Lecture notes Introduction to quantum mechanics

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Fiber Optics
Optical fiber is a cylindrical wave guide made of glass or plastic which transmits data in the form of
electromagnetic radiation at optical frequencies by the principle of total internal reflection (TIR).

Principle of propagation of light through an optical fiber: Total internal Reflection
This occurs when a light beam travelling in an optically denser medium of refractive index (n 1) is
incident on another medium of refractive index (n 2) with n1 >n2, at an angle greater than critical
angle.
The critical angle c is defined as the angle of incidence for which the light ray will graze along the
interface between the two media and is given as Sinc = (n2/n1). When a light ray travels from a
denser medium to a rarer medium, there exist three possibilities for the light ray to undergo
depending on the angle of incidence as in fig 4.31.
Let i be the angle of incidence, r be the angle of refraction and c Fig.4.31
be critical angle.
Case (1): when I <c, the angle incidence is less than the critical
angle, the light ray refracts into the second medium.
Case (2): when I =c, the angle incidence is equal to the critical
angle, the light ray grazes along the interface between the two
media.
Case (3): when
Construction of anIoptical
>c, the angle incidence is greater than the
fiber
critical angle, the light ray reflects
The construction of a typical optical into theessentially
fiber same medium.
consists of core, Fig: 4.32
cladding and the protective jacket as shown in fig 4.32. The core and
cladding are made up of either glass or plastic whose values of
refractive indices differ very slightly. The core is the wave guide that
caries light through the fiber via total internal reflection. The main
functionality of cladding is to confine light only to the core of the
fiber. The protective jacket is made up of a polyurethane material
which protects the fiber from mechanical stresses, abrasions, and
outer changes.
A typical glass fiber consists of a central core of thickness 10-100 microns surrounded by a
cladding of diameter 150-200 microns. By using the outer jacket, the fiber cable will not be damaged
during hard pulling, bending, stretching, or rolling though the fiber made up of brittle glass.

Acceptance Angle and Numerical Aperture (NA)
The maximum entrance angle on the core for which the light ray travels through the core of the fiber
by total internal reflection is known as acceptance angle.
Expression for Acceptance angle and Numerical aperture
Let us consider a cross sectional view of an optical fiber along its length as shown in figure 4.33. Let
n0, n1 and n2 are the refractive indices of the outer medium (air), core and the cladding such that n 0 <
n1> n2.
Let the light ray OA strikes the core at the interface of air medium with an angle of incidence 0
and refracts into the core with an angle of refraction 1. The refracted ray AB is again incident on the
core-cladding interface at an angle 90-1. If this 90-1 is equal to the critical angle of the core and
cladding media, then the ray grazes along the interface of core and cladding along path BC.
If a ray enters the core of the fiber at an angle greater than 0, it will refract into the fiber at angle
greater than 1, then after falling on the core-cladding interface it would refract into cladding
medium and gets lost. This is because the angle of incidence (90-1) at the core-clad interface is less
than the critical angle. But if the angle of incidence at the surface of the core is < 0, then 90-1 will be
greater than the critical angle. Therefore, total internal reflection takes place, and the light ray

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continues to propagate through fiber by multiple reflections. Hence 0 is the maximum entrance
angle on the core surface for which the light ray is confined to travel through core of the fiber. This
is known as the Acceptance angle.




Fig. 4.33
According to Snell’s law, at point A,

=> [1]
According to Snell’s law, at point B,


Is => [2]


[3]
Substituting equation [3] in equation [1],


[4]



Acceptance angle = [5]
Acceptance Cone
If the acceptance angle is rotated around the axis of the fiber in all the directions, it forms a cone of
semi-vertical angle 2o which is called as acceptance cone. Every light ray falling in the cone would
be allowed to travel through the core of the fiber. Thus, acceptance angle is also called as acceptance
cone-half angle.
Numerical Aperture (NA)
The light gathering capability of a given fiber is known as numerical aperture. It is numerically equal
to the sign of acceptance angle.


, For air medium no=1
Mode of propagation
An independent path provided for the light ray to transmit through the optical fiber is known as
Mode of propagation. Depending upon the number of paths available for propagation the fibers can
be classified into 2 categories, a single mode fiber and a multi-mode fiber.

Types of Fibers
Based on refractive index profile, the optical fibers are classified into 2 types.
1. Step index fiber 2. Graded index fiber
2.
Step index fibers Fig.4. 34(a) Fig.4.34(b)