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Introduction
Fibre optics deals with the light propagation through thin glass fibres. Fibre optics plays an important role in the field of communication to transmit voice, television and digital data signals from one place to another. The transmission of light along the thin cylindrical glass fibre by total internal reflection was first demonstrated by John Tyndall in 1870 and the application of this phenomenon in the field of communication is tried only from
- Today the applications of fibre optics are also extended to medical field in the form of endoscopes and to instrumentation engineering in the form of optical sensors. Generally, communication is transferred through carrier waves in any communication system. When the frequencies of the carrier waves are high then the information carrying capacity also enhances. As the propagation of light takes place in the form of high frequency waves, these light waves can be used to carry information, i.e., as carrier waves. For the proper guiding of information carrying light waves, we need a proper guiding medium or material. That material is the optical fibre.
1. Optical fibre
Optical fibre is a guiding medium or material which guides the information carrying light waves. To guide the light waves, optical fibre should be transparent. To minimize the transmission losses through the optical fibre it is made thin.
Thus Optical fibre is a thin transparent guiding medium or material which guides the information carrying light waves
2. The Basic principle of optical fibre (Or) Working principle of optical fibre (or) Total
internal reflection
The transmission of light in an optical fibre is based on the phenomenon of total internal reflection. Optical fibre consists of inner most layer known as core, a denser medium and next layer is known as cladding a rarer medium.
Total internal reflection: -
Definition : When the light ray travels from denser medium to rarer medium the refracted ray bends away
from the normal. When the angle of incidence is greater than the critical angle, the refracted ray again reflects into the same medium. This phenomenon is called total internal reflection.
Let us consider n 1 and n 2 are refractive indices of core and cladding mediums. Let, a light ray traveling
from core medium to cladding medium, then the refracted ray bends away from the normal with ᡡ is the angle of incidence and ᡰ is the angle of refraction.
In this we get three cases Case I: When ᡡ 㐇 ‖〰 , the light ray refracts into cladding medium. [Figure 1]
Case II:-
When ᡡ 㐇 ‖〰 , the light ray travels along the interface of core and cladding, θ C is known as critical angle. [Figure
2]
Core medium
Cladding medium
Dr. P. Venkata Ramana
When the angle of incidence is increased angle of reflection also increases and for a particular angle of
incidence ( i = θ C )the refracted ray travels along the interface of two mediums. This angle of incidence is known
as critical angle (^ θ^ C ).
n 1 Sin θ C = n 2 Sin 90
n 1 Sin θ C = n 2 ⇒ 2 n 1
Sin n
θ C =
1
1 2 n
n θ C Sin
Case III:- When ᡡ 㐈 ‖〰 , then the light ray will be reflected back into the core medium and undergoes total internal reflection. [Figure 3]
When the angle of incidence is greater than the critical angle ( i > θ C ), the refracted ray again reflects into
the same medium. This phenomenon is called total internal reflection
3. Construction of optical fibre
The optical fibre mainly consists the following six parts as shown in figure
- Core
- Cladding
- Silicon coating
- Buffer jacket
- Strength member
- Outer jacket
Core medium
Cladding medium
Core medium
Cladding medium
Core medium
Cladding medium
Dr. P. Venkata Ramana
6. Step index fibre- refractive index profile
In step index fibre the refractive index of the core medium is uniform and undergoes an abrupt change at the interface of core and cladding as shown in figure.
The diameter of core is about 50 to 200 micrometers in case of multi mode and 10 micrometers in single mode fibre.
Attenuation is more for step index multi mode fibres but less in step index single mode fibres Numerical aperture is more for step index multi mode fibres but it is less in step index single mode fibres. This fibre is called reflective type fibre.
Transmission of signal in step index fibre
Generally, the optical signal is transmitted through the fibre in the digital form i.e., in the form of 1’s and 0’s. the propagation of signals through the multi mode fibre is shown in fibre. The transmitted optical signal will cross the fibre axis during every reflection at the core cladding boundary. The shape of propagation of the optical signal is in zigzag manner. Generally the signal through the fibre is in digital form i.e. in the form of pulses representing 0s and 1s.
