Noises in such a system are mainly determined by the laser phase fluctuations,
which, in turn, mainly depends upon the spontaneous emission and they define the
generation line width of OEO MZ only in above-mentioned case of definite relations
between the system parameters of OEO MZ, such as the natural laser emission line
bandwidth Δν L , the laser generation frequency ν 0 , difference in delay time in the MZ
optical channels ΔT M , the level of spontaneous laser emission S β and the NA
amplification factor D FM .
6.5.15 Approximate Expression for the Suppression
Coefficient and PSD in OEO MZ
Neglecting in expressions by the effect of the σ U coefficient and taking into account
that the coefficient K FODL ¼ P L0 |K MZ ||K FOS ||K PD ||K F |, where |K MZ |, |K FOS |, |K PD |, |
K F | are relatively, modules of coefficients of the MZ modulator, FOS, RF filter, we
obtain the expression for PSD in the form:
S F
ð Þ ¼ K
2
ΓPN S L F
ð Þ þ S PD F
ð Þ þ S NA F
ð Þ
½
,
ð6:89Þ
where K
2
ΓPN % K
2
2ΓPN ¼
1
1À2K FOLD cos FT FOS
ð
Þ þK FOLD
ð
Þ
2
½
2 , S L (F), S PD (F), S NA (F) are
components of the poser spectral density of phase noises, relatively, of detected
laser noises in PD output, the PD shot noise, and the NA thermal noise. The
component of detected laser noises S L (F) in the PD output current is defined by
the expression: S L ¼ BΔν
D OA
4F
2 K FOLD U
2
10M , where D OA is the noise-factor of the
optical amplifier, Δν is the spectral line width (on level 0.5) of the laser optical
emission, U 10M is the voltage of the first harmonic of RF oscillations in the MZ
modulator input, B is the constant coefficient depending on the laser type:
S ΨOEO
P G
¼ K
2
2ΓPN K
2
PD
Á K
2
PD
S βPN
P 0L F
2 T
2
0L
þ
K
2
ΓPN
2S 01
3R PD S 03
Á 1 À
Y 00
S 01 P 0L
Á
2eS 0PD Á R PD
1
P 0L þ
D Y kT
1
!
8
<
:
9
=
;
:
ð6:90Þ
From expression (6.90), we see that under condition of small PD noises, the
reduction of PSD of the phase noise S(F) can be achieved due to the growth of the
delay time in RF FODL, the laser power P OL and the decrease of the width square Δν
of the laser spectral line. Neglecting by the first and second terms in Eq. (6.90) at the
frequency offset F ¼ Δν, we obtain the value S F
ð Þ % K
2
2ΓPN BK FOLD D OA =4 . For
instance, at F ¼ Δν ¼ 1 kHz, D OA ¼ 40, K FODL ¼ 1 K 2 ¼ K
2
2ΓPN ¼ 10
À2 , for
6.5 Differential Fluctuation Equations of OEO MZ
345
which, in turn, mainly depends upon the spontaneous emission and they define the
generation line width of OEO MZ only in above-mentioned case of definite relations
between the system parameters of OEO MZ, such as the natural laser emission line
bandwidth Δν L , the laser generation frequency ν 0 , difference in delay time in the MZ
optical channels ΔT M , the level of spontaneous laser emission S β and the NA
amplification factor D FM .
6.5.15 Approximate Expression for the Suppression
Coefficient and PSD in OEO MZ
Neglecting in expressions by the effect of the σ U coefficient and taking into account
that the coefficient K FODL ¼ P L0 |K MZ ||K FOS ||K PD ||K F |, where |K MZ |, |K FOS |, |K PD |, |
K F | are relatively, modules of coefficients of the MZ modulator, FOS, RF filter, we
obtain the expression for PSD in the form:
S F
ð Þ ¼ K
2
ΓPN S L F
ð Þ þ S PD F
ð Þ þ S NA F
ð Þ
½
,
ð6:89Þ
where K
2
ΓPN % K
2
2ΓPN ¼
1
1À2K FOLD cos FT FOS
ð
Þ þK FOLD
ð
Þ
2
½
2 , S L (F), S PD (F), S NA (F) are
components of the poser spectral density of phase noises, relatively, of detected
laser noises in PD output, the PD shot noise, and the NA thermal noise. The
component of detected laser noises S L (F) in the PD output current is defined by
the expression: S L ¼ BΔν
D OA
4F
2 K FOLD U
2
10M , where D OA is the noise-factor of the
optical amplifier, Δν is the spectral line width (on level 0.5) of the laser optical
emission, U 10M is the voltage of the first harmonic of RF oscillations in the MZ
modulator input, B is the constant coefficient depending on the laser type:
S ΨOEO
P G
¼ K
2
2ΓPN K
2
PD
Á K
2
PD
S βPN
P 0L F
2 T
2
0L
þ
K
2
ΓPN
2S 01
3R PD S 03
Á 1 À
Y 00
S 01 P 0L
Á
2eS 0PD Á R PD
1
P 0L þ
D Y kT
1
!
8
<
:
9
=
;
:
ð6:90Þ
From expression (6.90), we see that under condition of small PD noises, the
reduction of PSD of the phase noise S(F) can be achieved due to the growth of the
delay time in RF FODL, the laser power P OL and the decrease of the width square Δν
of the laser spectral line. Neglecting by the first and second terms in Eq. (6.90) at the
frequency offset F ¼ Δν, we obtain the value S F
ð Þ % K
2
2ΓPN BK FOLD D OA =4 . For
instance, at F ¼ Δν ¼ 1 kHz, D OA ¼ 40, K FODL ¼ 1 K 2 ¼ K
2
2ΓPN ¼ 10
À2 , for
6.5 Differential Fluctuation Equations of OEO MZ
345