noise in OEO DM, owing to the positive selective (in radio frequency) feedback,
which is formed by the fiber-optical system, the photodetector, the RF filter, and the
amplifier. From obtained analytic expression, it follows that the decrease by the
order and more of the amplitude noise of OEO DM follows at growth of the ratio of
the feedback loop gain to the QWLD gain, which is determined as the ratio of the
carriers’ lifetime to the photon lifetime in the resonator. Owing to introduction of the
positive feedback loop, the amplitude noise caused by QWLS spontaneous emission
is reduced by the order or more. Another three important mechanisms of phase noise
reduction of OEO DM are concerned, at first, to the coherent photo-self-heterodyning of two equal-in-amplitude but different in frequency optical components. In
other words, in OEO DM, which operates in the mode of two optical oscillations, the
statistical subtraction occurs of these two high-correlated optical components, each
of which is modulated by the laser “phase” noise. Secondly, the phase noise
suppression on OEO DM occurs owing to the mechanism of the optical delay in
the optical fiber with the oscillation delay by 1–50 μs. Thirdly, the decrease of the
phase noise in OEO DM is provided by a choice of the low-noise laser with small
level of spontaneous emission and with small spectral line width of the optical
generation of 1 MHz. Application of filtering of the laser DC pumping current and
the temperature stabilization of the laser active layer are the other mechanisms of
phase noise reduction in OEO DM.
As the result of OEO DM analysis, we can conclude that owing to the construction simplicity of QWLD, such OEOs in microwave and mm-wave ranges are
forward-looking oscillators. The main restriction of the OEO DM phase noise
improvement, i.e., QWLD DM, is the contradiction: to reduce the OEO phase
noise we must achieve the phase noise of the laser, which can be done by the
increase of the Q-factor of the oscillating optical system of the laser, the utilization
of lasers with specific narrowband resonators. But, on the other hand, at growth of
the equivalent time constant of the optical resonator, the laser modulation bandwidth
decreases at modulation by microwave oscillations, the laser modulation coefficient
decreases and, hence, the oscillation amplitude of OEO DM decreases. A choice of
the spectral line width of the laser optical emission of 1–10 MHz (at pumping excess
above the threshold value by 5–9 times) is optimal from the point of view of
reduction of the ratio of the phase noise and the microwave OEO oscillation
amplitude at the generation frequency of 10 GHz and at the laser optical frequency
about 129 THz. This contradiction can be resolved at separation (complication the
functional diagram) of the modulating emission source (the laser diode) into two
devices—the separate laser, the high-coherent with the bandwidth of 0.01–1 MHz of
the laser optical emission, and the electro-optical modulator itself (for instance, the
Mach–Zehnder modulator). The next Chap. 6 is devoted to investigation of OEO
MZ of such a type.
Representation of OEO MZ as the correlator of the random quantities and
examination of the structure in different operation modes (quadrature and
non-quadrature) gives a possibility to simplify the mathematical notation of the
autocorrelation function R MZ (u, t, t + τ) in the opened feedback loop in OEO
MZ. As the result, we obtain relatively simple formula (Eq. 5.94) for R MZ (u, t,
282
5 Optoelectronic oscillator (OEO) Differential Equations as the Laser System with. . .
which is formed by the fiber-optical system, the photodetector, the RF filter, and the
amplifier. From obtained analytic expression, it follows that the decrease by the
order and more of the amplitude noise of OEO DM follows at growth of the ratio of
the feedback loop gain to the QWLD gain, which is determined as the ratio of the
carriers’ lifetime to the photon lifetime in the resonator. Owing to introduction of the
positive feedback loop, the amplitude noise caused by QWLS spontaneous emission
is reduced by the order or more. Another three important mechanisms of phase noise
reduction of OEO DM are concerned, at first, to the coherent photo-self-heterodyning of two equal-in-amplitude but different in frequency optical components. In
other words, in OEO DM, which operates in the mode of two optical oscillations, the
statistical subtraction occurs of these two high-correlated optical components, each
of which is modulated by the laser “phase” noise. Secondly, the phase noise
suppression on OEO DM occurs owing to the mechanism of the optical delay in
the optical fiber with the oscillation delay by 1–50 μs. Thirdly, the decrease of the
phase noise in OEO DM is provided by a choice of the low-noise laser with small
level of spontaneous emission and with small spectral line width of the optical
generation of 1 MHz. Application of filtering of the laser DC pumping current and
the temperature stabilization of the laser active layer are the other mechanisms of
phase noise reduction in OEO DM.
As the result of OEO DM analysis, we can conclude that owing to the construction simplicity of QWLD, such OEOs in microwave and mm-wave ranges are
forward-looking oscillators. The main restriction of the OEO DM phase noise
improvement, i.e., QWLD DM, is the contradiction: to reduce the OEO phase
noise we must achieve the phase noise of the laser, which can be done by the
increase of the Q-factor of the oscillating optical system of the laser, the utilization
of lasers with specific narrowband resonators. But, on the other hand, at growth of
the equivalent time constant of the optical resonator, the laser modulation bandwidth
decreases at modulation by microwave oscillations, the laser modulation coefficient
decreases and, hence, the oscillation amplitude of OEO DM decreases. A choice of
the spectral line width of the laser optical emission of 1–10 MHz (at pumping excess
above the threshold value by 5–9 times) is optimal from the point of view of
reduction of the ratio of the phase noise and the microwave OEO oscillation
amplitude at the generation frequency of 10 GHz and at the laser optical frequency
about 129 THz. This contradiction can be resolved at separation (complication the
functional diagram) of the modulating emission source (the laser diode) into two
devices—the separate laser, the high-coherent with the bandwidth of 0.01–1 MHz of
the laser optical emission, and the electro-optical modulator itself (for instance, the
Mach–Zehnder modulator). The next Chap. 6 is devoted to investigation of OEO
MZ of such a type.
Representation of OEO MZ as the correlator of the random quantities and
examination of the structure in different operation modes (quadrature and
non-quadrature) gives a possibility to simplify the mathematical notation of the
autocorrelation function R MZ (u, t, t + τ) in the opened feedback loop in OEO
MZ. As the result, we obtain relatively simple formula (Eq. 5.94) for R MZ (u, t,
282
5 Optoelectronic oscillator (OEO) Differential Equations as the Laser System with. . .