From figure the ray 1 follows shortest path (i.e. travels along the axis of fibre) and the ray 2 follows longer path than ray 1. Hence the two rays reach the received end at different times. Therefore, the pulsed signal received at other end gets broadened. This is called intermodal dispersion. This difficulty is over come in graded index fibres.
7. Graded index fibre - refractive index profile:-
In graded index fibres, the refractive index of the core medium is varying in the parabolic manner such that the maximum refractive index is present at the center of the core.
The diameter of the core is about 50 micro meters. Attenuation is very less in graded index fibres Numerical aperture is less in graded index fibres This fibre is called reflective type fibre.
Transmission of signal in graded index fibre:- The shape of propagation of the optical is in helical or spiral manner. The transmitted optical signal will never cross the fibre axis during every reflection at the core cladding boundary.
To discuss intermodal dispersion, we consider two rays as shown in figure, the ray 1 is traveling along the axis of the core and the other ray 2 traveling away from the axis undergoes refraction and bent. Since, ray 2 is traveling in the lesser refractive index medium, so ray 2 moves slightly faster than ray 1. Hence the two rays reach the other end simultaneously. Thus the problem of intermodal dispersion can be overcome by using graded index fibre.
8. Single mode optical fibre:-
In single mode optical fibres only one mode of propagation is possible. These fibres have small core diameter and the difference between the refractive indices of core and cladding is very small. In single mode fibres there is no dispersion, so these are more suitable for communication. The single mode optical fibres are costly, because the fabrication is difficult. The process of launching of light into single mode fibres is very difficult. Fabrication is very difficult and the fibre is costly. The condition for single mode operation is
V a NA
Where a is the radius of the core of the fibre, n 1 is the refractive of the core, NA is the numerical
aperture and λ is the wave length of light traveling through the fibre
According to Snell’s law at point A ᡦ⡨ sin ‖⡨ 㐄 ᡦ⡩ sin ‖⡩
sin ‖⡨ 㐄
sin ‖⡩
According to Snell’s law at point B ᡦ⡩ sin䙦90 ㎘ ‖⡩䙧 㐄 ᡦ⡰ sin 90 ᡦ⡩ cos ‖⡩ 㐄 ᡦ⡰
cos ‖⡩ 㐄
sin ‖⡩ 㐄 㒓䙦1 ㎘ cos⡰^ ‖⡩䙧
sin ‖⡩ 㐄 㒕䙲1 ㎘ ぁㄘ
ㄘ ぁㄗㄘ䙳^ 㐄^
㒓䙦ぁㄗㄘ⡹ぁㄘㄘ䙧 ぁㄗ
sin ‖⡨ 㐄
ぁㄗ ぁㄖ^ sin ‖⡩^ 㐄^
ぁㄗ ぁㄖ
㒓䙦ぁㄗㄘ⡹ぁㄘㄘ䙧 ぁㄗ^ 㐄^
㒓䙦ぁㄗㄘ⡹ぁㄘㄘ䙧 ぁㄖ
sin ‖⡨ 㐄
㒓䙦ぁㄗㄘ⡹ぁㄘㄘ䙧 ぁㄖ
‖⡨ 㐄 sin⡹⡩^ 㐷
㒓䙦ᡦ⡩⡰^ ㎘ ᡦ⡰⡰䙧
Acceptance angle ‖⡨ 㐄 sin⡹⡩^ 㐶
㒓䙦ぁㄗㄘ⡹ぁㄘㄘ䙧 ぁㄖ^ 㑀
13. Acceptance cone
Definition:- A cone obtained by rotating a ray at the end face of an optical fibre, around the fibre axis with acceptance angle is known as acceptance cone.
14. Numerical aperture
Definition : -
Numerical aperture is defined as the light gathering capacity of an optical fibre and it is directly proportional to the acceptance angle.
