These features are determinative at account of OEO phase noises in the circuits
with direct QWLD amplitude modulation and external modulation with the help of
the MZ modulator.
We can conclude that in optical range, the laser phase noise, because of mentioned reasons, cannot be cancelled, as it was made in all previous OEO publications
of other authors [3–9] at the general phase noise analysis of RF oscillations.
Let us consider the OEO structure (Fig. 2.2) in detail.
2.1.5 A Laser in OEO Structure
The laser or QWLD in the OEO structure (Fig. 2.2) is formed by the optical
amplifier, the narrowband optical filter, closed into a loop. The optical generating
frequency ν in the laser (or QWLD) is determined (of course, under fulfillment of
excitation conditions) by so-called equations of the amplitude (power) balance and
the phase balance of steady-state optical oscillations. The phase balance equation has
a form:
φ optY ν
ð Þ þ φ optF ν, e Y1
ð
Þþφ optZ ν
ð Þ ¼ À2πn,
ð2:1Þ
where φ optY (ν) is the phase-frequency characteristics (PFC) of the nonlinear optical
amplifier, φ optF (ν, e Y1 ) ¼ φ OF is PFC of the narrowband optical filter with the natural
frequency ν 0L ¼ ν OF with the time constant T OF ¼ T optF ; φ optZ (ν) is the phase
incursion in the remaining parts of the laser equivalent circuit (besides OF and
NA); e Y1 is the DC control voltage, which is applied to OF to change its natural
optical frequency, n ¼ 1, 2, . . . . The sign minus in the right side of Eq. (2.1) shows
that the total PFC is the negative quantity.
On the other hand, OEO with the external MZ modulator (Fig. 2.2) represents the
RF oscillator, which is formed by a laser and the electro-optical MZ modulator, the
fiber-optical light guider, the photodetector, the nonlinear amplifier, the narrowband
RF filter closed into a loop. The generating radio frequency ω in the RF part of OEO
is determined by fulfillment of excitation conditions and the phase balance equation
of steady-state self-modulated
1 oscillations:
φ FODL ω
ð Þ þ φ k ω
ð Þ þ φ e ω
ð Þ ¼ À2πm,
ð2:2Þ
where φ FODL is PFC of the remaining part of RF FODL containing the MZ
modulator, RF FODL and the photodetector, with total group optical time delay in
1 Do not confuse yourself: speaking about self-modulation (or auto-modulation), we mean here not
the spurious self-modulation of traditional oscillator, caused by wrong choice of inertial auto-bias
circuit. We mean here the useful self-modulation of the optical oscillation by the RF output
microwave oscillation of OEO, which is principal useful process for OEO.
24
2 Nanostructural Optoelectronic Oscillators with the Fiber-Optical Delay Line
with direct QWLD amplitude modulation and external modulation with the help of
the MZ modulator.
We can conclude that in optical range, the laser phase noise, because of mentioned reasons, cannot be cancelled, as it was made in all previous OEO publications
of other authors [3–9] at the general phase noise analysis of RF oscillations.
Let us consider the OEO structure (Fig. 2.2) in detail.
2.1.5 A Laser in OEO Structure
The laser or QWLD in the OEO structure (Fig. 2.2) is formed by the optical
amplifier, the narrowband optical filter, closed into a loop. The optical generating
frequency ν in the laser (or QWLD) is determined (of course, under fulfillment of
excitation conditions) by so-called equations of the amplitude (power) balance and
the phase balance of steady-state optical oscillations. The phase balance equation has
a form:
φ optY ν
ð Þ þ φ optF ν, e Y1
ð
Þþφ optZ ν
ð Þ ¼ À2πn,
ð2:1Þ
where φ optY (ν) is the phase-frequency characteristics (PFC) of the nonlinear optical
amplifier, φ optF (ν, e Y1 ) ¼ φ OF is PFC of the narrowband optical filter with the natural
frequency ν 0L ¼ ν OF with the time constant T OF ¼ T optF ; φ optZ (ν) is the phase
incursion in the remaining parts of the laser equivalent circuit (besides OF and
NA); e Y1 is the DC control voltage, which is applied to OF to change its natural
optical frequency, n ¼ 1, 2, . . . . The sign minus in the right side of Eq. (2.1) shows
that the total PFC is the negative quantity.
On the other hand, OEO with the external MZ modulator (Fig. 2.2) represents the
RF oscillator, which is formed by a laser and the electro-optical MZ modulator, the
fiber-optical light guider, the photodetector, the nonlinear amplifier, the narrowband
RF filter closed into a loop. The generating radio frequency ω in the RF part of OEO
is determined by fulfillment of excitation conditions and the phase balance equation
of steady-state self-modulated
1 oscillations:
φ FODL ω
ð Þ þ φ k ω
ð Þ þ φ e ω
ð Þ ¼ À2πm,
ð2:2Þ
where φ FODL is PFC of the remaining part of RF FODL containing the MZ
modulator, RF FODL and the photodetector, with total group optical time delay in
1 Do not confuse yourself: speaking about self-modulation (or auto-modulation), we mean here not
the spurious self-modulation of traditional oscillator, caused by wrong choice of inertial auto-bias
circuit. We mean here the useful self-modulation of the optical oscillation by the RF output
microwave oscillation of OEO, which is principal useful process for OEO.
24
2 Nanostructural Optoelectronic Oscillators with the Fiber-Optical Delay Line