Biomedical Engineering Reference
In-Depth Information
n
2
n
1
θ
c
θ
0
x
θ
lim
θ
1
0
θ
FIGURE 17.20
Basic model of an optical fiber with a cylindrical core with index of refraction (
n
1
) and cladding
index (
n
2
), where (
n
<
n
1
).
2
can be understood with a simple geometrical model. As shown in Figure 17.20,thefiber
can be thought of as a long rod of transparent material in which the rod or core of the
fiber has a higher index of refraction (
n
1
) than the surrounding cylindrical shell material
or cladding (
n
2
). The propagation of the light occurs down the core because of the total
internal reflection of the light from the core-cladding interface, which, from Snell's laws,
occurs when the angle of reflection at this interface is greater than the critical angle. In
order for the light to be internally reflected at the core-cladding interface, the light
injected into the end of the fiber must be smaller than a cone with some limiting angle
y
o
defined by
1
=
2
2
1
2
2
n
0
sin
ðy
o
Þ¼ð
n
n
Þ
¼
NA
ð
17
:
84
Þ
where NA, which stands for “numerical aperture,” is defined by this limiting value. In sil-
ica fibers the NA is generally between 0.2 and 0.4. As can be depicted in Eq. (17.84), increas-
ing the difference in the index of refraction of the core and the cladding will increase the
NA and also the acceptance angle. A large NA and acceptance angle produce a large num-
ber of rays with different reflection angles or, rather, different transmission modes. A differ-
ent zigzag of the beam path is thus made for each mode. For a small core diameter, a single
mode propagation can be generated in a fiber.
There are many different kinds of optical fibers that have been created with different
structure, geometry, and materials, depending on the ultimate application. For instance,
the tips of the fibers can be changed to produce side-firing beams for therapeutic applica-
tions such as coagulation of prostate tissue. The fiber tips can also be tapered for pinpoint
application of the light beam or made as a diffuse tip for broad uniform application of the
light. In general, optical fibers have been classified in terms of the refractive index profile of
the core and whether there are single modes or multimodes propagating in the fiber. For
instance, as shown in Figure 17.21, if the fiber core has a uniform or constant refractive
index, it is called a step-index fiber; if it has a nonuniform, typically parabolic refractive
index that decreases from the center to the cladding interface, it is known as a graded-index
fiber; and if the fiber core is small with a low NA, only a single mode will propagate. The
graded index fibers have been shown to reduce the modal dispersion by a factor of 100
times and increase the bandwidth over a comparably sized step-index fiber. These general
classifications apply to most fibers, but special fiber geometries are often required, as