Numerically it is equal to the sin of the acceptance angle. ᡀᠧ 㐄 sin䙦ᡓᡕᡕᡗᡨᡲᡓᡦᡕᡗ ᡓᡦᡙᡤᡗ䙧
Dr. P. Venkata Ramana
Dr. P. Sreenivasulu Reddy M.Sc , PhD www.engineeringphysics.weebly.com Page 8
( )
0
2 2
2 1 1 n
n n NA Sin Sin
( )
0
2 2
2 1 n
n n NA
If the refractive index of the air medium is equal to unity then
NA = ( n 12 − n 22 )
Fractional change in refractive index
1
1 2 n
n − n ∆ =
n 1 ∆= ( n 1 − n 2 )
NA = ( n 1 − n 2 )( n 1 + n 2 )
NA = n 1 ∆ ( n 1 + n 2 ) Q n 1^ ∆=(^ n 1 − n 2 )
NA = n 1 ∆ 2 n 1 Q n 1^ ≈ n 2 ;^ n 1 + n 2 =^2 n 1 NA = n 1 2 ∆
The above equation gives a relationship between numerical aperture and fractional change in relative refractive index.
15. Optical fibre communication system
An efficient optical fibre communication system requires high information carrying capacity, fast operating speed over long distances with a minimum number of repeaters. An optical fibre communication system mainly consists of the following parts as shown in figure.
- Encoder Encoder is an electronic system that converts the analog information like voice, figures, objects etc., into binary data.
- Transmitter It contain two parts, they are drive circuit and light source. Drive circuit supplies the electric signals to the light source from the encoder in the required form. The light source converts the electrical signals into optical form. With the help of specially made connector optical signals will be injected into wave guide from the transmitter.
Electric signal input
Encoder Drive Circui t
Light Sourc e
Photo Detector
Signal Restorer Amplifier
Analog Input
Decoder Analog Output
Transmitter
Wave guide
Receiver
Dr. P. Venkata Ramana
Dr. P. Sreenivasulu Reddy M.Sc , PhD www.engineeringphysics.weebly.com Page 10
17. Differences between step index fibres and graded index fibres:-
Step index fibre Graded index fibre
- In step index fibres the refractive index of the core medium is uniform through and undergoes an abrupt change at the interface of core and cladding.
- In graded index fibres, the refractive index of the core medium is varying in the parabolic manner such that the maximum refractive index is present at the center of the core.
- The diameter of core is about 50 to 200 micrometers in case of multi mode and 10 micrometers in single mode fibre
- The diameter of the core is about 50 micro meters.
- The transmitted optical signal will cross the fibre axis during every reflection at the core cladding boundary.
- The transmitted optical signal will never cross the fibre axis at any time.
- The shape of propagation of the optical signal is in zigzag manner.
- The shape of propagation of the optical signal appears in the helical or spiral manner
- Attenuation is more for multi mode step index fibres but Attenuation is less in single mode step index fibres
- Attenuation is very less in graded index fibres
- Numerical aperture is more for multi mode step index fibres but it is less in single mode step index fibres
- Numerical aperture is less in graded index fibres
18. Differences between single mode and multi mode fibres:-
Single mode fibre Multi mode fibre
- In single mode optical fibres only one mode of propagation is possible
- In multi mode optical fibres many mummer of modes of propagation are possible.
- These fibres have small core diameter and the difference between the refractive indices of core and cladding is very small.
- These fibres have large core diameter and the difference between the refractive indices of core and cladding is also large compared to the single mode fibres.
- In single mode fibres there is no dispersion, so these are more suitable for communication.
- Due to multi mode transmission, the dispersion is large, so these fibres are not used for communication purposes.
- The process of launching of light into single mode fibres is very difficult
- The process of launching of light into single mode fibres is very easy.
- The condition for single mode operation is
V a NA λ
2 π
V λ an 1
π
Multi mode optical fibre
- The condition for multi mode propagation is 2
= ^ •
d NA
N
Where d the radius of the core of the fibre and NA
is the numerical aperture.
- Fabrication is very difficult and the fibre is costly.
- Fabrication is very easy and the fibre is cheaper.
Dr. P. Venkata Ramana
