part (the optical channel of the laser resonator) apart of the optical filter and the
nonlinear optical amplifier, n ¼ 1, 2, . . . .
At satisfaction of self-excitement conditions, the emission is generated on the
laser output, which EMF strength is equal: E L (t) ¼ E 0L cos(2πν 0L t + φ 0L ).
3.4.2 Equations of Amplitude and Phase Balance for the RF
Part of OEO DM and OEO MZ
3.4.2.1 OEO MZ in the “First Harmonic” Mode
Determination of the generated radio frequency 2πf in the RF part of OEO MZ can
be explained from the equations of the amplitude and phase balance of the steadystate auto-modulated oscillations as:
K L f , U 0MZ , ν 0L
ð
Þ K FOS f
ð ÞK PD K EF f
ð ÞK EA f
ð Þ ¼ 1,
φ 1MZ f , U 0MZ , ν 0L
ð
Þþφ FOS f
ð Þ þ φ PD f
ð Þ þ φ EF f
ð Þ þ φ EA f
ð Þ ¼ À2πm
&
,
ð3:43Þ
where K 1MZ ( f ), K FOS ( f ), K PD , K EF ( f ), K EA ( f ) are the modules (AFC), relatively,
of the MZ modulator, the fiber optical system, the photodetector, the RF filter, the RF
amplifier; φ 1MZ ( f ), φ FOS ( f ), φ PD ( f ), φ EF ( f ), φ EA ( f ) are arguments (PFC), relatively, of the MZ modulator, the fiber optical system, the photodetector, the RF filter,
the RF amplifier; U 0MZ is DC bias voltage of MZ; ν 0L is the optical laser frequency,
m ¼ 1, 2, . . . .
If the self-excitation conditions are satisfied in the closed loop, the oscillation will
be generated on the OEO electrical output, which voltage (or current) is:
U e (t) ¼ U 0e cos(2πf 0e t + ϕ 0e ) where U 0e is the amplitude, f 0e is the average optical
generated frequency, ϕ 0e is the constant initial phase shift. In this case, we do not
take into consideration the amplitude and phase fluctuations m e and ψ me .
3.4.2.2 OEO DM in the “First Harmonic” Mode
The system of AFB equations for OEO DM in the “first harmonic” mode can be
written in the similar manner as for OEO MZ:
K L f , J 0 , ν 0L
ð
Þ K FOS f
ð ÞK PD K EF f
ð ÞK EA f
ð Þ ¼ 1,
φ L f , J 0 , ν 0L
ð
Þþφ FOS f
ð Þ þ φ PD f
ð Þ þ φ EF f
ð Þ þ φ EA f
ð Þ ¼ À2πm,
&
ð3:44Þ
where K L ( f, J 0 , ν 0L ), K FOS ( f ), K PD , K EF ( f ), K EA ( f ) are modules (AFC), relatively,
of the MZ modulator, the fiber optical system, the photodetector, the RF filter, the RF
amplifier; φ 1L ( f, J 0 , ν 0L ), φ FOS ( f ), φ PD ( f ), φ EF ( f ), φ EA ( f ) are arguments (PFC),
3.4 Equations of Amplitude and Phase Balance for the Laser and for OEO
115
nonlinear optical amplifier, n ¼ 1, 2, . . . .
At satisfaction of self-excitement conditions, the emission is generated on the
laser output, which EMF strength is equal: E L (t) ¼ E 0L cos(2πν 0L t + φ 0L ).
3.4.2 Equations of Amplitude and Phase Balance for the RF
Part of OEO DM and OEO MZ
3.4.2.1 OEO MZ in the “First Harmonic” Mode
Determination of the generated radio frequency 2πf in the RF part of OEO MZ can
be explained from the equations of the amplitude and phase balance of the steadystate auto-modulated oscillations as:
K L f , U 0MZ , ν 0L
ð
Þ K FOS f
ð ÞK PD K EF f
ð ÞK EA f
ð Þ ¼ 1,
φ 1MZ f , U 0MZ , ν 0L
ð
Þþφ FOS f
ð Þ þ φ PD f
ð Þ þ φ EF f
ð Þ þ φ EA f
ð Þ ¼ À2πm
&
,
ð3:43Þ
where K 1MZ ( f ), K FOS ( f ), K PD , K EF ( f ), K EA ( f ) are the modules (AFC), relatively,
of the MZ modulator, the fiber optical system, the photodetector, the RF filter, the RF
amplifier; φ 1MZ ( f ), φ FOS ( f ), φ PD ( f ), φ EF ( f ), φ EA ( f ) are arguments (PFC), relatively, of the MZ modulator, the fiber optical system, the photodetector, the RF filter,
the RF amplifier; U 0MZ is DC bias voltage of MZ; ν 0L is the optical laser frequency,
m ¼ 1, 2, . . . .
If the self-excitation conditions are satisfied in the closed loop, the oscillation will
be generated on the OEO electrical output, which voltage (or current) is:
U e (t) ¼ U 0e cos(2πf 0e t + ϕ 0e ) where U 0e is the amplitude, f 0e is the average optical
generated frequency, ϕ 0e is the constant initial phase shift. In this case, we do not
take into consideration the amplitude and phase fluctuations m e and ψ me .
3.4.2.2 OEO DM in the “First Harmonic” Mode
The system of AFB equations for OEO DM in the “first harmonic” mode can be
written in the similar manner as for OEO MZ:
K L f , J 0 , ν 0L
ð
Þ K FOS f
ð ÞK PD K EF f
ð ÞK EA f
ð Þ ¼ 1,
φ L f , J 0 , ν 0L
ð
Þþφ FOS f
ð Þ þ φ PD f
ð Þ þ φ EF f
ð Þ þ φ EA f
ð Þ ¼ À2πm,
&
ð3:44Þ
where K L ( f, J 0 , ν 0L ), K FOS ( f ), K PD , K EF ( f ), K EA ( f ) are modules (AFC), relatively,
of the MZ modulator, the fiber optical system, the photodetector, the RF filter, the RF
amplifier; φ 1L ( f, J 0 , ν 0L ), φ FOS ( f ), φ PD ( f ), φ EF ( f ), φ EA ( f ) are arguments (PFC),
3.4 Equations of Amplitude and Phase Balance for the Laser and for OEO
115