2.4. DISPERSION-INDUCED LIMITATIONS 53
Figure 2.14: Dispersion-limitedBLproduct as a function of the chirp parameter for Gaussian
(solid curve) and super-Gaussian (dashed curve) input pulses. (After Ref. [58];©c1986 OSA;
reprinted with permission.)
by 20% was obtained forT 0 =125 ps andβ 2 =−20 ps^2 /km. As expected, theBL
product is smaller for super-Gaussian pulses because such pulses broaden more rapidly
than Gaussian pulses. TheBLproduct is reduced dramatically for negative values of
the chirp parameterC. This is due to enhanced broadening occurring whenβ 2 Cis
positive (see Fig. 2.12). Unfortunately,Cis generally negative for directly modulated
semiconductor lasers with a typical value of−6 at 1.55μm. SinceBL<100 (Gb/s)-km
under such conditions, fiber dispersion limits the bit rate to about 2 Gb/s forL=50 km.
This problem can be overcome by using dispersion-shifted fibers or by using dispersion
management (see Chapter 7).
2.4.4 Fiber Bandwidth
The concept of fiber bandwidth originates from the general theory of time-invariant
linear systems [59]. If the optical fiber can be treated as alinear system, its input and
output powers should be related by a general relation
Pout(t)=∫∞−∞h(t−t′)Pin(t′)dt′. (2.4.35)For an impulsePin(t)=δ(t), whereδ(t)is the delta function, andPout(t)=h(t).For
this reason,h(t)is called theimpulse responseof the linear system. Its Fourier trans-
form,
H(f)=∫∞−∞h(t)exp( 2 πift)dt, (2.4.36)