UNIT-II
FIBER OPTICS
OPTICAL FIBERS
An Optical fiber is a thin long cylindrical fiber of glass or any transparent dielectric
medium in which light is transmitted through multiple total internal reflection.
Principle:
An optical fiber works on the principle of total internal reflection. Total internal
reflection occurs when light travels from a denser medium to rarer medium. Light that is
launched into an optic fiber undergoes total internal reflections at the boundary between the core
and the cladding. The core has a refractive index larger than that of the cladding. Light that
enters the core is made to reflect off the interface of the core & cladding by total internal
reflection such that no light is lost. Light eventually bounces back and forth along the entire
length of the fiber and emerges out. For total internal reflection to take place the incident light
must be confined to a cone whose vertex angle ‘’ should not be greater than a certain allowed
value. This value of the angle is called the acceptance angle.
Construction:
An optic fiber consists of a core (roughly 10-50 m radius) made of a transparent
material like glass or plastic, a cladding surrounding the core (50-150 m radius) also made of a
transparent material and a protective jacket made of opaque material (Polyurethane).
The cladding not only helps in total internal refection for light but also ensures
mechanical strength of the fiber. The protective coating prevents damage to the fiber in the form
of scratches.
1 Fiber Optics
Optical fiber and total internal reflection:
Optical fibers are based on the principal of total internal reflection. The cladding in a
optical fiber always has a lower refractive index than that of the core. The light signal which
enters into the core can strike core-cladding interface at large angles. These angles are greater
than critical angle of core-cladding boundary. Therefore, the light signal under go reflection after
reflection, with in the fiber. Since each reflection is a total internal reflection the light confines it
self completely with in the core during propagation.
Acceptance Angle, Acceptance Cone and Numerical Aperture (NA):
Consider an Optical fiber inot which light is launched. Let the refractive index of the core
n1 and the refractive index of the cladding be n2 but in optical fibers n1 > n2.
2 Fiber Optics
Let n0 be the refractive index of the medium from which light is launched into the fiber.
Suppose a light ray OA enter into the fiber at an angle θi to the axis of the fiber. The ray refractes
at an angle θr and strikes the core-cladding interface at an angle φ (shown in figure).
If φ is greater than critical angle φc, the ray under goes total internal reflection at the corecladding interface. As long as the angle φ is greater than φc the light will stay within the fiber.
Let us calculate the incident angle θi for which φ > φc
Applying Snell’s law at the point of entry of the ray OA into the core, we get
……………..(1)
If θi is increased beyond a limit, φ will drop below the critical value φc and ray enter into
the cladding. The maximum value of θi = θm occurs when φ = φc.
Applying Snell’s law at the core-cladding boundary where light ray incident with critical
angle φc .
…………(2)
From ∆ ABC θr + φc = 900
θr = 900 - φc
3 Fiber Optics
From Equation (2)
If the surrounding medium is air n0=1
The angle θm is called the Acceptance angle of the fiber. This angle is a measure of the
light gathering power of the optical fiber.
Acceptance angle may be defined as the maximum angle that light ray can have relative
to the axis of the fiber so that it propagates down the fiber under total internal reflection.
The light rays contained within the cone having angle 2θm are accepted and transmitted
along the fiber. Therefore, the cone is called the acceptance cone. Light ray incident beyond this
cone refracts into cladding.
4 Fiber Optics
The Numerical Aperture is defined as the sine of the acceptance angle
Where
is fractional difference between the core refractive index and the
cladding refractive index.
Numerical Aperture determines the light gathering ability of the fiber. It is a measure of
the amount of light that can be accepted by a fiber.
5 Fiber Optics