242 CHAPTER 6. OPTICAL AMPLIFIERS
cascaded SOAs [21]. SOAs have also been employed to overcome distribution losses
in the local-area network (LAN) applications. In one experiment, an SOA was used as
a dual-function device [22]. It amplified five channels, but at the same time the SOA
was used to monitor the network performance through a baseband control channel. The
100-Mb/s baseband control signal modulated the carrier density of the amplifier, which
in turn produced a corresponding electric signal that was used for monitoring.
Although SOAs can be used to amplify several channels simultaneously, they suffer
from a fundamental problem related to their relatively fast response. Ideally, the signal
in each channel should be amplified by the same amount. In practice, several nonlinear
phenomena in SOAs induceinterchannel crosstalk, an undesirable feature that should
be minimized for practical lightwave systems. Two such nonlinear phenomena are
cross-gain saturationandfour-wave mixing(FWM). Both of them originate from the
stimulated recombination term in Eq. (6.2.6). In the case of multichannel amplification,
the powerPin this equation is replaced with
P=
1
2
∣
∣
∣
∣
∣
M∑
j= 1Ajexp(−iωjt)+c.c.∣
∣
∣
∣
∣
2
, (6.2.24)where c.c. stands for the complex conjugate,Mis the number of channels,Ajis the
amplitude, andωjis the carrier frequency of thejth channel. Because of the coher-
ent addition of individual channel fields, Eq. (6.2.24) contains time-dependent terms
resulting from beating of the signal in different channels, i.e.,
P=
M∑
j= 1Pj+M∑
j= 1M∑
k=j2
√
PjPkcos(Ωjkt+φj−φk), (6.2.25)whereAj=
√
Pjexp(iφj)was assumed together withΩjk=ωj−ωk. When Eq.
(6.2.25) is substituted in Eq. (6.2.6), the carrier population is also found to oscillate
at the beat frequencyΩjk. Since the gain and the refractive index both depend onN,
they are also modulated at the frequencyΩjk; such a modulation creates gain and index
gratings, which induce interchannel crosstalk by scattering a part of the signal from one
channel to another. This phenomenon can also be viewed as FWM [16].
The origin of cross-gain saturation is also evident from Eq. (6.2.25). The first term
on the right side shows that the powerPin Eq. (6.2.7) should be replaced by the total
power in all channels. Thus, the gain of a specific channel is saturated not only by
its own power but also by the power of neighboring channels, a phenomenon known
as cross-gain saturation. It is undesirable in WDM systems since the amplifier gain
changes with time depending on the bit pattern of neighboring channels. As a result, the
amplified signal appears to fluctuate more or less randomly. Such fluctuations degrade
the effective SNR at the receiver. The interchannel crosstalk occurs regardless of the
channel spacing. It can be avoided only by reducing the channel powers to low enough
values that the SOA operates in the unsaturated regime. Interchannel crosstalk induced
by FWM occurs for all WDM lightwave systems irrespective of the modulation format
used [23]–[26]. Its impact is most severe for coherent systems because of a relatively
small channel spacing [25]. FWM can occur even for widely spaced channels through
intraband nonlinearities [17] occurring at fast time scales (<1 ps).