OEO oscillations in the rigid more without the external oscillator, as a rule, is
impossible. Oscillating OEO systems returns to the quiescent state.
The transient processes of oscillation setting in ОEO DM without and with the
retard in the positive feedback loop are depicted in Fig. 5.1. As the result of computer
modeling, it is proved that the transient of the exit to the OEO generation mode is
accompanies by ripples. At large oscillation amplitude, the strong nonlinear distortions occur, which are caused by the multiplicative nonlinearity of the laser
described in Chap. 3. The level of nonlinear distortions depends upon a choice of
the DC pumping current.
The mode of small amplitude of OEO oscillations (less than 1–10% of the
maximal possible values) is performed at a choice DC bias current of small
(on the level from 1.5 to 5.0) relative exceeding of the threshold pumping current
of the laser. A choice of the nonlinearity type of the RF amplifier, the natural
frequency of the RF filter, the delay value in RF FODL determine the character,
and the transient duration of OEO oscillations. The limit cycle setting occurs in the
soft mode, at a choice of the amplifier nonlinearity type taking into consideration the
laser multiplicative nonlinearity.
Figure 5.5 show the modeling of differential equations of QWLD with the
positive selective feedback. The transient processes of OEO oscillation setting
without (a–c) and with the delay (d–f) in the positive feedback loop.
Plots in Fig. 5.5 show that at delay existence, after the strength and population
setting, the oscillating process of the AC laser pumping current occurs with the time
delay equaled to the delay in optical fiber. After that, the pumping oscillations, which
increasing in the amplitude, modulate the laser population and strength.
We would like to make some conclusions that the ОEO analysis is performed at
representation of laser differential equations by semiclassical equations for the
emission field strength and for the inversed population and the electrical pumping
current. The positive feedback is included in the DE system with account of optical
emission photodetection, of selectivity in radio frequency and the nonlinear amplification on the nonlinear amplifier. The new fact is that laser differential equations
(which are adopted to call in mathematic as the Lotka–Volterra equation) for the
strength (or for the intensity) of the optical field, the inversed population and the
optical phase with the positive selective feedback with the retarded argument are
finally reduced to the van-der-Pol differential equation for the electric pumping
current at definite restrictions and conditions described earlier.
The analysis of solutions of the second-order differential equations shows that in
such a system of OEO DM, the single-frequency and the double-frequency modes
are possible in the radio frequency. The necessary condition of the stable singlefrequency generation mode (in radio frequency) is more than the double excess of
the RF circuit Q-factor of the laser relaxation oscillations, which is defined by the
time constant of the electron relaxation in the laser active layer, by the laser optical
amplification coefficient, and by the pumping excess over the threshold level. At
that, for the single-frequency generation mode (in the radio frequency), the transmission is possible in the optical channel from the laser to the PD of two optical
frequencies: one of the frequencies is the central optical frequency of the laser, while
5.3 Dynamics of Transients in ОЕО DM and the Oscillation Amplitude
231
impossible. Oscillating OEO systems returns to the quiescent state.
The transient processes of oscillation setting in ОEO DM without and with the
retard in the positive feedback loop are depicted in Fig. 5.1. As the result of computer
modeling, it is proved that the transient of the exit to the OEO generation mode is
accompanies by ripples. At large oscillation amplitude, the strong nonlinear distortions occur, which are caused by the multiplicative nonlinearity of the laser
described in Chap. 3. The level of nonlinear distortions depends upon a choice of
the DC pumping current.
The mode of small amplitude of OEO oscillations (less than 1–10% of the
maximal possible values) is performed at a choice DC bias current of small
(on the level from 1.5 to 5.0) relative exceeding of the threshold pumping current
of the laser. A choice of the nonlinearity type of the RF amplifier, the natural
frequency of the RF filter, the delay value in RF FODL determine the character,
and the transient duration of OEO oscillations. The limit cycle setting occurs in the
soft mode, at a choice of the amplifier nonlinearity type taking into consideration the
laser multiplicative nonlinearity.
Figure 5.5 show the modeling of differential equations of QWLD with the
positive selective feedback. The transient processes of OEO oscillation setting
without (a–c) and with the delay (d–f) in the positive feedback loop.
Plots in Fig. 5.5 show that at delay existence, after the strength and population
setting, the oscillating process of the AC laser pumping current occurs with the time
delay equaled to the delay in optical fiber. After that, the pumping oscillations, which
increasing in the amplitude, modulate the laser population and strength.
We would like to make some conclusions that the ОEO analysis is performed at
representation of laser differential equations by semiclassical equations for the
emission field strength and for the inversed population and the electrical pumping
current. The positive feedback is included in the DE system with account of optical
emission photodetection, of selectivity in radio frequency and the nonlinear amplification on the nonlinear amplifier. The new fact is that laser differential equations
(which are adopted to call in mathematic as the Lotka–Volterra equation) for the
strength (or for the intensity) of the optical field, the inversed population and the
optical phase with the positive selective feedback with the retarded argument are
finally reduced to the van-der-Pol differential equation for the electric pumping
current at definite restrictions and conditions described earlier.
The analysis of solutions of the second-order differential equations shows that in
such a system of OEO DM, the single-frequency and the double-frequency modes
are possible in the radio frequency. The necessary condition of the stable singlefrequency generation mode (in radio frequency) is more than the double excess of
the RF circuit Q-factor of the laser relaxation oscillations, which is defined by the
time constant of the electron relaxation in the laser active layer, by the laser optical
amplification coefficient, and by the pumping excess over the threshold level. At
that, for the single-frequency generation mode (in the radio frequency), the transmission is possible in the optical channel from the laser to the PD of two optical
frequencies: one of the frequencies is the central optical frequency of the laser, while
5.3 Dynamics of Transients in ОЕО DM and the Oscillation Amplitude
231