280 CHAPTER 7. DISPERSION MANAGEMENT
consisting of more than 50 million kilometers of the “standard” single-mode fiber with
λZD≈ 1. 31 μm. Since the dispersion parameterD≈16 ps/(km-nm) in the 1.55-μm re-
gion of such fibers, the GVD severely limits the performance when the bit rate exceeds
2 Gb/s (see Fig. 2.13). For a directly modulated DFB laser, we can use Eq. (2.4.26) for
estimating the maximum transmission distance so that
L<( 4 B|D|sλ)−^1 , (7.1.1)wheresλis the root-mean-square (RMS) width of the pulse spectrum broadened con-
siderably by frequency chirping (see Section 3.5.3). UsingD=16 ps/(km-nm) and
sλ= 0 .15 nm in Eq. (7.1.1), lightwave systems operating at 2.5 Gb/s are limited to
L≈42 km. Indeed, such systems use electronic regenerators, spaced apart by about 40
km, and cannot benefit from the availability of optical amplifiers. Furthermore, their
bit rate cannot be increased beyond 2.5 Gb/s because the regenerator spacing becomes
too small to be feasible economically.
System performance can be improved considerably by using an external modulator
and thus avoiding spectral broadening induced by frequency chirping. This option has
become practical with the commercialization of transmitters containing DFB lasers
with a monolithically integrated modulator. Thesλ=0 line in Fig. 2.13 provides the
dispersion limit when such transmitters are used with the standard fibers. The limiting
transmission distance is then obtained from Eq. (2.4.31) and is given by
L<( 16 |β 2 |B^2 )−^1 , (7.1.2)whereβ 2 is the GVD coefficient related toDby Eq. (2.3.5). If we use a typical value
β 2 =−20 ps^2 /km at 1.55μm,L<500 km at 2.5 Gb/s. Although improved consid-
erably compared with the case of directly modulated DFB lasers, this dispersion limit
becomes of concern when in-line amplifiers are used for loss compensation. Moreover,
if the bit rate is increased to 10 Gb/s, the GVD-limited transmission distance drops to
30 km, a value so low that optical amplifiers cannot be used in designing such light-
wave systems. It is evident from Eq. (7.1.2) that the relatively large GVD of standard
single-mode fibers severely limits the performance of 1.55-μm systems designed to use
the existing telecommunication network at a bit rate of 10 Gb/s or more.
A dispersion-management scheme attempts to solve this practical problem. The
basic idea behind all such schemes is quite simple and can be understood by using the
pulse-propagation equation derived in Section 2.4.1 and written as
∂A
∂z+
iβ 2
2∂^2 A
∂t^2−
β 3
6∂^3 A
∂t^3= 0 , (7.1.3)
whereAis the pulse-envelope amplitude. The effects of third-order dispersion are
included by theβ 3 term. In practice, this term can be neglected when|β 2 |exceeds
0.1 ps^2 /km. Equation (7.1.3) has been solved in Section 2.4.2, and the solution is given
by Eq. (2.4.15). In the specific case ofβ 3 =0 the solution becomes
A(z,t)=1
2 π∫∞−∞A ̃( 0 ,ω)exp(
i
2β 2 zω^2 −iωt)
dω, (7.1.4)