versus the input voltage i ¼ α NA u, α NA, thr is the minimal slope of the current
nonlinear function, at which the excitation of OEO oscillations occurs.
The offset is defined as: θ ¼ 2π(T 2FOS À T 1FOS )( f EF À f 0 ). Here f EF is the natural
frequency of the RF filter, f 0 is the mean (or reference) frequency of OEO generation.
The settling time T sett of the oscillation amplitude and the frequency for OEO with
differential RF FODL is about: T sett > (4 – 10)(AT 1FOS + BT 2FOS ).
On the base of Eqs. (7.43) and (7.44), the analysis of the effect on the character of
transients for the laser optical frequency at its fast variations. As the result of this
investigation, the conclusion is made that fast modulations of QWLD optical
frequency lead to the modulation of the amplitude and the phase of RF oscillations.
At spasmodic variations of the QWLD optical frequency, the oscillations’ settling
time of OEO with differential combined RF FODL depends on the excitation
coefficients А and В of FOS1 and FOS2 light guides, on natural frequency of
OEO filter. At that, it is found out that the character of oscillations settling is similar
to the dynamics of oscillations settling at modulation of the natural frequency of the
RF filter.
The dynamics of transients in OEO with RF FODL has the interesting feature at
variation of the excitation coefficient A of the FOS1 light guide.
Figure 7.22a–c show the plots of the frequency f and the amplitude U settling of
the generation signal for the excitation coefficient A ¼ 0.4; 0.5; 0.6; 0.7; 0.8, at that,
В ¼ 1 À А for different values of the excitation reserve δ ¼ 0.5 (Fig. 7.22a, b),
δ ¼ 1.15 (Fig. 7.22c). As we see, dynamics of transient is complicate and manifold.
At the value of the excitation coefficients of the light-guiding channels А and
B ¼ 1 À A for A ¼ 0; 0.13; 0.23; 0.33, the process of oscillation formation has the
character of the interrupted generation. With the growth of the excitation coefficient
A of the first channel, the oscillation amplitude of the interrupted generation
increases and at A ¼ 0.43; 0.49 it has the stable character. At A ¼ 0.509; 0.529;
0.555, which corresponds to the minimum in AFC of combined RF FODL, the
oscillation character again becomes unstable. At further increase of A ¼ 0.595;
0.605, oscillations have the stable character, and the process from the interrupted
generation becomes the continuous wave and the amplitude after (4 – 5)
Á (T 2FOS + T 1FOS )/2 “comes out” to the steady-state level. Variations of excitation
coefficients А and В lead to change of the transient character, to variation of oscillation
settling time and to the oscillation disruption
From Fig. 7.22b, we see that at values of the excitation coefficient 0.2; 0.3, OEO
does not come out into the steady-state generation mode, which is explained by
nonfulfillment of the phase balance condition at these values.
The oscillation settling time T sett decreases with the growth of the excitation
reserve δ and may be T sett ¼ (4 – 15)(T 1FOS + T 2FOS )/2, where Т 1 , Т 2 are the delays
of the signal in FOS1 and FOS2, relatively.
The value of the modulation frequency Ω, at which the inertial properties are
strongly manifested in OEO with the combined RF FODL, which are comparable
with the inverse mean delay in FOS, i.e.: Ω > 1/[T 0FOS + (T 1FOS + T 2FOS )/2].
The main determining factors, which affect the process of oscillation formation,
are: (1) the value of excitation reserve δ ¼ S del ; (2) the ratio of delay time difference
414
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .
nonlinear function, at which the excitation of OEO oscillations occurs.
The offset is defined as: θ ¼ 2π(T 2FOS À T 1FOS )( f EF À f 0 ). Here f EF is the natural
frequency of the RF filter, f 0 is the mean (or reference) frequency of OEO generation.
The settling time T sett of the oscillation amplitude and the frequency for OEO with
differential RF FODL is about: T sett > (4 – 10)(AT 1FOS + BT 2FOS ).
On the base of Eqs. (7.43) and (7.44), the analysis of the effect on the character of
transients for the laser optical frequency at its fast variations. As the result of this
investigation, the conclusion is made that fast modulations of QWLD optical
frequency lead to the modulation of the amplitude and the phase of RF oscillations.
At spasmodic variations of the QWLD optical frequency, the oscillations’ settling
time of OEO with differential combined RF FODL depends on the excitation
coefficients А and В of FOS1 and FOS2 light guides, on natural frequency of
OEO filter. At that, it is found out that the character of oscillations settling is similar
to the dynamics of oscillations settling at modulation of the natural frequency of the
RF filter.
The dynamics of transients in OEO with RF FODL has the interesting feature at
variation of the excitation coefficient A of the FOS1 light guide.
Figure 7.22a–c show the plots of the frequency f and the amplitude U settling of
the generation signal for the excitation coefficient A ¼ 0.4; 0.5; 0.6; 0.7; 0.8, at that,
В ¼ 1 À А for different values of the excitation reserve δ ¼ 0.5 (Fig. 7.22a, b),
δ ¼ 1.15 (Fig. 7.22c). As we see, dynamics of transient is complicate and manifold.
At the value of the excitation coefficients of the light-guiding channels А and
B ¼ 1 À A for A ¼ 0; 0.13; 0.23; 0.33, the process of oscillation formation has the
character of the interrupted generation. With the growth of the excitation coefficient
A of the first channel, the oscillation amplitude of the interrupted generation
increases and at A ¼ 0.43; 0.49 it has the stable character. At A ¼ 0.509; 0.529;
0.555, which corresponds to the minimum in AFC of combined RF FODL, the
oscillation character again becomes unstable. At further increase of A ¼ 0.595;
0.605, oscillations have the stable character, and the process from the interrupted
generation becomes the continuous wave and the amplitude after (4 – 5)
Á (T 2FOS + T 1FOS )/2 “comes out” to the steady-state level. Variations of excitation
coefficients А and В lead to change of the transient character, to variation of oscillation
settling time and to the oscillation disruption
From Fig. 7.22b, we see that at values of the excitation coefficient 0.2; 0.3, OEO
does not come out into the steady-state generation mode, which is explained by
nonfulfillment of the phase balance condition at these values.
The oscillation settling time T sett decreases with the growth of the excitation
reserve δ and may be T sett ¼ (4 – 15)(T 1FOS + T 2FOS )/2, where Т 1 , Т 2 are the delays
of the signal in FOS1 and FOS2, relatively.
The value of the modulation frequency Ω, at which the inertial properties are
strongly manifested in OEO with the combined RF FODL, which are comparable
with the inverse mean delay in FOS, i.e.: Ω > 1/[T 0FOS + (T 1FOS + T 2FOS )/2].
The main determining factors, which affect the process of oscillation formation,
are: (1) the value of excitation reserve δ ¼ S del ; (2) the ratio of delay time difference
414
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .