MZ. As the result, we obtain the relatively simple formula (Eq. 5.94) for R MZ (u, t,
t + τ), which reflects the sense of statistical processes in OEO MZ and explains the
process of laser phase noise transformation into the phase RF noise of OEO. The
autocorrelation function R MZ (u, t, t + τ) is determined by three components: the DC
component, which passes to the PD area after passage of MZ and the optical fiber
R MZ0 , and also by AC components R MZ1 and R MZ2 , the values of which depend on
φ 0MZ or the DC bias voltage on MZ.
Now we proceed to further examination of processes of statistical impact in
OEO MZ.
5.5.8 The Convolution Operation of Strength Squares
of the Laser Field and the Radio-Frequency Oscillation
in OEO MZ
The convolution operation of two oscillation spectra, which are formed by the laser
optical emission, takes the special place in OEO MZ correlator (Figs. 5.10 and 5.11)
of random quantities. Let the electric field of the optical carrier, which passes to the
MZ optical input, be expressed as E L (t) ¼ E 0L cos [2πν 0L t + φ 0L + φ Lm (t)] .
At the open switch Sw (Figs. 5.10 and 5.11), the voltage from the external
oscillator (the generator is not shown in Figs. 5.10 and 5.11), which passes to
the
MZ
electrical
input,
can
be
described
as:
u g (t) ¼ [U 10 + m em (t)] cos [2πf 0 t + ϕ 0e + φ em (t)] .
Then, the electrical current oscillation in the PD load represents the product of
ACF of the laser oscillation passed through the MZ modulator and ACF of u g (t)
oscillations affected on the MZ electrical input: R PD (t, t À τ) ¼ R L (τ) Á R RFL (τ).
–10
–15
1
2
3
–20
–25
–30
–10
–35
Spectral densities S , dB
offset optical frequency 2π (V–V 0 )'T M , rad.
–5
5
10
Fig. 5.16 Plots of the laser
emission spectral densities
before (plot 1) and after
(plot 2 ) the passage of the
MZ modulator. Spectral
densities are shown in the
“quadrature” (“π/2”) mode
(plot 2). Spectral densities
are shown in the quadrature
(cos) and the non-quadrature
(“π”) modes (plot 3). The
plot of the laser spectral
density (plot 1) at the input
of MZ has the form of the
Lorentz function
5.5 Correlator’s Mathematical Model in OEO MZ
271
t + τ), which reflects the sense of statistical processes in OEO MZ and explains the
process of laser phase noise transformation into the phase RF noise of OEO. The
autocorrelation function R MZ (u, t, t + τ) is determined by three components: the DC
component, which passes to the PD area after passage of MZ and the optical fiber
R MZ0 , and also by AC components R MZ1 and R MZ2 , the values of which depend on
φ 0MZ or the DC bias voltage on MZ.
Now we proceed to further examination of processes of statistical impact in
OEO MZ.
5.5.8 The Convolution Operation of Strength Squares
of the Laser Field and the Radio-Frequency Oscillation
in OEO MZ
The convolution operation of two oscillation spectra, which are formed by the laser
optical emission, takes the special place in OEO MZ correlator (Figs. 5.10 and 5.11)
of random quantities. Let the electric field of the optical carrier, which passes to the
MZ optical input, be expressed as E L (t) ¼ E 0L cos [2πν 0L t + φ 0L + φ Lm (t)] .
At the open switch Sw (Figs. 5.10 and 5.11), the voltage from the external
oscillator (the generator is not shown in Figs. 5.10 and 5.11), which passes to
the
MZ
electrical
input,
can
be
described
as:
u g (t) ¼ [U 10 + m em (t)] cos [2πf 0 t + ϕ 0e + φ em (t)] .
Then, the electrical current oscillation in the PD load represents the product of
ACF of the laser oscillation passed through the MZ modulator and ACF of u g (t)
oscillations affected on the MZ electrical input: R PD (t, t À τ) ¼ R L (τ) Á R RFL (τ).
–10
–15
1
2
3
–20
–25
–30
–10
–35
Spectral densities S , dB
offset optical frequency 2π (V–V 0 )'T M , rad.
–5
5
10
Fig. 5.16 Plots of the laser
emission spectral densities
before (plot 1) and after
(plot 2 ) the passage of the
MZ modulator. Spectral
densities are shown in the
“quadrature” (“π/2”) mode
(plot 2). Spectral densities
are shown in the quadrature
(cos) and the non-quadrature
(“π”) modes (plot 3). The
plot of the laser spectral
density (plot 1) at the input
of MZ has the form of the
Lorentz function
5.5 Correlator’s Mathematical Model in OEO MZ
271