An analysis of differential equation solutions shows that in OEO DM, the
necessary condition of the stable single-frequency mode of the microwave generation is more than the double excess of the Q-factor of the radio-frequency filter with
regard to the equivalent Q-factor of the optical filter in QWLD, which is determined
by the electron relaxation time constant in the laser active layer, by the coefficient of
the laser optical amplification and the pumping excess above the threshold value. As
a result of studying of OEO DM solutions, we fulfilled an analysis of the local
stability of the single-frequency oscillation mode on the base of the Rauth–Gurvitz
method assuming the quadratic nonlinearity of the watt–ampere laser static characteristic. We proved that to achieve the “soft” mode of oscillation setting in OEO DM
at the amplifier nonlinearity choice, we must take into account the multiplicative
(close to quadratic) nonlinearity in the laser.
We performed the computer analog modeling of differential equations of OEO
DM. We proved that at pumping switch-on, the transient of the exit to the singlefrequency steady-state generation in OEO DM is accompanied by ripples. At large
oscillation amplitude, the strong nonlinear distortions arise, which are caused by the
nonlinear dependence of emission intensity on the QWLD pumping current. The
level of nonlinear distortions depends on a choice of the bias DC current. The mode
of small amplitudes in OEO (less than 1%...10% of the maximal value) is provided at
the choice of the laser pumping DC current on the level from 1.5 to 5.0 relative
excesses above its threshold value of the laser pumping current. A choice of the
nonlinearity type of the RF amplifier, the natural frequency of the RF filter, the delay
value in FOS determines the character and duration of the transient in OEO DM. The
limit cycle in the phase space is stable and oscillation setting occurs in the soft mode
at the choice of the nonlinearity type, taking into account the laser multiplicative
nonlinearity.
The fluctuation differential equations obtained at the OEO analysis represent a
system of four differential equations for the strength square, the population, the
optical phase of QWLD emission, the electrical pumping current. At consideration
of the small-signal mode on the base of fluctuation DE solutions for OEO DM, we
obtain expressions for the amplitude, the generation frequency, PSD of amplitude
and phase fluctuations.
We formed the fluctuation differential equations of OEO DM with Langevinian
noise sources. The task of an analysis of fluctuation DE of OEO DM is to determine
the connection of the noise influence of QWLD spontaneous emission on the RF
phase noise of OEO. As the result of fluctuation DE solution in the small-signal
mode, we obtained the analytical expressions for laser amplitude and phase noises,
which are caused by the laser spontaneous emission. It stated that the one from
important features of OEO DM is its high quality of oscillations (or the high SNR).
This OEO DM is concerned to the microwave oscillation sources with the extra-low
phase noise level (on the level À110 to À140 dB/Hz at frequency offset of 1–10 kHz
from the nominal generation frequency of 10 GHz). We determine the main mechanisms of such a low phase noise in OEO DM.
The mechanism of natural QWLD noise suppression, which is caused by the
spontaneous emission, is the base mechanism of decrease of the amplitude and phase
5.6 Conclusions
281
necessary condition of the stable single-frequency mode of the microwave generation is more than the double excess of the Q-factor of the radio-frequency filter with
regard to the equivalent Q-factor of the optical filter in QWLD, which is determined
by the electron relaxation time constant in the laser active layer, by the coefficient of
the laser optical amplification and the pumping excess above the threshold value. As
a result of studying of OEO DM solutions, we fulfilled an analysis of the local
stability of the single-frequency oscillation mode on the base of the Rauth–Gurvitz
method assuming the quadratic nonlinearity of the watt–ampere laser static characteristic. We proved that to achieve the “soft” mode of oscillation setting in OEO DM
at the amplifier nonlinearity choice, we must take into account the multiplicative
(close to quadratic) nonlinearity in the laser.
We performed the computer analog modeling of differential equations of OEO
DM. We proved that at pumping switch-on, the transient of the exit to the singlefrequency steady-state generation in OEO DM is accompanied by ripples. At large
oscillation amplitude, the strong nonlinear distortions arise, which are caused by the
nonlinear dependence of emission intensity on the QWLD pumping current. The
level of nonlinear distortions depends on a choice of the bias DC current. The mode
of small amplitudes in OEO (less than 1%...10% of the maximal value) is provided at
the choice of the laser pumping DC current on the level from 1.5 to 5.0 relative
excesses above its threshold value of the laser pumping current. A choice of the
nonlinearity type of the RF amplifier, the natural frequency of the RF filter, the delay
value in FOS determines the character and duration of the transient in OEO DM. The
limit cycle in the phase space is stable and oscillation setting occurs in the soft mode
at the choice of the nonlinearity type, taking into account the laser multiplicative
nonlinearity.
The fluctuation differential equations obtained at the OEO analysis represent a
system of four differential equations for the strength square, the population, the
optical phase of QWLD emission, the electrical pumping current. At consideration
of the small-signal mode on the base of fluctuation DE solutions for OEO DM, we
obtain expressions for the amplitude, the generation frequency, PSD of amplitude
and phase fluctuations.
We formed the fluctuation differential equations of OEO DM with Langevinian
noise sources. The task of an analysis of fluctuation DE of OEO DM is to determine
the connection of the noise influence of QWLD spontaneous emission on the RF
phase noise of OEO. As the result of fluctuation DE solution in the small-signal
mode, we obtained the analytical expressions for laser amplitude and phase noises,
which are caused by the laser spontaneous emission. It stated that the one from
important features of OEO DM is its high quality of oscillations (or the high SNR).
This OEO DM is concerned to the microwave oscillation sources with the extra-low
phase noise level (on the level À110 to À140 dB/Hz at frequency offset of 1–10 kHz
from the nominal generation frequency of 10 GHz). We determine the main mechanisms of such a low phase noise in OEO DM.
The mechanism of natural QWLD noise suppression, which is caused by the
spontaneous emission, is the base mechanism of decrease of the amplitude and phase
5.6 Conclusions
281