FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

1
The light-ray concept is a convenient approximate approach
that may be used to introduce other important
concepts such as total internal reflection and ray trapping.
To extend the theory of light propagation farther,
however, it is necesaary to take into account the
notions that light is an electromagnetic wave phenomenon
and that optical fibers are cylindrical dielectric
waveguides. With these in mind it is possible to
develop concepts regarding the allowed electromagnetic
propagation modes of a cylindrical waveguide and to
introduce the frequently encountered optical fiber waveguide
V-Parameter (V-value) that must be considered
when selecting a suitable fiber for a particular application.
In accordance with the ray theory of light
propagation, a light beam incident from below on the
interface surface between two transparent media, at an
angle e 1 with the interface surface behaves as shown in
Fig. 2.3. When fll ia large, part of the incident beam
Fig. 2.3
MEDIUM2 ! .-”’”
X6;
n2
k
n1>n2
Reflection and refraction at the interface
when a lightwave travels from a higher to
a lower refractive index medium.
is transmitted into the upper medium and vart is reflected.
Their relative intensities depend upon the
refractive indices of the two media. The refractive
index of a medium is defined as the ratio of the velocity
of light in a vacuum to the velocity of light in
the medium. The higher the refractive index of a medium
the slower light will travel in it. The refractive
index of medium 1 is designated as nl and that
for medium 2 as n2 as shown in Fig. 2.3.
These indices alao determine the direction
of the beam transmitted into medium 2, i.e., @2 in
Fig. 2.3 is determined by the indexes of both media.
Snell’s law of refraction of light at an interface predicts
that the ratio of the cosine of the angle 131 to
the cosine of the angle of t12 is equal to the ratio
n2/nl which is equal to the velocity ratio v1/v2. Thus,
as shown in Fig. 2.3, if light propagates in medium 1
at a lower velocity than in medium 2, the angle 01 will
be greater than the angle 02 and the ray will be bent
toward the interface when entering medium 2. The angle
of the reflected beam is equal to the angle of the incident
beam. These are an application of the well known
laws (Snell’s laws) of refraction and reflection that
aPPIY in ray treatments of wave phenomena.
nl > n2
+’*NG)
v,< V2
I \ MEOIUMI’(CORE)
CASEI 01>0, CASE2 e)=ec CASE3: 01 n2. There is both a refracted and a reflected
beam and, from the conservation of energy, the sum of
their energies must equal the energy in the incident
beam.
2-2
Fig. 2.5
A step-index optical fiber showing the
critical angle, 6C for total internal reflection.