"Introduction". In: Fiber-Optic Communication Systems

6.2. SEMICONDUCTOR OPTICAL AMPLIFIERS 239

Figure 6.7: Time-dependent amplification factor for super-Gaussian input pulses of input energy
such thatEin/Esat= 0 .1. The unsaturated valueG 0 is 30 dB in all cases. The input pulse is
Gaussian form=1 but becomes nearly rectangular asmincreases.

As seen from Eq. (6.2.15), gain saturation leads to a time-dependent phase shift
across the pulse. This phase shift is found by integrating Eq. (6.2.15) over the amplifier
length and is given by

φ(τ)=−^12 βc

∫L

0

g(z,τ)dz=−^12 βch(τ)=−^12 βcln[G(τ)]. (6.2.22)

Since the pulse modulates its own phase through gain saturation, this phenomenon is
referred to assaturation-inducedself-phase modulation [18]. The frequency chirp is
related to the phase derivative as

∆νc=−

1

2 π

dφ

dτ

=

βc

4 π

dh

dτ

=−

βcPin(τ)

4 πEsat

[G(τ)− 1 ], (6.2.23)

where Eq. (6.2.19) was used. Figure 6.8 shows the chirp profiles for several input pulse
energies when a Gaussian pulse is amplified in a SOA with 30-dB unsaturated gain.
The frequency chirp is larger for more energetic pulses simply because gain saturation
sets in earlier for such pulses.
Self-phase modulation and the associated frequency chirp can affect lightwave sys-
tems considerably. The spectrum of the amplified pulse becomes considerably broad
and contains several peaks of different amplitudes [18]. The dominant peak is shifted
toward the red side and is broader than the input spectrum. It is also accompanied
by one or more satellite peaks. Figure 6.9 shows the expected shape and spectrum of
amplified pulses when a Gaussian pulse of energy such thatEin/Esat= 0 .1 is amplified