minimum “shifts to the right along the abscissa axis” to FT FOS ¼ 3, and the value of
the first minimum is two-orders lesser than at σ U ¼ 1.02.
Plots K
2
ΓPN2 T FOS
ð
Þpresented in Fig. 6.25c–f at F ¼ 1 kHz and T c ¼ 0.001 – 10 s
well show that the phase noise suppression by 10–1000 times at the delay, for
example, T FOS ¼ 3.5 Á 10
À4 s (the optical fiber length is 70,000 m) is possible at
offsets F ¼ 1 kHz at laser coherence times more than T c ¼ 10
À3 s. We more than
K 2
ΓPN
K 2
ΓPN2 ,(FT
FOS ),
G
12 [a.u]
0.001
0.05 0.10
0.50
(a)
(b)
(c)
(d)
(e)
(f)
delay time FT FOS [a.u]
F =1kHz
T c =1s
1
1 0
5
1
0.100
0.010
10
G 12
K 2
ΓPN
K 2
ΓPN2 ,(T
FOS ),
G
12 [a.u]
0.0005
0.0015
0.0010
0.0020
delay time T FOS [s]
10 –4
10 –6
10 –8
1
0.01
G 12
F =1kHz
T c =0.001 s
K 2
ΓPN2 ,(T
FOS ),
G
12 [a.u]
0.0005
0.0015
0.0010
0.0020
delay time T FOS [s]
0.100
0.001
10 –8
1000
10
F =1kHz
T c =0.1 s
K 2
ΓPN2 ,(T
FOS ),
G
12 [a.u]
0.0005
0.0015
0.0010
0.0020
delay time T FOS [s]
0.001
10 –5
10 –7
10
0.100
F =1kHz
T c =10 s
K 2
ΓPN
K 2
ΓPN
K 2
ΓPN2 ,(T
FOS ),
G
12 [a.u]
0.0005
0.0015
0.0010
0.0020
delay time T FOS [s]
10 –4
10 –6
10 –10
10 –8
1
0.01
G 12
G 12
K 2
ΓPN
K 2
ΓPN2 ,(FT
FOS ),
G
12 [a.u]
10 –4
delay time FT FOS [a.u]
15
10
5
1
0.010
0.100
0.001
10
G 12
Fig. 6.25 Functions of the suppression coefficients of the phase noise K
2
ΓPN2 T FOS
ð
Þ (6.77) and
G 12 in OEO MZ at P 0L /Y 00 ¼ 1.01 and 1.8 for σ U ¼ 1.02 at G 12 ¼ {1 À γ k Á exp [ÀFT FOS /(FT c )]} at
FT c ¼ 10 and γ k ¼ k 01 /k 02 ¼ 1; on abscissa axis the logarithm scale (a), the linear scale (b),
K
2
ΓPN2 T FOS
ð
Þat F ¼ 1 kHz, T c ¼ 1 s (c), K
2
ΓPN2 T FOS
ð
Þat F ¼ 1 kHz, T c ¼ 10 s (d). K
2
ΓPN2 T FOS
ð
Þ
at F ¼ 1 kHz, T c ¼ 0.1 s (e)
6.5 Differential Fluctuation Equations of OEO MZ
339