Handbook for Sound Engineers

454 Chapter 15

between the two descriptions, depending on our needs.
For example the characteristics of many optical fibers
vary with wavelength, so the wave description is used.
On the other hand, the emission of a light by a source, a
light emitting diode (LED), or its absorption by a posi-
tive-intrinsic-negative detector (PIN), is best treated by
particle theory.

Light Rays. The easiest way to view light in fiber
optics is by using light ray theory, where the light is
treated as a simple ray drawn by a line. The direction of
propagation is shown on the line by an arrow. The
movement of light through the fiber optic system can be
analyzed with simple geometry. This approach simpli-
fies the analysis and makes the operation of an optical
fiber simple to understand.

Refraction and Reflection. The index of refraction (n)
is a dimensionless number expressing the ratio of the
velocity of light in free space (c) to its velocity in a spe-
cific medium (v)

(15-4)

The following are typical indices of refraction:

Vacuum 1.0
Air 1.0003
(generalized to 1)
Wa t e r 1. 3 3
Fused Quartz 1.46
Glass 1.5
Diamond 2.0
Gallium Arsenide 3.35
Silicon 3.5
Aluminum Gallium Arsenide 3.6
Germanium 4.0

Although the index of refraction is affected by light
wavelength, the influence of wavelength is small
enough to be ignored in determining the refractive
indices of optical fibers.
Refraction of a ray of light as it passes from one
material to another depends on the refractive index of
each material. In discussing refraction, three terms are
important. The normal is an imaginary line perpendic-
ular to the interface of the two materials. The angle of
incidence is the angle between the incident ray and the
normal. The angle of refraction is the angle between the
normal and the refracted ray.
When light passes from one medium to another that
has a higher refractive index, the light is refracted
toward the normal as shown in Fig. 15-4A. When the

index of the first material is higher than that of the

second, most of the light is refracted away from the

normal, Fig. 15-4B. A small portion is reflected back

into the first material by Fresnel reflection. The greater

the difference in the indices of two materials the greater

the reflection. The magnitude of the Fresnel reflection

at the boundary between any two materials is

approximately

(15-5)

where,

R is the Fresnel reflection,

n 1 is the index of refraction of material 1,

n 2 is the index of refraction of material 2.

In decibels, this loss of transmitted light is

.(15-6)

As the angle of incidence increases, the angle of

refraction approaches 90° with the normal. The angle of

incidence that yields a 90° angle of refraction is called

the critical angle, Fig. 15-4C. If the angle of incidence is

increased past the critical, the light is totally reflected

back into the first material and does not enter the second

material and the angle of reflection equals the angle of

incidence, Fig. 15-4D.

A single optical fiber is comprised of two concentric

layers. The inner layer, the core, contains a very pure

glass (very clear glass); it has a refractive index higher

than the outer layer, or cladding, which is made of less

pure glass (not so clear glass). Fig. 15-5 shows the

arrangement. As a result, light injected into the core and

striking the core-to-cladding interface at an angle

greater than the critical is reflected back into the core.

Since the angles of incidence and reflection are equal,

the ray continues zigzagging down the length of the

core by total internal reflection, as shown in Fig. 15-6.

The light is trapped in the core, however, the light

striking the interface at less than the critical angle

passes into the cladding and is lost. The cladding is

usually surrounded by a third layer, the buffer, whose

purpose is to protect the optical properties of the clad-

ding and core.

Total internal reflection forms the basis for light

propagation in optical fiber. Most analyses of light

propagation in a fiber evaluate meridional rays—those

which pass through the fiber axis each time they are

reflected. To help you to understand how an optical

fiber works, let us look at Snell’s Law which describes

n c

v

=--

R

n 1 – n 2

n 1 +n 2

------------------

©¹

§·

2

=

LF= –1 10 log – R dB