LIGHT PROPAGATION IN OPTICAL FIBER

2.1 Introduction

        The transmission of light via a dielectric was first suggested in 1910. Hondros and Debye conducted an experiment using a glass rod surrounded by air. In 1950, a cladded dielectric rod was introduced . It consist of a core cladded by another layer of different refractive index.The refractive index of the core is n₁ and that of the cladding is n₂ .The cladding supports the waveguide structure whilst also, when sufficiently thick, substantially reduces the radiation loss into the surrounding air.

2.2 Optical Waveguiding

There are three common type of fibers in terms of the material used:

   i. Glass core with glass cladding - all glass fiber

The refractive index range of glass is limited and this causes the refractive index difference n₁-n₂ to be small. This small value then reduces the light coupling efficiency of the fiber, i.e. large loss of light during coupling. The attenuation loss is the lowest compared to the other two fiber. It suitable for long and high capacity. Typical size for all glass fiber are 10/125 m, 62.5/l2.5 m m, 50/125 m m and 100/140 m m.

This fibers have higher loss than the all glass fiber and is suitable for shorter links. Normally, the range of refractive index achievable with plastic fibers are larger. This allows a larger range for the value of refractive index difference. Therefore the light coupling efficiency is better. Typical size are 62.5/12.5m m 50/ 125m m and 100/140 m m and 2OOm m.

iii. All-plastic fiber

This type has the highest loss during transmission. The are normally used for very short links. The core size are large therefore light coupling efficiency is high. The core size can be as large as 1mm.

2.3 Ray Transmission Theory

1.In any medium, ray travel at speed

V = c/n

c= 3x 10⁸ m/s

n = refractive index of the medium

Air, n = 1.0

Glass, n= 1.5

2 .Rays travel in straight path unless deflected by some change in the medium

3.When a ray is reflected at any boundary, the angle of reflection = angle of incidence

4. When a ray is incident on the interface between two dielectric of differing refractive indices, (e.g. glass-air) refraction occurs

5. If the ray travels from a medium with ref index n₁ into a medium with, n₂, then the following happens:

• if n₁ > n₂ , the refracted ray travels emerging away from the normal

• If n₁ < n₂ the ray emerges close to the normal

6. n varies with wavelength ,l . Normally specified at l = 589nm (yellow light from heated sodium)

7. At a particular angle of incidence, the refracted ray emerges parallel to the interface between the dielectric and this angle of incidence is known as critical angle. Any ray incidence at an angle greater than the critical angle will be reflected back into the originating dielectric medium. This phenomena is known as total internal reflection (TIR).

8. The value of critical angle is given by sin Æ _c = n₂ /n₁ where_{, Æ c} is known as the critical angle .

        Any rays which are incident into the fiber at an angle greater than the acceptance angle will not be reflected internally. Rays to be transmitted within the fiber core must be incident on the fiber core within an acceptance cone defined by the conical half angle q _a, Figure shows the propagation of light through a perfect optical fiber. It may be observed that ray A enters the fiber core at an angle q _a to the fiber axis and is refracted at the air-core interface before transmission to be core-cladding interface at the critical angle.

        As seen from figure ray B enters the core at angle grater than q _a. This ray will be refracted into the cladding and eventually lost. Thus, for rays to be transmitted through total internal reflection within the fiber core, they must be incident on the fiber core within an acceptance cone define by conical half angle q _a

For n₂ < n_1> n₀ we could get the equation for acceptance angle ,q _a.

q _a = sin ^–1 (n²₁ -n² ₂ ) ^½

        Numerical aperture (NA) relates the acceptance angle to the refractive index of the core and cladding. It gives a measure of the ability of the fiber to receive light and is desired to be as large as possible in multimode fiber.

NA = sin q _a

_{NA =}(n²₁ -n² ₂ ) ^½ = n₁ (2 ) ^½

where , = relative refractive index difference

relative refractive index different= =( n₁ -n ₂ ) / n₁

Numerical aperture is a useful measure on the light-collecting ability of a fiber. It is independent of the core size. Plastic fibers are better than glass fibers in terms of numerical aperture therefore the acceptance angle for plastic fiber are also greater.

2.4 Types of Fiber

The two types of fiber are step index fiber and graded index fiber.

        Optical fibers with a core of constant refractive index n₁ and a cladding of a slightly lower refractive index n₂ is known as step index fiber. This is because of a step variation in refractive index at the core cladding interface. This type could be multimode or single mode. The index profile may defined as:

n(r ) =   n₁, r <a     or  r£ a

and

       n( r ) = n₂ ,          r ³ a          or r> a

        This fiber do not have a constant refractive index in the core but a decreasing core index n(r) with radial distance, r from a maximum value of n₁ at the axis to a constant value n₂ beyond the core radius a, in the cladding. The index variation is described by

N(r ) = n₁ ( 1 - 2 (r /a)a )^½ ;r< a

and

N(r ) =n₁ (1- 2 ) ^½ = n₂ ; r ³ a

where , = relative refractive index difference

a =profile parameter

Normal profile is when a =2 ( parabolic profile), found to yield the best result for optical communication.

2.5 Cut-off wavelength

        The wavelength above which a particular fiber becomes single mode. If Vc is the cut-off normalized frequency and V is the normalized frequency corresponding to wavelength l , then the cutoff wavelength l c is given by:

l c/l = V/ Vc