5.6 Conclusions
In this chapter, the analysis of OEO oscillating system is performed as the two
oscillation sources with different frequencies—optical and radio. At that, OEO is
enclosed by the positive feedback loop from the optical output to the electrical input.
The positive selective feedback is provided by means of the photodiode, the radiofrequency filter, and the nonlinear RF amplifier. On the other hand, we can consider
that the radio front-end is enclosed by the optoelectronic feedback including the
laser, the optical fiber, and the photodetector.
The mathematical analysis of OEO is performed at laser (QWLD) representation
by the differential semiclassical equations for the electromagnetic field strength (the
optical emission) and kinetic equations for the emission intensity, the inversed
population and the electrical pumping current. The positive feedback is included
into the system of differential equations taking into consideration: the delay in the
optical fiber, the photodetection of the optical emission, the extraction (selection) in
radio frequency, the nonlinear amplification in the amplifier. The new results are that
on the base of the laser differential equations, which are described by the Lotka–
Volterra differential equations for the optical field intensity, the inversed population
and the optical phase, we obtain the differential equations of OEO DM without and
with fluctuations taking into account the positive selective feedback with the
retarded argument.
We compose and discuss the analog models of OEO DM and OEO MZ without
and with account of noises. The main principal difference of the OEO MZ analog
model with regard to the OEO DM analog model is the potential possibility in OEO
MZ to use the extra-low-noise QWLDs. This follows from the fact that in the laser
model for OEO MZ, the carrier noise suppression can be arranged directly in the
internal closed loop of the optical feedback or in the optical resonator. For this, we
must not only decrease the value of noise sources, but to apply the high-Q optical
resonator. The growth of the resonator Q-factor will significantly decrease the laser
modulation bandwidth in radio frequency. The excessive increase of the optical
resonator Q-factor leads in OEO DM to reduction of the oscillation amplitude. The
external modulation is used in OEO MZ. The modulation index of the optical
emission does not depend on the growth of the optical resonator Q-factor. The
increase of this Q-factor will lead to the improvement of oscillation spectrum purity
or to the decrease of the laser phase noise. Another principal feature, which follows
from an analysis of the presented analog model of OEO MZ, is the fact that
suppression of the carrier fluctuations can be provided in the feedback loop in
population. The increase of the time constant or the carrier lifetime on the upper
operation level T 1 also leads to significant decrease of the laser phase noise. In OEO
MZ, it becomes possible to use the high-coherent fiber lasers with the large carrier
lifetime of T 1 ¼ 1 – 100 μs. As we mentioned earlier, the modern compact ОЕО
MZs use the semiconductor QWLDs with the spectral line width from 1 kHz to
10 NHz. The compact commercial samples of semiconductor lasers appear with the
spectral line width 10–500 Hz.
280
5 Optoelectronic oscillator (OEO) Differential Equations as the Laser System with. . .
In this chapter, the analysis of OEO oscillating system is performed as the two
oscillation sources with different frequencies—optical and radio. At that, OEO is
enclosed by the positive feedback loop from the optical output to the electrical input.
The positive selective feedback is provided by means of the photodiode, the radiofrequency filter, and the nonlinear RF amplifier. On the other hand, we can consider
that the radio front-end is enclosed by the optoelectronic feedback including the
laser, the optical fiber, and the photodetector.
The mathematical analysis of OEO is performed at laser (QWLD) representation
by the differential semiclassical equations for the electromagnetic field strength (the
optical emission) and kinetic equations for the emission intensity, the inversed
population and the electrical pumping current. The positive feedback is included
into the system of differential equations taking into consideration: the delay in the
optical fiber, the photodetection of the optical emission, the extraction (selection) in
radio frequency, the nonlinear amplification in the amplifier. The new results are that
on the base of the laser differential equations, which are described by the Lotka–
Volterra differential equations for the optical field intensity, the inversed population
and the optical phase, we obtain the differential equations of OEO DM without and
with fluctuations taking into account the positive selective feedback with the
retarded argument.
We compose and discuss the analog models of OEO DM and OEO MZ without
and with account of noises. The main principal difference of the OEO MZ analog
model with regard to the OEO DM analog model is the potential possibility in OEO
MZ to use the extra-low-noise QWLDs. This follows from the fact that in the laser
model for OEO MZ, the carrier noise suppression can be arranged directly in the
internal closed loop of the optical feedback or in the optical resonator. For this, we
must not only decrease the value of noise sources, but to apply the high-Q optical
resonator. The growth of the resonator Q-factor will significantly decrease the laser
modulation bandwidth in radio frequency. The excessive increase of the optical
resonator Q-factor leads in OEO DM to reduction of the oscillation amplitude. The
external modulation is used in OEO MZ. The modulation index of the optical
emission does not depend on the growth of the optical resonator Q-factor. The
increase of this Q-factor will lead to the improvement of oscillation spectrum purity
or to the decrease of the laser phase noise. Another principal feature, which follows
from an analysis of the presented analog model of OEO MZ, is the fact that
suppression of the carrier fluctuations can be provided in the feedback loop in
population. The increase of the time constant or the carrier lifetime on the upper
operation level T 1 also leads to significant decrease of the laser phase noise. In OEO
MZ, it becomes possible to use the high-coherent fiber lasers with the large carrier
lifetime of T 1 ¼ 1 – 100 μs. As we mentioned earlier, the modern compact ОЕО
MZs use the semiconductor QWLDs with the spectral line width from 1 kHz to
10 NHz. The compact commercial samples of semiconductor lasers appear with the
spectral line width 10–500 Hz.
280
5 Optoelectronic oscillator (OEO) Differential Equations as the Laser System with. . .