Page 214 - Photonics Essentials an introduction with experiments

Optical Fibers and Optical Fiber Amplifiers

208 Advanced Topics

The material dispersion of SiO 2 has been measured and is shown in
Fig. 9.10.
Estimation of the pulse spreading due to material dispersion can be
written simply:
M = L( )M (9.19)

where is the linewidth of the laser source under modulation.

Example 9.2
To illustrate the importance of the role of modulation bandwidth in
dispersion, consider the pulse broadening of a narrow-line width, sin-
gle-mode laser operating near 1300 nm, at which the material disper-
sion is small.
The line width of a single-mode distributed feedback laser diode is
typically less than 0.1 nm. Under low-frequency modulation condi-
tions (e.g., a modulation frequency less than 1 MHz), the broadening
of a pulse due to material dispersion is
M = L( )M = L(0.1)3 = 0.3 psec/km

However, at a modulation frequency of 1 MHz, the pulse width itself
6
is already ~10 psec in width. After transmission through 100 km of
fiber, the intrinsic pulse duration is still four orders of magnitude
larger than the broadening due to dispersion.
Now consider a laser modulated at 10 Gbits/sec. The time duration
of this pulse is approximately :

1
t = = 100 psec
9
(10 × 10 )
The frequency bandwidth of the pulse is
2
f = 2 × 10 10 Hz
t
The central frequency of the light pulse at 1300 nm is 2.3 × 10 14 Hz.
10
The modulation of the laser broadens the frequency by 2 × 10 /2.3 ×
–4
10 14 0.9 × 10 . The wavelength spread of the emission is the same
percentage, so that = 0.1 nm. As a result the wavelength broaden-
ing under modulation is now significant = 0.1 nm + 0.1 nm = 0.2 nm.
The pulse width broadening is now two times larger than the case
at 1 MHz or 0.6 psec per km. After 100 km, this results in a broad-
ening of 60 psec. Remember that the width of the pulse at 10
Gbits/sec is 100 psec. So dispersion has broadened the signal pulse
to almost two-thirds more than its allotted bit period. Clearly, this is
a problem. Some dispersion correction is needed. At the next lower

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