Page 94 - Fiber Optic Communications Fund

Optical Fiber Transmission 75

where D is called the dispersion parameter. Since
c
f = , (2.200)

c
df =− d. (2.201)
2
Using Eq. (2.201) in Eq. (2.199) and making use of Eq. (2.193), we obtain
−2c
D = . (2.202)
2
2
Substituting Eq. (2.202) in Eq. (2.197), the differential delay can be rewritten as
ΔT = DLΔ, (2.203)
2
where Δ =−cΔf∕f . The above relation can be understood from the fact that is the delay per unit length
1
1
and D is the delay per unit length per unit wavelength (Eq. (2.199)).
Fiber dispersion can be divided into two parts: (i) material dispersion and (ii) waveguide dispersion. Material
dispersion is due to the frequency dependence of the refractive index of glass. Just like a prism spreads white
light into a rainbow of colors (see Section 1.10), different frequency components travel at different speeds
in glass, leading to pulse spreading. The second contribution to fiber dispersion comes from the waveguide
effect and is known as waveguide dispersion. The dependence of the propagation constant on frequency can
be varied by changing the refractive index profile. For example, if we change the refractive index profile from
step index to parabolic index, the dispersion coefficient could vary significantly. In a hypothetical case in
2
which the refractive index of core/cladding does not change with frequency, the fiber dispersion coefficient
could be nonzero because of waveguide dispersion. The product of the dispersion parameters D and fiber
2
length is called accumulated dispersion.
A curve fitting to an experimentally measured dispersion parameter of a standard single-mode fiber (SSMF)
is given by
[ 4 ]
S 0 0
D()= − ps∕(nm ⋅ km), (2.204)
4 3
2
where = 1317 nm and S = 0.088 ps∕(nm ⋅ km). From Eq. (2.204), at = , D( )= 0 and, therefore,
0
0
0
0
is called the zero dispersion wavelength and
0
dD |
| = S . (2.205)
0
|
d |= 0
S is called the dispersion slope at . Fiber loss is the lowest at 1550 nm and, therefore, most of the opti-
0
0
cal communication systems operate in the wavelength range 1520–1620 nm. In this wavelength range, the
dispersion parameter of a standard SMF is quite high, which leads to strong intersymbol interference (ISI)
at the receiver. To avoid this problem, dispersion-shifted (DS) fibers were invented in the 1980s and 1990s
[26, 27] which have = 1550 nm. In the absence of fiber nonlinearity, the ideal characteristics of a fiber
0
are low dispersion parameter |D| and low loss, which can be achieved using DS fibers. However, it was soon
realized that DS fibers are not suitable for WDM systems since nonlinear interactions between channels, such
as four-wave mixing (FWM) and cross-phase modulation (XPM), are enhanced because of low dispersion
(see Chapter 10). In the mid-1990s, nonzero dispersion-shifted fibers (NZ-DSFs) were invented, for which 0
is chosen to be out of the wavelength region 1530–1565 nm [28]. For NZ-DSFs, dispersion near 1550 nm is
large enough to suppress the nonlinear effects and yet low enough to avoid strong ISI due to dispersion. Alter-
natively, the dispersion of the transmission fiber can be compensated for by using dispersion-compensating
fibers (DCFs) (see Section 2.8) or using an equalizer in the electrical domain. This topic is discussed in detail
in Chapter 11.