2.5. FIBER LOSSES 55
The limiting bit rate can be related tof3dBby using Eq. (2.4.28) and is given by
B≤ 0. 574 f3dB. Again, the fiber bandwidth provides a measure of the dispersion-
limited bit rate. As a numerical estimate, consider a 1.55-μm lightwave system em-
ploying dispersion-shifted fibers and multimode semiconductor lasers. By usingS=
0 .05 ps/(km-nm^2 ) andσλ=1 nm as typical values,f3dBL≈32 THz-km. By con-
trast, the bandwidth–distance product is reduced to 0.1 THz-km for standard fibers
withD=18 ps/(km-nm).
2.5 Fiber Losses
Section 2.4 shows that fiber dispersion limits the performance of optical communi-
cation systems by broadening optical pulses as they propagate inside the fiber. Fiber
losses represent another limiting factor because they reduce the signal power reaching
the receiver. As optical receivers need a certain minimum amount of power for re-
covering the signal accurately, the transmission distance is inherently limited by fiber
losses. In fact, the use of silica fibers for optical communications became practical only
when losses were reduced to an acceptable level during the 1970s. With the advent of
optical amplifiers in the 1990s, transmission distances can exceed several thousands
kilometers by compensating accumulated losses periodically. However, low-loss fibers
are still required since spacing among amplifiers is set by fiber losses. This section is
devoted to a discussion of various loss mechanisms in optical fibers.
2.5.1 Attenuation Coefficient.....................
Under quite general conditions, changes in the average optical powerPof a bit stream
propagating inside an optical fiber are governed by Beer’s law:
dP/dz=−αP, (2.5.1)whereαis the attenuation coefficient. Although denoted by the same symbol as the
absorption coefficient in Eq. (2.2.12),αin Eq. (2.5.1) includes not only material ab-
sorption but also other sources of power attenuation. IfPinis the power launched at the
input end of a fiber of lengthL, the output powerPoutfrom Eq. (2.5.1) is given by
Pout=Pinexp(−αL). (2.5.2)It is customary to expressαin units of dB/km by using the relation
α(dB/km)=−10
L
log 10(
Pout
Pin)
≈ 4. 343 α, (2.5.3)and refer to it as the fiber-loss parameter.
Fiber losses depend on the wavelength of transmitted light. Figure 2.15 shows the
loss spectrumα(λ)of a single-mode fiber made in 1979 with 9.4-μm core diameter,
∆= 1. 9 × 10 −^3 , and 1.1-μm cutoff wavelength [11]. The fiber exhibited a loss of
only about 0.2 dB/km in the wavelength region near 1.55μm, the lowest value first
realized in 1979. This value is close to the fundamental limit of about 0.16 dB/km for