6.1. BASIC CONCEPTS 231
mixes with the amplified signal and produces the currentI=R|
√
GEin+Esp|^2 at the
photodetector of responsivityR. Noting thatEinandEsposcillate at different frequen-
cies with a random phase difference, it is easy to see that the beating of spontaneous
emission with the signal will produce a noise current∆I= 2 R(GPin)^1 /^2 |Esp|cosθ,
whereθis a rapidly varying random phase. Averaging over the phase, and neglect-
ing all other noise sources, the variance of the photocurrent can be written as
σ^2 ≈ 4 (RGPin)(RSsp)∆f, (6.1.17)where cos^2 θwas replaced by its average value^12. The SNR of the amplified signal is
thus given by
(SNR)out=〈I〉^2
σ^2=
(RGPin)^2
σ^2≈
GPin
4 Ssp∆f. (6.1.18)
The amplifier noise figure can now be obtained by substituting Eqs. (6.1.13) and
(6.1.18) in Eq. (6.1.12). If we also use Eq. (6.1.15) forSsp,
Fn= 2 nsp(G− 1 )/G≈ 2 nsp. (6.1.19)This equation shows that the SNR of the amplified signal is degraded by 3 dB even for
an ideal amplifier for whichnsp=1. For most practical amplifiers,Fnexceeds 3 dB
and can be as large as 6–8 dB. For its application in optical communication systems,
an optical amplifier should haveFnas low as possible.
6.1.4 Amplifier Applications
Optical amplifiers can serve several purposes in the design of fiber-optic communica-
tion systems: three common applications are shown schematically in Fig. 6.3. The
most important application for long-haul systems consists of using amplifiers as in-line
amplifiers which replace electronic regenerators (see Section 5.1). Many optical ampli-
fiers can be cascaded in the form of a periodic chain as long as the system performance
is not limited by the cumulative effects of fiber dispersion, fiber nonlinearity, and am-
plifier noise. The use of optical amplifiers is particularly attractive for WDM lightwave
systems as all channels can be amplified simultaneously.
Another way to use optical amplifiers is to increase the transmitter power by placing
an amplifier just after the transmitter. Such amplifiers are called power amplifiers or
power boosters, as their main purpose is to boost the power transmitted. A power
amplifier can increase the transmission distance by 100 km or more depending on the
amplifier gain and fiber losses. Transmission distance can also be increased by putting
an amplifier just before the receiver to boost the received power. Such amplifiers are
calledoptical preamplifiersand are commonly used to improve the receiver sensitivity.
Another application of optical amplifiers is to use them for compensating distribution
losses in local-area networks. As discussed in Section 5.1, distribution losses often
limit the number of nodes in a network. Many other applications of optical amplifiers
are discussed in Chapter 8 devoted to WDM lightwave systems.