K
2
ΓPN F
ð Þ ¼
Y
P 0L
cos FT FOS
ð
ÞÀσ U
h
i 2
Y 00
P 0L
h i 2 À
Y 00
P 0L
Á 1 þ σ U
ð
Þcos FT FOS
½
þσ U
&
' 2 :
ð6:58Þ
Figures 6.18 and 6.19 show the plots depicted by expressions (6.57) and (6.58) of
suppression coefficients of the amplitude K
2
ΓAN F
ð Þ and the phase K
2
ΓPN F
ð Þ noise in
OEO MZ for different values of σ U and P 0L /Y 00 .
From analysis of plots in Figs. 6.18 and 6.19 for suppression coefficients of the
amplitude and phase noises in OEO MZ, we can conclude that at fulfillment of the
condition S aμRe Á (Y aRe À 1)
2
( S aμIm Á [Y aIm ]
2 , the maximal suppression of PSD of
phase noises occurs at small values of σ U and P 0L /Y 00 (Fig. 6.19), which are close to
the stability boundary of the OEO MZ generation mode. At that, we observe the
significant level of peak values at multiple offsets FT FOS ¼ 2πm, where m is the
integer number. The power increase (or the normalized value of P 0L /Y 00 ) in this case
leads to reduction of phase noise suppression (Fig. 6.19).
6.5.8 The Function of the Suppression Coefficient of PSD
of the Phase Noise in OEO MZ Versus the Laser Power
The function of PSD of the phase noise of the laser power P 0L is defined by
Eq. (6.55). The specific feature of OEO MZ is the fact that the coefficient of the
local slope σ U also depends on P 0L . The formula for interconnection of σ U of P 0L
at approximation of NA nonlinear characteristic by the cubic polynomial is:
σ U ¼ 1 À
S 03
S 01
U
2
10MZ ¼
1
3 1 À
4Y 00
P 0L
1
S 01
. Such function σ U is defined by the square
amplitude U
2
10MZ with expression obtained from the abbreviated equation of OEO
MZ in the Chap. 3 (Eq. 3.59) at fulfillment of self-excitation conditions and the
K 2
*PN
K 2
*AN
K 2
*AN (σ
U ) , K 2
*PN (σ
U )
Local slope
–5
1
0.100
0.010
0.001
10 –4
10
–10
5
10
Fig. 6.17 Suppression
coefficient of the amplitude
K
2
ΓAN F
ð Þ and the phase
K
2
ΓPN F
ð Þ noise depicted by
expressions (6.54) and
(6.55) in OEO MZ at
different σ U at the
normalized offset F ¼ 3
324
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .
2
ΓPN F
ð Þ ¼
Y
P 0L
cos FT FOS
ð
ÞÀσ U
h
i 2
Y 00
P 0L
h i 2 À
Y 00
P 0L
Á 1 þ σ U
ð
Þcos FT FOS
½
þσ U
&
' 2 :
ð6:58Þ
Figures 6.18 and 6.19 show the plots depicted by expressions (6.57) and (6.58) of
suppression coefficients of the amplitude K
2
ΓAN F
ð Þ and the phase K
2
ΓPN F
ð Þ noise in
OEO MZ for different values of σ U and P 0L /Y 00 .
From analysis of plots in Figs. 6.18 and 6.19 for suppression coefficients of the
amplitude and phase noises in OEO MZ, we can conclude that at fulfillment of the
condition S aμRe Á (Y aRe À 1)
2
( S aμIm Á [Y aIm ]
2 , the maximal suppression of PSD of
phase noises occurs at small values of σ U and P 0L /Y 00 (Fig. 6.19), which are close to
the stability boundary of the OEO MZ generation mode. At that, we observe the
significant level of peak values at multiple offsets FT FOS ¼ 2πm, where m is the
integer number. The power increase (or the normalized value of P 0L /Y 00 ) in this case
leads to reduction of phase noise suppression (Fig. 6.19).
6.5.8 The Function of the Suppression Coefficient of PSD
of the Phase Noise in OEO MZ Versus the Laser Power
The function of PSD of the phase noise of the laser power P 0L is defined by
Eq. (6.55). The specific feature of OEO MZ is the fact that the coefficient of the
local slope σ U also depends on P 0L . The formula for interconnection of σ U of P 0L
at approximation of NA nonlinear characteristic by the cubic polynomial is:
σ U ¼ 1 À
S 03
S 01
U
2
10MZ ¼
1
3 1 À
4Y 00
P 0L
1
S 01
. Such function σ U is defined by the square
amplitude U
2
10MZ with expression obtained from the abbreviated equation of OEO
MZ in the Chap. 3 (Eq. 3.59) at fulfillment of self-excitation conditions and the
K 2
*PN
K 2
*AN
K 2
*AN (σ
U ) , K 2
*PN (σ
U )
Local slope
–5
1
0.100
0.010
0.001
10 –4
10
–10
5
10
Fig. 6.17 Suppression
coefficient of the amplitude
K
2
ΓAN F
ð Þ and the phase
K
2
ΓPN F
ð Þ noise depicted by
expressions (6.54) and
(6.55) in OEO MZ at
different σ U at the
normalized offset F ¼ 3
324
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .