Digital Signal Processing Reference
In-Depth Information
One can find detailed derivation for noise calculations in silicon waveguides
in, but here noise induced by FWM process and contributions from other com-
ponents are considered to estimate the NF which impacts our simulations. To
calculate the NF due to FWM process, mean output photon number and mean
photon number fluctuations through the silicon waveguide are calculated using
the signal wave Eqs. (
8.3
-
8.5
), and amplification based on photon fluctuations
will be:
T
+
N
loss
+
N
gain
T
N
gain
(
T
+
N
loss
)
T
2
|
a
|
2
(8.11)
NF
sili con
=
+
where
L
(8.11a)
T
=
exp
(
g
(
z
) −
l
(
z
)
dz
)
0
is the net gain and
L
L
N
gain
=
g
(
z
)
exp
(
g
(
x
) −
l
(
x
)
dx
)
dz
(8.11b)
z
0
L
L
N
loss
=
l
(
z
)
exp
(
g
(
x
) −
l
(
x
)
dx
)
dz
(8.11c)
z
0
are the photon fluctuations due to gain and loss. Parameter
L
is the waveguide
length,
g
(
z
) is the gain parameter that can be numerically calculated from Eqs.
(
8.3
-
8.5
).
l
(
z
) = α + α
FC A
(
z
) +
2
β
I
(
z
)
is the experienced loss coefficient
and
|
a
|
2
is the photon number at the input frequency. Considering high-input sig-
nal power lets the second term in Eq. (
8.11
) negligible and (
8.11a
-
8.11c
) can be
numerically solved. Neglecting the pump relative intensity noise (RIN) the total
NF will be
NF
=
NF
sili con
+
NF
p
(8.12)
In a 1 cm silicon waveguide operating in anomalous dispersion regime at
1,550 nm, the typical NF spectra of the pump with 1-ps pulses operating at repeti-
tion rate of 10 GHz are given in Fig. (
8.7
). as illustrated, the NF contribution from
gain and loss fluctuations in the silicon waveguide is the dominant noise source of
the silicon FWM process.
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