Optical Fibers - Civil Engineering (CE) PDF Download

Optical Fibers
Optical fibers are transparent Dielectrics, which guide light over long distances with the help of successive Total Internal Reflections.

It consists of three regions
(1) The innermost Light guiding region called Core.
(2) The middle region-covering core made of material similar to Core is called Cladding. The RI of Cladding is less than that of Core.
(3) The outermost protecting layer for Core and Cladding from moisture, crushing and chemical reaction etc., is called Sheath. The Optical Fibers are either made as a single fiber or a flexible bundle or Cables. A Bundle fiber is a number of fibers in single jacket.

Principle of Optical fibres:
It is based on the principle of Total Internal reflection. Consider a ray of light passing from denser medium to rarer medium. As the angle of incidence increases the angle of refraction also increases. For a particular angle of incidence called Critical Angle the refracted ray just grazes the interface (Angle of refraction is 900 ). If the angle of incidence is greater than Critical Angle then the ray reflected back to the denser medium. This phenomenon is called Total Internal Reflection.

Propagation of light through fiber(Optical fiber as a light guide): 
The main function of the Optical fiber is to accept maximum light and transmit the same with minimum attenuation. The incident light enters the core and strikes the interface of the Core and Cladding at large angles as shown in fig. Since the Cladding has lower RI than Core the light suffers multiple Total Internal Reflections. This is possible since by geometry the angle of incidence at the interface is greater than the Critical angle. Since the Total internal reflection is the reflection at the rarer medium there is no energy loss. Entire energy is transmitted through the fiber. The propagation continues even if the fiber is bent but not too sharply. Since the fiber guides light it is called as fiber light guide or fiber waveguide.

Angle of Acceptance and Numerical Aperature
Light gathering ability of a fiber depends on two facts.
(1) Core size.
(2) Numerical Aperture.

Numerical aperture of fiber is determined by Acceptance angle. Let a light beam enter at an angle “i” to the axis of the fiber (On the launching face). The ray gets refracted at an angle “r” and strikes the Core Cladding interface at an angle θ. If θ > θ_c (Critical angle) for the system T I R takes place. It means as long as θ is greater than Critical angle light stays within the fiber.

In order to maintain θ to be greater than Critical angle, the angle of incidence relative to Axis of the fiber (At the launching face) should not be greater than a value θ₀. The ray corresponding to θ₀ can be used to describe a Conical surface. The cone formed is called Acceptance cone and the angle θ₀ is called Acceptance angle. The sine of acceptance angle (ie. sin θ₀ ) is called Numerical aperture.

Expression for Numerical Aperture Let n₀, n₁ and n₂ be the Refractive indices of Surrounding, Core and Cladding respectively. Also RI of Core is Greater than RI of Cladding (i.e n₁ > n₂). By applying Snell’s law for the Launching face of Fiber

By applying Snell’s law at ‘B’

n1 sin(90 − θ1) = n₂ sin(90)

Where (90 − θ₁) is Critical angle

Substituting for sin θ₁ in (6.1)

for air n₀ = 1

If ‘i’ is the angle of incidence at the launching face then the condition for propagation of light through the optical fiber is

sine of the angle of incidence must be less than or equal to numerical aperture Fractional RI Change(∆): 
It is the ratio of RI difference between Core and Cladding to the RI of core

Relation between NA and ∆