Fibre-Optic Communications.pdf

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Fiber-Optic Communications
Since P and ∆ are low, this value which is close to 2 depends on λ: the gradedindex
fiber can only be optimized for a single wavelength. In theory, it is possible to
reach less than 100 ps/km for ∆ = 1%, but in order to do this, the theoretical index
profile must be very precisely respected. In fact, ∆τim increases very rapidly as soon
as the profile slightly moves away. In practice, it has an value in the range of 1
ns/km, for a less severe tolerance making it possible to produce an economical fiber.
However, the most recent graded-index fibers, optimized for very high bandwidth
local area networks, almost reach theoretical values.
1.5.3. Chromatic dispersion
As we have seen for plane wave guides, it adds to intermodal dispersion a
chromatic dispersion effect ∆τc, caused by the variation of the group delay τg with
the source’s wavelength.
First, for a fiber length L, we can write:
∆τc = Dc.L.∆λ with:
– ∆λ spectral source width; pulse broadening is proportional to it. This value
will therefore be high with light-emitting diodes, with very large linewidth;
– Dc chromatic dispersion coefficient, which depends on fiber and wavelength
parameters. We can calculate this by:
dτg
Dc =
dλ
expressed in ps/nm/km, as ∆λ is in nm and ∆τc in ps/km.
It is divided into: Dc = DM + DG where DM is the material dispersion, caused by
variation of material index with the wavelength, and DG is the guide dispersion. For
multimode fibers, this last term is different for each mode, but it is negligible in
practice. For single-mode fibers on the other hand, it plays an important role and we
will discuss it in detail in Chapter 2. The material dispersion curve in silica (see
Figure 1.14) cancels out at approximately 1.27 µm. The chromatic dispersion
coefficient is negative under this wavelength, which means that light speed increases
with the wavelength (ordinary dispersion), and it is the opposite above
(extraordinary dispersion).