OPTICAL FIBER

Chapter 1 Introduction to Basic theory

__________________________________________________Communication may be broadly defined as the transfer of information from one point to

another. When the information is to be conveyed over a distance a ‘Communication’ system

is required. Within the communication system the information transfer is often achieved by

superimposing or modulating the information into an Electromagnetic wave which acts as a

carrier for the information signal. This modulated carrier is then transmitted to its destination

where it is received and the original information is retrieved by Demodulation. Over the years

sophisticated techniques have been developed for the process using EM carrier waves

operating at Radio, Micro and millimetre wavelengths. Communication may also be achieved

by using EM waves from the Infra-Red and Optical range of frequencies. This involves the

use of Optical Fiber technology

1.1 Evolution of Fiber-Optic Communication

Contrary to popular belief the use of light for communication has been common for several

years. Simple systems such as Fire Signals, Reflection mirrors, Signalling lamps etc. have

proved successful, although limited in transferring information. As early as 1880 Alexander

Graham Bell reported the transmission of speech using a light beam. In fact the Photophone

as the device was called invented four years before the telephone modulated sunlight using a

diaphragm to transmit speech. Optical communication did not meet with much success due

various reasons. Some of these reasons were

(a) Lack of suitable light source.

(b) Light transmission in atmosphere is restricted to line of sight.

(c) Light is severely affected by disturbances such as rain, snow, fog, mist dust and

atmospheric turbulences etc.

These problems were greatly overcome with lower frequency (higher wavelength) EM waves

in the radio and microwave regions. The only limitation of these waves was the amount of

information they could carry. The amount of information that can be carried is directly

related to the bandwidth of the frequency extent by modulated carrier, which is a fixed

fraction of the carrier frequency. Theoretically information carrying capacity is directly

proportional to the carrier frequency. This region of the EM spectrum has been exploited to

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OPTICAL FIBER

the maximum extent with the development of VHF, UHF, millimetre and microwave

communication. These cover a frequency range ~ 0 to 1012 Hz (5000km > λ > 0.3mm). Now

the Infra- Red from the far Infra- Red to the optical span a frequency range of 1012 – 1015

~1016Hz (0.3mm > λ > 0.4 µm). It is obvious that communication in optical frequencies

increases the potentially usable bandwidth by a factor of 103 – 104.

Interest in optical communication was renewed in the early 1960’s with the invention of

LASER, which provided a coherent, intense, monochromatic low divergent light beam which

offered the possibility of modulation at high frequencies. However the previously mentioned

problem of atmospheric transmission limited the free space communication system based on

LASER to short distances (E.g.: Linking TV cameras to base vehicle, data link between

buildings~ 100m etc.). The breakthrough was achieved in 1966 with the development of

dielectric waveguides or Optical Fibers fabricated with glass to avoid degradation of signal

by atmosphere. Such systems were viewed as replacement for coaxial or cable transmission

lines based systems. Initially the Fibers exhibited very high attenuation ~1000dB/Km and

hence were not comparable to metallic coaxial cables which had an attenuation ~ 5 – 10

dB /Km. other problems involved joining of Fibers to achieve low loss. Nevertheless with a

span of about 10 years Fiber losses were reduced to less than 5dB/Km and suitable low loss

joining techniques were perfected.

Simultaneously attention was diverted to fabricate other optical components which would

constitute an optical communication system based on optical Fibers. Due to the extremely

low wavelength of Infra-red and optical waves, new technology was required. Semiconductor

optical sources (Injection LASER, LED) and detectors (Photo diode, Phototransistor) etc

were fabricated to enable a full-fledged optical communication system.

1.2 Understanding Communication Systems

The function of a communication system is to convey the signal from the Information source

to its destination over a transmission medium. A schematic block diagram of a general

Communication system is shown in fig 1.1. We shall first describe the functions of the

various components of an Electrical Communication system.

1. Information source: This provides an electrical signal, usually derived from a message

signal which is not electrical (sound/video) to the transmitter

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OPTICAL FIBER

2. Transmitter: The transmitter has electrical and electronic components converts the

electrical signal into a suitable form for propagation over a transmission medium. This is

usually achieved by modulating a carrier (generally an EM wave).

Fig 1.1 the General Communication System

3. Transmission Medium: This can be a Pair of wires, A Co-axial Cable or a Radio link

through free space down which the signal is transmitted to the receiver.

4. Receiver: The receiver demodulates the incoming signal from the carrier into the original

electrical signal and is passed to the destination, where it is reconverted back to the original

audio or video information

It must be noted that in any transmission medium the signal is attenuated i.e. suffers losses

and is subject to degradations due to contamination by random signals and unwanted noise as

well as distortions imposed by the medium itself. Hence in any communication system there

is a maximum distance between the transmitter and the receiver, after which the signal

becomes unintelligent. For long distance communication we need Repeaters or line amplifiers

at regular intervals both to remove signal distortion and to increase signal strength.

