12.3 Stimulated Raman Scattering
483
To see the effects of SRS, consider a WDM system that has N channels equally
spaced in a 30-nm band centered at 1545 nm. Channel 0, which is at the lowest
(shortest) wavelength, is affected the worst because power gets transferred from this
channel to all longer-wavelength channels. For simplicity, assume that the transmitted
power P is the same on all channels, that the Raman gain increases linearly as shown
by the dashed line in Fig. 12.5, and that there is no interaction between the other
channels. If F out ( j) is the fraction of power coupled from channel 0 to channel j, then
the total fraction of power coupled out of channel 0 to all the other channels is [6].
F out =
N −1
j=1
F out ( j) =
N −1
j=1
g R, peak
jν s
ν c
P L e f f
2 A e f f
=
g R, peak ν s P L e f f
2ν c A e f f
N (N − 1)
2
(12.2)
The power penalty for this channel then is −10 log (1−F out ). To keep the penalty
below 0.5 dB, it is necessary to have F out < 0.l. Using Eq. 12.2, and with A eff = 55
μm
2 and g R,peak = 7 × 10
−14 m/W from Fig. 12.5, gives the criterion
[N P][N − 1][ν s ]L e f f < 5 × 10
3 mW · THz · km
(12.3)
Here, NP is the total power from N sources coupled into the fiber, (N−l) ν s is the
total occupied optical bandwidth, and L eff is the effective length, which takes into
account absorption along the length of the fiber.
Example 12.1 The power penalty in decibels per channel due to SRS can be calculated from Eq. (12.2) as PP SRS = − 10 log (1 – F out ). Assume the following parameter
values: g R = 4.7 × 10
−14 m/W, L eff = 21 km, ν c = 125 GHz, and A eff = 55 μm
2 .
Table 12.3 shows the maximum allowed launch power per channel for an SRS power
penalty of 0.5 dB in links having channel counts of N = 8, 16, 40 and 80 and for
DWDM channel spacing of ν s = 50 and 100 GHz. This table indicates that the SRS
power penalty becomes less as the channel spacing decreases or as the number of
DWDM channels decreases.
Table 12.3 Approximate
allowed optical signal launch
power to have a maximum
SRS Power penalty of 0.5 dB
Maximum launch power (dBm)
Channel count
50 GHz
100 GHz
8
21
18
16
14.7
11.6
40
6.6
3.6
80
0.5
−2.5
483
To see the effects of SRS, consider a WDM system that has N channels equally
spaced in a 30-nm band centered at 1545 nm. Channel 0, which is at the lowest
(shortest) wavelength, is affected the worst because power gets transferred from this
channel to all longer-wavelength channels. For simplicity, assume that the transmitted
power P is the same on all channels, that the Raman gain increases linearly as shown
by the dashed line in Fig. 12.5, and that there is no interaction between the other
channels. If F out ( j) is the fraction of power coupled from channel 0 to channel j, then
the total fraction of power coupled out of channel 0 to all the other channels is [6].
F out =
N −1
j=1
F out ( j) =
N −1
j=1
g R, peak
jν s
ν c
P L e f f
2 A e f f
=
g R, peak ν s P L e f f
2ν c A e f f
N (N − 1)
2
(12.2)
The power penalty for this channel then is −10 log (1−F out ). To keep the penalty
below 0.5 dB, it is necessary to have F out < 0.l. Using Eq. 12.2, and with A eff = 55
μm
2 and g R,peak = 7 × 10
−14 m/W from Fig. 12.5, gives the criterion
[N P][N − 1][ν s ]L e f f < 5 × 10
3 mW · THz · km
(12.3)
Here, NP is the total power from N sources coupled into the fiber, (N−l) ν s is the
total occupied optical bandwidth, and L eff is the effective length, which takes into
account absorption along the length of the fiber.
Example 12.1 The power penalty in decibels per channel due to SRS can be calculated from Eq. (12.2) as PP SRS = − 10 log (1 – F out ). Assume the following parameter
values: g R = 4.7 × 10
−14 m/W, L eff = 21 km, ν c = 125 GHz, and A eff = 55 μm
2 .
Table 12.3 shows the maximum allowed launch power per channel for an SRS power
penalty of 0.5 dB in links having channel counts of N = 8, 16, 40 and 80 and for
DWDM channel spacing of ν s = 50 and 100 GHz. This table indicates that the SRS
power penalty becomes less as the channel spacing decreases or as the number of
DWDM channels decreases.
Table 12.3 Approximate
allowed optical signal launch
power to have a maximum
SRS Power penalty of 0.5 dB
Maximum launch power (dBm)
Channel count
50 GHz
100 GHz
8
21
18
16
14.7
11.6
40
6.6
3.6
80
0.5
−2.5