Page 210 - Photonics Essentials an introduction with experiments

Optical Fibers and Optical Fiber Amplifiers

204 Advanced Topics

If the numerical aperture of the fiber happens to be 0.1, then we
3
know immediately that the core diameter of the fiber is 9.87 × 10 nm
or 9.87 microns. As it turns out, this is not too different from the pa-
rameters for commercial optical fibers. An important consideration
comes from fiber manufacturing. There are fluctuations that must oc-
cur in the position of the fiber core and its diameter during the draw-
ing process. For example, Corning, Samsung, and Alcatel control the
position of the core inside the cladding to 0.5 microns. These fluctua-
tions do not depend strongly on the fiber core diameter. So increasing
the core diameter makes these fluctuations less important overall. At
the same time, increasing the core diameter means that the fiber nu-
merical aperture must be reduced, and this means that the index of
refraction difference needs to be reduced also. The index of the core is
differentiated from that of the cladding by Ge doping. There are also
fluctuations in the doping level that naturally occur during manufac-
ture. As the intentional Ge doping is decreased in order to reduce the
NA, these fluctuations tend to become more important. Hence, you
would prefer to make the index difference larger. Thus, there are com-
peting tendencies in manufacturing both to raise the index difference
and to increase the fiber core diameter. A compromise solution is a
core diameter of about 9 microns and a numerical aperture of about
0.1.
The lowest-order HE 11 mode propagates alone under single-mode
conditions. It has a simple spatial structure, having circular symme-
try, and maximum intensity in the center of the core. The radial mode
field amplitude is described by a Bessel function, but it can be well ap-
proximated by a simple Gaussian function:
2 2
I(r) = I 0 e –(2r /r ) (9.11)
0
The mode field diameter is defined as 2r 0 . The mode field diameter
depends on the fiber V parameter, and it can be either larger than or
smaller than the fiber core physical diameter d. A convenient and ac-
curate empirical expression developed by Jeunhomme (see Bibliogra-
phy) can be used to determine r 0 :

2r 0 –1.5 –6
= 0.65 + 1.619V + 2.879V (9.12)
d

9.5 More Capacity
Cables of optical fiber with low losses were installed in the ground
and under the ocean during the 1980s. Simultaneously, engineers
were developing the semiconductor lasers for the transmitters. There
was general agreement in the industry that the wavelength of choice

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