μ PN‐AN ¼ 2 Δψ L
ð
Þ
2 sin 2πν 0 T 1M À T 2M
ð
Þþπ U 0MZ =U π0MZ
ð
Þ
½
Á U 10MZ cos 2π f 0 t
ð
Þ,
ð6:19Þ
Thus, as the result of heterodyning, the spectrum of fluctuations of the PD output
current is obtained by the “transfer” of the optical noise spectrum from the laser
(or QWLD) generation frequency ν 0 to the OEO radio-frequency generation f 0 . To
Eqs. (6.18) and (6.19), we must add the noise current in the photodetector load,
which obtained from the detected noise of the DC of the laser emission.
6.4.5 Power Spectral Density of the Detected Laser
Fluctuations
The PSD S μ (ω) of the detected laser fluctuations of each type of μ AN , μ AN ‐ PN , μ PN
voltages in the PD load is determined as the result of the Fourier transform of its
correlation functions.
For the amplitude noises, which are usually much less than the conversion
AN-PN noises, the power spectral density of the in-phase S μRe ¼ S LRe (ω) and the
quadrature S μIm (ω) ¼ S LIm (ω) components of the current fluctuations is described,
relatively, by the following relations:
S L Re ω
ð Þ ¼ G 12 Á S μAN þ S μAN‐PN
À
Á
¼ G 12 S μAN þ
S βPN D FA U
2
0MZ sin 2πν 0 T 1M À T 2M
ð
Þ
½
Á G 12
ω À ω 0
ð
Þ
2 T
2
0L Á 0:25 Á B
2
L
,
ð6:20Þ
S LIm ω
ð Þ %
4S βPN D PN U
2
10MZ G 12
ω À ω 0
ð
Þ
2 T
2
0L P 0L
,
ð6:21Þ
where G 12 is the coefficient of the phase fluctuation suppression of the laser optical
emission at the expense of correlation of the random phase of laser emission in the
system “MZ–optical fiber—photodetector.”
At the closed feedback loop of OEO MZ, G 12 is: G 12 ¼ 1 À (A 1 /
A 2 ) Á exp (À2ΔT FOS Á Δν L ), while at the opened feedback loop of OEO MZ, G 12
is: G 12 ¼ 1 À (A 1 /A 2 ) Á exp (À2ΔT M Á Δν L ), where the coefficient A 1 /A 2 % 1, Δν L is
the laser spectral line width Δν L ¼ 1/T c , T c is the laser coherence time.
We cannot create the ideal caseA 1 /A 2 % 1 and really, the suppression coefficient is
G 12 % 10
À1
– 10
À3
.
Taking into consideration the transfer function of the nonlinear amplifier and the
pass-band filter of the microwave range, the expression for the instantaneous value
of the u PD ¼ Re U PD exp (Àj2πf 0 t) voltage on the load impedance Z PD of PD or the
NA input voltage can be written as:
6.4 Characteristics and the Transfer Function of the MZ Modulator in OEO
309
ð
Þ
2 sin 2πν 0 T 1M À T 2M
ð
Þþπ U 0MZ =U π0MZ
ð
Þ
½
Á U 10MZ cos 2π f 0 t
ð
Þ,
ð6:19Þ
Thus, as the result of heterodyning, the spectrum of fluctuations of the PD output
current is obtained by the “transfer” of the optical noise spectrum from the laser
(or QWLD) generation frequency ν 0 to the OEO radio-frequency generation f 0 . To
Eqs. (6.18) and (6.19), we must add the noise current in the photodetector load,
which obtained from the detected noise of the DC of the laser emission.
6.4.5 Power Spectral Density of the Detected Laser
Fluctuations
The PSD S μ (ω) of the detected laser fluctuations of each type of μ AN , μ AN ‐ PN , μ PN
voltages in the PD load is determined as the result of the Fourier transform of its
correlation functions.
For the amplitude noises, which are usually much less than the conversion
AN-PN noises, the power spectral density of the in-phase S μRe ¼ S LRe (ω) and the
quadrature S μIm (ω) ¼ S LIm (ω) components of the current fluctuations is described,
relatively, by the following relations:
S L Re ω
ð Þ ¼ G 12 Á S μAN þ S μAN‐PN
À
Á
¼ G 12 S μAN þ
S βPN D FA U
2
0MZ sin 2πν 0 T 1M À T 2M
ð
Þ
½
Á G 12
ω À ω 0
ð
Þ
2 T
2
0L Á 0:25 Á B
2
L
,
ð6:20Þ
S LIm ω
ð Þ %
4S βPN D PN U
2
10MZ G 12
ω À ω 0
ð
Þ
2 T
2
0L P 0L
,
ð6:21Þ
where G 12 is the coefficient of the phase fluctuation suppression of the laser optical
emission at the expense of correlation of the random phase of laser emission in the
system “MZ–optical fiber—photodetector.”
At the closed feedback loop of OEO MZ, G 12 is: G 12 ¼ 1 À (A 1 /
A 2 ) Á exp (À2ΔT FOS Á Δν L ), while at the opened feedback loop of OEO MZ, G 12
is: G 12 ¼ 1 À (A 1 /A 2 ) Á exp (À2ΔT M Á Δν L ), where the coefficient A 1 /A 2 % 1, Δν L is
the laser spectral line width Δν L ¼ 1/T c , T c is the laser coherence time.
We cannot create the ideal caseA 1 /A 2 % 1 and really, the suppression coefficient is
G 12 % 10
À1
– 10
À3
.
Taking into consideration the transfer function of the nonlinear amplifier and the
pass-band filter of the microwave range, the expression for the instantaneous value
of the u PD ¼ Re U PD exp (Àj2πf 0 t) voltage on the load impedance Z PD of PD or the
NA input voltage can be written as:
6.4 Characteristics and the Transfer Function of the MZ Modulator in OEO
309