6.2. SEMICONDUCTOR OPTICAL AMPLIFIERS 237
Figure 6.6: Three configurations used to reduce the polarization sensitivity of semiconductor
optical amplifiers: (a) twin amplifiers in series; (b) twin amplifiers in parallel; and (c) double
pass through a single amplifier.
6.2.3 Pulse Amplification
One can adapt the formulation developed in Section 2.4 for pulse propagation in optical
fibers to the case of SOAs by making a few changes. The dispersive effects are not
important for SOAs because of negligible material dispersion and a short amplifier
length (<1 mm in most cases). The amplifier gain can be included by adding the term
gA/2 on the right side of Eq. (2.4.7). By settingβ 2 =β 3 =0, the amplitudeA(z,t)of
the pulse envelope then evolves as [18]
∂A
∂z+
1
vg∂A
∂t=
1
2
( 1 −iβc)gA, (6.2.11)where carrier-induced index changes are included through the linewidth enhancement
factorβc(see Section 3.5.2). The time dependence ofgis governed by Eqs. (6.2.5) and
(6.2.6). The two equations can be combined to yield
∂g
∂t=
g 0 −g
τc−
g|A|^2
Esat, (6.2.12)
where the saturation energyEsatis defined as
Esat=hν(σm/σg), (6.2.13)andg 0 is given by Eq. (6.2.8). TypicallyEsat∼1 pJ.