Fig 1.2 An Optical Fiber Communication system

1. Information Source: This provides an electrical to an electrical transmitter.

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DestinationReceiver Demodulator

Transmission Medium

Transmitter Modulator

Info Source

Destination

Optical Fiber Cable

Optical Source

Electrical Transmit

Info Source

Optical Detector

Electrical Drive

OPTICAL FIBER

2. Electric transmitter: This drives an Optical Source to give a modulated Light wave

3. Optical Source: This is an Electro-Optic Converter like a Semiconductor LASER or a

LED

4. Optical Fiber Cable: This is the Transmission Medium

5. Optical Detector: This is the receiver which acts as a demodulator and drives another

electrical drive to provide electrical signal from which the original information is recovered

and sent to its destination. Photo Diode (like P-N, P-I-N, Avalanche), Photo transistors and

Photoconductors are utilized for this purpose

We note the need for electrical interfacing at either end of the optical link and at present the

signal processing is done electrically (Recently at lot of work is being done in the area of

optical signal processing)

Modulation of the optical carrier wave.

The optical carrier may be modulated using either an analog or Digital information system.

In analog modulation the intensity of light emitted from the optical source is varied in a

continuous manner, While in Digital modulation discrete changes are made in the intensity

of light. Even though analog modulation is simpler to implement it is less efficient requiring a

higher Signal to Noise ratio at the receiver than digitally modulated signals. Also the linearity

need for analog modulation is not often provided by the semiconductor optical sources,

especially at high frequencies. Thus analog optical Fiber communication links are limited to

short distances and lower bandwidth operation.

1.4 Advantages of Optical Fiber Communication

There are several advantages of an optical Fiber communication system over conventional

communication system. We list below some of its more attractive features.

1. Enormous Potential Bandwidth. The optical frequency in the range 1013 to 1016 ( Near IR

around 1014 to 1015) yields a far greater potential bandwidth than metallic co-axial cable

systems or even millimetre wave radio systems. The table below lists the Bandwidth length

product for a coaxial, millimetre wave radio system and optical Fiber system. We note the

tremendous increase in Bandwidth and hence information carrying capacity of optical Fibers.

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OPTICAL FIBER

Bandwidth length product usually expressed in MHz km

is a parameter that characterises the information carrying

capacity of a Fiber. There is usually a trade-off between

the Bandwidth of the signal and the distance it can be

carried. For example, a common multi-mode Fiber with

bandwidth–distance product of 500 MHz·km could carry a

500MHz signal for 1km or a 1000MHz signal for 0.5km.

2. Small Size and weight. Optical Fibers have very small diameters often less than the diameter of a

human hair. So, even when they are covered with protective coatings and coverings they are much

smaller and lighter than metallic cables. This obviously reduces cost and makes it ideal for

application in ships, aircrafts satellites etc.

3. Electrical isolation. Optical Fibers are fabricated with glass and polymers which are electrical

insulators. This reduces electrical hazards such as arcing or sparks short circuits etc.

4. Immunity from Interference and Cross talk: Optical Fibers are dielectric waveguides and

therefore free from electromagnetic interference. It requires no Electromagnetic shielding. It is also

not susceptible to lightning strikes if used overhead. Most importantly it is much easier to ensure

there is no optical interference between Fibers (unlike electrical interference between electrical

conductors) and hence Cross talk is negligible

5. Signal Security: The light from optical Fibers does not radiate significantly and therefore provide a

high degree of signal security. Unlike the situation with copper cable a transmitted optical signal

cannot be obtained from a Fiber in a non-invasive( i.e. without drawing power from the cable).

Hence in theory any attempt to acquire a message signal transmitted optically can be detected. This

feature is particularly attractive for Banking, military and general data transmission (i.e. Computer

network applications)

6. Low Transmission Loss: As mentioned earlier optical Fiber has extremely low attenuation

compared with the best copper cable. This reduces the number of repeaters which has an impact on

cost

7. Ruggedness and Flexibility: Although protective coatings are essential Fibers with high tensile

strength have been manufactured. The Fibers may be bent into small radii and twisted without

damage. In terms of size and weight these Fibers are far superior in terms of storage, maintenance,

handling, transportation and installation compared to copper cables

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Coaxial

Cable

100MHz km

Millimetre

Radio system

150MHz km

Optical Fiber 5000GHz km

OPTICAL FIBER

8. System reliability and maintenance: This feature is due to the loss property of optical Fibers,

which reduces the requirement for line amplifiers or repeaters. Hence with fewer boosters, system

reliability is generally enhanced. Furthermore the optical components easily have a life of 20 to 30

years requiring low maintenance.

9. Low cost potential: The glass which is generally used for manufacture of optical Fiber used silica

or sand, which is available in plenty. This straightaway reduces the cost.

1.5 Optical Fiber waveguides

Optical fiber is a dielectric waveguide that operates on Infra-Red and optical frequencies. The

fiber guide is usually cylindrical in form. It confines Electromagnetic energy in the form of

light to within its surface and guides the light in a direction parallel to its axis. The

transmission properties of an optical waveguide are dictated by its structural characteristics.

