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Thursday, March 31, 2011

Optical Fiber Snell's Law

When light is directed into an optical fiber the effectiveness of the wire depends
on its ability to guide the light ray far distances with little scattering or absorption of the
light as possible. Doing so means that the optical fiber must exhibit total internal
reflection within the wire. Thus when considering the propagation of light for an optical
fiber the refractive index of the dielectric medium needs to be accounted for. As light
rays become incident on an interface between two dielectrics with different index of
refractions, refraction occurs between the two mediums. This can be best described by
using Snell’s Law of Refraction which states:
n1 sin φ1 = n2 sin φ2
This equation shows that at certain angles partial internal reflection will arise, as well at
other angles total internal reflection will occur.













This relationship can then be used to find the critical angle φc which serves as the
limiting case of refraction and the angle of incidence
[5]
. By launching the light ray at an
angle φ > φc as seen in figure #2, it is reflected at the same angle to the normal, leading
to total internal reflection within the optical fiber. A typical optical fiber with two
dielectric mediums is shown in figure #2, with the silica core having the index refraction
of n1 and the silica cladding with a lower index of refraction of n2 . With this setup it is
possible to send packets of information through light rays which can propagate through
an optical fiber with very little loss or distortion. However other factors will influence the
effectiveness of the optical fiber due such things like impurities but this will be discussed
in detail in later sections of this paper.
















OPTICAL FIBER TYPES
There are 3 basic types of optical fibers: multimode graded-index fiber,
multimode step-index fiber and single-mode step-index fibers.
A multimode fiber can propagate hundreds of light modes at one time while single-mode
fibers only propagate one mode
[12]
as shown in figure #3.
Figure #3 Optical Fiber Modes
13
The difference between graded-index and step-index fibers is that in a gradedindex
fiber it has a core whose refractive index varies with the distance from the fiber
axis, while the step-index has core with the same refractive index throughout the fiber
[14]
.
Since the single-mode fibers propagate light in one clearly defined path,
intermodal dispersion effects is not present, allowing the fiber to operate at larger
bandwidths than a multimode fiber
[15]
. On the other hand, multimode fibers have large
intermodal dispersion effects due to the many light modes of propagations it handles at
one time. Because of this multimode fibers operate at lower bandwidths, however they
are typically used for enterprise systems such as offices, buildings, universities since they
are more cost effective than single mode ones.

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