Page 89 - Fiber Optic Communications Fund

70 Fiber Optic Communications

At the fiber input,
2
P = P(0)= |A()| . (2.174)
in
At the fiber output z = L,
2
P = P(L)= |A()| exp (−L)= P (t) exp (−L). (2.175)
out in
The optical power loss in dB units due to propagation in a fiber of length L is defined as
P out
loss(dB)=−10 log =−10(−L) log e = 4.343L. (2.176)
10 10
P
in
−1
Here, is the attenuation coefficient in units of km . The loss per unit length is
(dB∕km)= 4.343. (2.177)
Next, let us consider the origin of fiber loss. The light wave is attenuated as it propagates in fiber mainly
due to (i) Rayleigh scattering and (ii) material absorption. In the following subsections, we discuss these
mechanisms in detail.

2.7.2.1 Rayleigh Scattering
Consider a perfect crystal with uniformly spaced atoms or molecules. When a light wave is incident on this
crystal, electrons in the atoms oscillate and emit light waves of the same frequency as the incident light
wave under a linear approximation (see Chapter 10). In other words, each atom acts as a tiny receiving and
transmitting antenna. The light emitted by an atom could be in all directions. However, for a perfect crystal
with uniformly spaced atoms or molecules, it can be shown that the emitted light waves add up coherently in
the direction of the incident light wave; in any other direction, we get no light as they add up destructively [20].
In other words, in a perfect crystal, there is no scattering of incident light. Next, consider a crystal with defects
such as atoms missing or irregularly placed in the lattice structure. In this case, light waves emitted by atoms
may not add up destructively over a range of directions, which leads to scattering.
Rayleigh scattering is the scattering of light by atoms or molecules of size much smaller than the wave-
length of the light. It is an important mechanism arising from local microscopic fluctuations in density and
compositional variations. The fluctuations in density correspond to irregularly spaced atoms or molecules in
a lattice structure and as a result, incident light is scattered over a range of angles as shown in Fig. 2.33. If
the angle of scattering is less than the critical angle, it will escape to the cladding and then be absorbed
at the polymer jacket. A part of the optical field is back-reflected as well, due to Rayleigh scattering which
propagates as a backward-propagating mode. These effects lead to loss of power in the forward-propagating

Figure 2.33 Rayleigh scattering in optical fibers.