coefficient of RF oscillations in OEO for different levels of the relative laser phase
noise (RIN-1 and RIN-2).
For calculation the K
2
OEO plots presented in Figs. 6.33 and 6.34, we use the
expression: K
2
OEO ¼ K
2
LPN Á K
2
ΓPN , in which we use, relatively, the expression (6.79)
for K
2
ΓPN , and (6.107) for K
2
LPN . Calculations are performed for the dimensionless
offset FT 1 from the carrier, and in Eq. (6.105), we neglect by the first term for
simplicity.
The frequency of the laser natural relaxation resonance is F 00L ¼ 2/T 1 .
On the presented plot in Fig. 6.34 we obviously see that with the growth of FT FOS
and at coincidence of resonance peaks in K
2
ΓPN F
ð Þ and K
2
LPN F
ð Þ, for example, for
F 00L T 1 ¼ FT FOS ¼ 2, the peak level in K
2
OEO sharply grows.
For examination of laser resonance influence on PSD of OEO, which is formed by
the photon–electron resonance, authors calculated PSD of the phase noise, taking
into consideration PSD of the phase noises of the laser. PSD of the phase noises of
the laser were calculated on the base of formulas obtained in Chaps. 5 and 6 at
solution of the differential equation system with fluctuations.
At calculations, we take OEO with RF FODL, which consists of three optical
fibers of different length, which are connected in the inputs by the couplers. This
permitted (at correct choice of geometrical length difference of FOS included in RF
FODL) to suppress the own resonances determined be the delay time on RF FODL.
The calculation results of PSD of the phase noise of RF oscillation in OEO MZ for
different variants of QWLD (“RIN-1” and “RIN-2”) with different levels of the
phase noise. The natural frequency of the photon–electron resonance of QWLD
“RIN-1” was equal 10,000 kHz, and relatively, for QWLD “RIN-2” was equal to
20 kHz.
At calculations, we used expressions for laser PSD taking into account the
photon–electron resonance of QWLD obtained in Chap. 5 for different values of
the laser resonator Q-factor. The differential RF FODL consists of three optical
fibers of different length L ¼ 6 km, 6.2 km, 6.5 km. Optical fibers were connected in
their inputs and outputs by the directional couplers of Y-type. The calculation is
performed on the base of analytical expressions for PSD of the phase noise, which
0.05 0.10
0.50 1
10
5
K 2
LPN
K 2
LPN
K 2
OEO
K 2
LPN [FT
1 ] ,
K 2
LPN [FT
1 ] , K 2
OEO [FT
1 ]
FOS
LD
10 –6
10 –4
0.01
1
frequency offset [FT 1 ]
Fig. 6.34 The power
spectral density of the phase
noise of RF oscillations of
OEO for different levels of
the relative laser phase noise
(RIN-1 and RIN-2)
360
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .
noise (RIN-1 and RIN-2).
For calculation the K
2
OEO plots presented in Figs. 6.33 and 6.34, we use the
expression: K
2
OEO ¼ K
2
LPN Á K
2
ΓPN , in which we use, relatively, the expression (6.79)
for K
2
ΓPN , and (6.107) for K
2
LPN . Calculations are performed for the dimensionless
offset FT 1 from the carrier, and in Eq. (6.105), we neglect by the first term for
simplicity.
The frequency of the laser natural relaxation resonance is F 00L ¼ 2/T 1 .
On the presented plot in Fig. 6.34 we obviously see that with the growth of FT FOS
and at coincidence of resonance peaks in K
2
ΓPN F
ð Þ and K
2
LPN F
ð Þ, for example, for
F 00L T 1 ¼ FT FOS ¼ 2, the peak level in K
2
OEO sharply grows.
For examination of laser resonance influence on PSD of OEO, which is formed by
the photon–electron resonance, authors calculated PSD of the phase noise, taking
into consideration PSD of the phase noises of the laser. PSD of the phase noises of
the laser were calculated on the base of formulas obtained in Chaps. 5 and 6 at
solution of the differential equation system with fluctuations.
At calculations, we take OEO with RF FODL, which consists of three optical
fibers of different length, which are connected in the inputs by the couplers. This
permitted (at correct choice of geometrical length difference of FOS included in RF
FODL) to suppress the own resonances determined be the delay time on RF FODL.
The calculation results of PSD of the phase noise of RF oscillation in OEO MZ for
different variants of QWLD (“RIN-1” and “RIN-2”) with different levels of the
phase noise. The natural frequency of the photon–electron resonance of QWLD
“RIN-1” was equal 10,000 kHz, and relatively, for QWLD “RIN-2” was equal to
20 kHz.
At calculations, we used expressions for laser PSD taking into account the
photon–electron resonance of QWLD obtained in Chap. 5 for different values of
the laser resonator Q-factor. The differential RF FODL consists of three optical
fibers of different length L ¼ 6 km, 6.2 km, 6.5 km. Optical fibers were connected in
their inputs and outputs by the directional couplers of Y-type. The calculation is
performed on the base of analytical expressions for PSD of the phase noise, which
0.05 0.10
0.50 1
10
5
K 2
LPN
K 2
LPN
K 2
OEO
K 2
LPN [FT
1 ] ,
K 2
LPN [FT
1 ] , K 2
OEO [FT
1 ]
FOS
LD
10 –6
10 –4
0.01
1
frequency offset [FT 1 ]
Fig. 6.34 The power
spectral density of the phase
noise of RF oscillations of
OEO for different levels of
the relative laser phase noise
(RIN-1 and RIN-2)
360
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .