppose that D PN ¼ D AN .
Fulfillment of mentioned conditions is possible in the case of the non-quadrature
mode, when sin[2πν 0 (T 1M À T 2M ) + πU 0MZ /U πMZ ] % 0 or
2πν 0 (T 1M À T 2M ) + πU 0MZ /U πMZ ¼ πm. Then, the second term in Eq. (6.27)
becomes neglibly small. i.e., S μAN ‐ PN % 0 and S μψ1PN (F) > S μAN (F). In these
assumptions, expressions (6.49) and (6.50) for S mOEO (F) and S ΨOEO (F) take the
form:
S mOEO F
ð Þ ¼
Y aIm
½
Š
2 S aμIm
Y a Re À σ U
½
ŠY a Re À 1
½
Šþ Y aIm
½
Š
2
n
o 2 ,
S ΨOEO F
ð Þ ¼
Y a Re À σ U
ð
Þ
2 S aμIm
Y a Re À σ U
½
ŠY a Re À 1
½
Šþ Y aIm
½
Š
2
n
o 2 :
ð6:56Þ
Then expressions (6.36) and (6.55) for (6.62), (6.63) can be written as follows:
S mOEO ¼ S aμ Re K
2
ΓAN , S ΨOEO ¼ S aμIm K
2
ΓPN , where coefficients K
2
ΓAN F
ð Þ and
K
2
ΓPN F
ð Þ have the form:
5
0.50
1
0.05
0.10
0.01
0.05
σ U =1.02;
=1.8
P 0L
Y 00
0.10
0.50
Offset frequency
K 2
*PN
K 2
*AN
K 2
*AN (F) , K 2
*PN (F)
(a)
1
5 1 0
0.50
1
0.05
0.10
0.01
0.05
σ U =1.02;
=1.8
P 0L
Y 00
0.10
0.50
Offset frequency
K 2
*PN
K 2
*AN
K 2
*AN (F) , K 2
*PN (F)
(b)
1
5 1 0
0.50
1
0.05
0.10
0.01
0.05
σ U =1.02;
=10
P 0L
Y 00
0.10
0.50
Offset frequency
K 2
*PN
K 2
*AN
K 2
*AN (F) , K 2
*PN (F)
(c)
1
5 1 0
Fig. 6.15 Suppression coefficient of the amplitude K
2
ΓAN F
ð Þand the phase K
2
ΓPN F
ð Þnoise depicted
by expressions (6.54) and (6.55) in OEO MZ at σ U ¼ 1.02 and P 0L /Y 00 ¼ 1.8 (a); σ U ¼ 1.02 and
P 0L /Y 00 ¼ 1.1 for (b), σ U ¼ 1.02 and P 0L /Y 00 ¼ 10 for (с)
322
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .