this part of T FODL % T FOS ; T FOS —time delay in optical fiber; φ k ¼ arctan[2π( f À f eF )
T eF ] is PFC of the narrowband RF filter with the natural resonance frequency
ω F ¼ 2πf 0F and the time constant T F ¼ T eF ¼ T EF ; φ e (ω) is the phase incursion in
the wideband electronic nonlinear amplifier, m ¼ 1, 2, . . . .
In the circuit of Fig. 2.2, a laser, on the one hand, performs the energy pumping of
the RF oscillator, and on the other hand, is the main element of OEO with RF FODL.
2.1.6 MZ Modulator in OEO Structure
Laser optical emission (on the carrying optical frequency) passes to the input of the
MZ modulator, in which the emission is modulated by the electric signal u ¼ u g (t) at
microwave frequency. Then, the optical emission passes to the light-sensitive area of
the photodetector (the optical input of PD) through the optical modulator. RF
oscillations (subcarrier) obtained on low-frequency PD load pass to the transistor
nonlinear amplifier and to the frequency-selective RF filter and are directed to the
microwave control input of the MZ modulator within this loop system through the
directional coupler (C).
If OEO excitation conditions are satisfied for the “electronic” part of OEO (where
exactly u ¼ u g (t)), then RF microwave oscillations of the electric voltage u ¼ u g (t)
arise, which are self-modulating for optical emission. The instantaneous value of this
voltage can be written as
u g t
ð Þ ¼ U 0 cos 2πf 0 t þ ϕ 0e
ð
Þ ,
ð2:3Þ
where U 0 ¼ U 0M ¼ U 0F is the oscillation amplitude of the controlling (modulating)
microwave voltage at the input of the MZ modulator or at the output of the RF filter,
f 0 is the microwave frequency of generated steady-state oscillations, ϕ 0e is an initial
phase of the u g (t) voltage (the constant phase shift). When using of QWLD, which is
controlled by the microwave component of the bias current, the direct amplitude
modulation occurs and, as a consequence, the laser intensity modulation.
Let us consider now peculiarities of microwave generation in OEO at formation
of modulated laser emission with a small modulation index for the case when the
laser emission spectrum width Δν L is much less than a RF subcarrier frequency f 0 :
Δν L ( f. The spectrum of modulated optical emission represents the definite
equidistant set of components, which is apart one from another by the subcarrier
frequency (modulation frequency) of f 0 . We are limited by consideration of the
“mode with two sidebands”, i.e., only three optical spectral components, which
optical frequencies are, relatively, ν 1 ¼ ν 1 À f 0 , ν 2 ¼ ν 0 , ν 3 ¼ ν 3 À f 0 . Two of
these optical frequencies ν 1 and ν 2 are spaced from the central optical laser frequency
ν 0 by the subcarrier frequency f 0 .
In the further discussion, we examine OEO with the modulated light source, in
which the optical phase MZ modulator plays a role of the OEO modulator (or the
intensity modulator, as it is often called).
2.1 Operation Principle and Functional Diagram of OEO with RF FODL
25
T eF ] is PFC of the narrowband RF filter with the natural resonance frequency
ω F ¼ 2πf 0F and the time constant T F ¼ T eF ¼ T EF ; φ e (ω) is the phase incursion in
the wideband electronic nonlinear amplifier, m ¼ 1, 2, . . . .
In the circuit of Fig. 2.2, a laser, on the one hand, performs the energy pumping of
the RF oscillator, and on the other hand, is the main element of OEO with RF FODL.
2.1.6 MZ Modulator in OEO Structure
Laser optical emission (on the carrying optical frequency) passes to the input of the
MZ modulator, in which the emission is modulated by the electric signal u ¼ u g (t) at
microwave frequency. Then, the optical emission passes to the light-sensitive area of
the photodetector (the optical input of PD) through the optical modulator. RF
oscillations (subcarrier) obtained on low-frequency PD load pass to the transistor
nonlinear amplifier and to the frequency-selective RF filter and are directed to the
microwave control input of the MZ modulator within this loop system through the
directional coupler (C).
If OEO excitation conditions are satisfied for the “electronic” part of OEO (where
exactly u ¼ u g (t)), then RF microwave oscillations of the electric voltage u ¼ u g (t)
arise, which are self-modulating for optical emission. The instantaneous value of this
voltage can be written as
u g t
ð Þ ¼ U 0 cos 2πf 0 t þ ϕ 0e
ð
Þ ,
ð2:3Þ
where U 0 ¼ U 0M ¼ U 0F is the oscillation amplitude of the controlling (modulating)
microwave voltage at the input of the MZ modulator or at the output of the RF filter,
f 0 is the microwave frequency of generated steady-state oscillations, ϕ 0e is an initial
phase of the u g (t) voltage (the constant phase shift). When using of QWLD, which is
controlled by the microwave component of the bias current, the direct amplitude
modulation occurs and, as a consequence, the laser intensity modulation.
Let us consider now peculiarities of microwave generation in OEO at formation
of modulated laser emission with a small modulation index for the case when the
laser emission spectrum width Δν L is much less than a RF subcarrier frequency f 0 :
Δν L ( f. The spectrum of modulated optical emission represents the definite
equidistant set of components, which is apart one from another by the subcarrier
frequency (modulation frequency) of f 0 . We are limited by consideration of the
“mode with two sidebands”, i.e., only three optical spectral components, which
optical frequencies are, relatively, ν 1 ¼ ν 1 À f 0 , ν 2 ¼ ν 0 , ν 3 ¼ ν 3 À f 0 . Two of
these optical frequencies ν 1 and ν 2 are spaced from the central optical laser frequency
ν 0 by the subcarrier frequency f 0 .
In the further discussion, we examine OEO with the modulated light source, in
which the optical phase MZ modulator plays a role of the OEO modulator (or the
intensity modulator, as it is often called).
2.1 Operation Principle and Functional Diagram of OEO with RF FODL
25