446
11 Basics of Optical Amplifiers
where g 0 is the unsaturated medium gain per unit length in the absence of signal input,
P s (z) is the internal signal power at point z, and P amp,sat is the amplifier saturation
power, which is defined as the internal power level at which the gain per unit length
has been halved. Thus, from Eq. (11.9) the gain decreases with increasing signal
power. In particular, the gain parameter in Eq. (11.10) is reduced by a factor of 2
when the internal signal power is equal to the amplifier saturation power.
Given that g(z) is the gain per unit length, in an incremental length dz the light
power increases by
d P = g(z)P s (z)dz
(11.11)
Substituting Eq. (11.10) into Eq. (11.11) and rearranging terms gives
g 0 (z)dz =
1
P s (z)
+
1
P amp,sat
d P
(11.12a)
Integrating this equation from z = 0 to z = L yields
L
0
g 0 dz =
P s,out
P s,in
1
P s (z)
+
1
P amp,sat
d P
(11.12b)
Defining the single-pass gain in the absence of light to be G 0 = exp(g 0 L), and using
Eq. (11.8), then yields
G = 1 +
P amp,sat
P s,in
ln
G 0
G
= G 0 ex p
−
G − 1
G
P s,out
P amp,sat
(11.13)
Figure 11.3 illustrates the dependence of the gain on the input power. Here, the
zero-signal gain (or small-signal gain) is G 0 = 30 dB, which is a gain factor of 1000.
The curve shows that as the input signal power is increased, the gain first stays near
the small-signal level and then starts to decrease. After decreasing linearly in the gain
saturation region, it finally approaches an asymptotic value of 0 dB (a unity gain) for
high input powers. Also shown is the output saturation power P amp,sat , which is the
point at which the gain is reduced by 3 dB.
The wavelength at which the SOA has a maximum gain can be tailored to occur
anywhere between about 1200 and 1700 nm by changing the composition of the active
InGaAsP material. As an example, Fig. 11.4 shows a typical gain versus wavelength
characteristic for a device with a peak gain of 25 dB at 1530 nm. The wavelength
span over which the gain decreases by less than 3 dB with respect to the maximum
gain is known as the gain bandwidth or the 3-dB optical bandwidth. In the example
shown in Fig. 11.4 the 3-dB optical bandwidth is 85 nm. Values of up to 100 nm can
be achieved.
11 Basics of Optical Amplifiers
where g 0 is the unsaturated medium gain per unit length in the absence of signal input,
P s (z) is the internal signal power at point z, and P amp,sat is the amplifier saturation
power, which is defined as the internal power level at which the gain per unit length
has been halved. Thus, from Eq. (11.9) the gain decreases with increasing signal
power. In particular, the gain parameter in Eq. (11.10) is reduced by a factor of 2
when the internal signal power is equal to the amplifier saturation power.
Given that g(z) is the gain per unit length, in an incremental length dz the light
power increases by
d P = g(z)P s (z)dz
(11.11)
Substituting Eq. (11.10) into Eq. (11.11) and rearranging terms gives
g 0 (z)dz =
1
P s (z)
+
1
P amp,sat
d P
(11.12a)
Integrating this equation from z = 0 to z = L yields
L
0
g 0 dz =
P s,out
P s,in
1
P s (z)
+
1
P amp,sat
d P
(11.12b)
Defining the single-pass gain in the absence of light to be G 0 = exp(g 0 L), and using
Eq. (11.8), then yields
G = 1 +
P amp,sat
P s,in
ln
G 0
G
= G 0 ex p
−
G − 1
G
P s,out
P amp,sat
(11.13)
Figure 11.3 illustrates the dependence of the gain on the input power. Here, the
zero-signal gain (or small-signal gain) is G 0 = 30 dB, which is a gain factor of 1000.
The curve shows that as the input signal power is increased, the gain first stays near
the small-signal level and then starts to decrease. After decreasing linearly in the gain
saturation region, it finally approaches an asymptotic value of 0 dB (a unity gain) for
high input powers. Also shown is the output saturation power P amp,sat , which is the
point at which the gain is reduced by 3 dB.
The wavelength at which the SOA has a maximum gain can be tailored to occur
anywhere between about 1200 and 1700 nm by changing the composition of the active
InGaAsP material. As an example, Fig. 11.4 shows a typical gain versus wavelength
characteristic for a device with a peak gain of 25 dB at 1530 nm. The wavelength
span over which the gain decreases by less than 3 dB with respect to the maximum
gain is known as the gain bandwidth or the 3-dB optical bandwidth. In the example
shown in Fig. 11.4 the 3-dB optical bandwidth is 85 nm. Values of up to 100 nm can
be achieved.