Page 212 - Photonics Essentials an introduction with experiments

Optical Fibers and Optical Fiber Amplifiers

206 Advanced Topics

sion. Dispersion can come from several sources, but the result is the
same. If the pulse spreads out into the bit period, then it acts as if
noise has been added to the signal. The signal needs to be recondi-
tioned. As the modulation rate is increased, the distance that a signal
can propagate before it must be reconditioned gets shorter. Today, it
is often the case that dispersion, and not loss, limits the propagation
distance in an optical fiber.
Pulse dispersion in single-mode optical fibers can be divided into
two categories: structural dispersion and polarization-mode disper-
sion. Both kinds are important. Structural dispersion refers to effects
that are frozen into the fiber. It can be measured in the factory. This
makes the effect straightforward to characterize and correct. Polar-
ization mode dispersion changes over time, with temperature fluctua-
tions and changes in stress on the fiber. To correct for polarization
dispersion, continuous monitoring of the fiber performance is required
while it is being used.
The group velocity of an optical pulse is defined as the change in its
frequency with respect to its wavevector k:

d
v g = (9.13)
dk
where = 2
f and k = 2
/ . For light propagating in air, v g is a con-
stant, c. For light traveling in glass, v g is no longer a constant because
the index n varies with wavelength.
df df
2
v g = = – (9.14)

1
d
d

where is the wavelength of light inside the fiber.
The wavelength of light inside the fiber is related to the free-space
wavelength by the index of refraction: = 0 /n. It is more convenient
to continue in terms of the free-space wavelength, because this is
what you measure:
2
df df d 0 df 1 0 dn –n c 1 0 dn –1
–1
= · = – = –
d d 0 d d 0 n n 2 d 0 0 2 n n 2 d 0
c
v g = (9.15)
n – 0
dn
d 0
The quantity in the denominator of Eq. 9.15 acts like an effective
index, and it is called the material group index. This equation shows
that different wavelengths travel in general with different velocities.

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