This determines how an optical signal is affected as it propagates along the fiber.

Theoretical description of propagation of light.

Electromagnetic wave description

The propagation of light along a waveguide can be described in terms of a set of guided

electromagnetic waves called Modes of the waveguide. These guided modes are referred to

as Bound or Trapped modes of waveguide. Each guided mode is a pattern of Electric or

Magnetic field lines that is repeated along the fiber at intervals equal to wavelength. Only

certain discrete numbers of modes are capable of propagating along the guide. These modes

are those that satisfy by the homogeneous wave function in the fiber and the boundary

condition at the waveguide surfaces.

Geometrical Optics- ray description

Another method of studying the propagation characteristics of light in an optical fiber is the

geometric optics or ray tracing approach. This method is a good approximation when the

ratio of fiber radius to wavelength is large (r/λ >> 1). This is known as large wavelength

limit. [Strictly valid for the limit λ → 0] It is however reasonably accurate and extremely

valuable for non- zero wavelength when the number of guided modes is large,.i.e.for

multimode fiber.The main advantage of ray tracing method is it gives physical interpretation

of light propagation characteristics in a fiber.

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OPTICAL FIBER

Fiber Types

The transmission of light via a dielectric waveguide was first proposed and investigated in the

beginning of the twentieth century. However a transparent dielectric rod typically of silica

glass with a refractive index of ~1.5 surrounded by air proved impractical due to its

unsupported structure and extremely high loss at the glass-air interface. Around 1966 the

invention of Clad Waveguide (fig 1.3) which consists of a transparent dielectric Core of

refractive index n1 surrounded by another transparent dielectric (medium) Cladding of lower

refractive index n2 completely revolutionised optical Fiber systems. We shall now study the

propagation of light through such structures using two models (a) Ray Theory (b)

Electromagnetic mode (wave) theory

Fig 1.3 Optical Fiber (wave guide) showing Core /Cladding structure

Why we need Cladding.

(1) It can be shown from Electromagnetic theory that to guide an EM wave in a cylindrical

dielectric the difference between the Refractive index of the dielectric and the surrounding

medium at the boundary or interface between the dielectric and surrounding should be very

small. So merely having a core surrounded by air will not suffice.

(2) It adds mechanical strength and protection to the core as well

(3) It protects core from absorbing surface contaminants.

(4) Cladding reduces scattering loss, resulting from dielectric discontinuity at the core surface.

Material used for Optical fibres- Why Glass is preferred. In low/medium loss fiber the

core material is generally glass and is surrounded by another glass or plastic, while high loss

plastic core fiber is also available.. Most fibers are encapsuled in elastic abrasion resistant

plastic material. It adds further strength to the fiber and mechanically isolates or Buffers the

fiber from small geometrical irregularities, distortion, and roughness of adjacent surfaces.

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Core

CladdingBuffer

OPTICAL FIBER

This perturbation can otherwise cause losses induced by random microscopic bends that arise

when fibers are incorporated into cables.

Materials used for a fibre must satisfy the following

1. Two material that are transparent in the same operating wavelength with slightly different

refractive indices.

2. The dielectric material should have low attenuation ( < 5dB/Km)

3. Good thermal and mechanical properties.

4. Should be capable of being made into thin fiber of small diameters( particularly for large

Band width > 5GHz)

5. Transparent only to the operating wavelength to guide light effectively.

The material which satisfies all the above criteria is glass (and some plastic of late). Further

graded Index Fiber ( i.e. fiber with gradually varying Refractive Index) can be fabricated with

glass but not so with plastic. (It suffers from very high attenuation). So generally Plastic is

used for short distance communication while Glass is universally preferred for long distance

communications

Also glass is made by fusing a mixture of metal Oxide, Sulphides, Selenides, etc. with

Silica( SiO2) The material has a randomly connected network structure rather than a well-

defined crystalline structure. So it does not have a well-defined melting point. It remains a

solid over several hundred degree Celsius above room temperature as a solid, and becomes a

viscous liquid only at very high temperature. This is a major advantage. To produce two

transparent material of different refractive indices Silica is doped with Fluorine and other

oxides like GeO2, P2O2, Al2O3 which increases the refractive index and B2O3 which decreases

the refractive index.

Material for Core Material for Cladding

P2O2 - SiO2 SiO2

SiO2 B2O3 – SiO2

GeO2- SiO2 SiO2

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OPTICAL FIBER

1.6 Propagation of light through an Optical Fiber.

LOW INDEX CLADDING n2

HIGH INDEX CORE n1

Fig 1.4 The passage of light through a perfect optic Fiber

As seen in figure 1.4 the mechanism by which light propagates along a Fiber is by a

series of Total internal reflection which occurs at the interface between the two dielectric

media, of different refractive index, the core and the cladding.( the difference ~1%).Clearly

such propagation occurs with low loss. The ray has an angle of incidence ϑ > θC at the

interface and is reflected at the same angle. The ray shown in figure 1.4 is known as

Meridional ray as it passes through the axis of the Fiber after each reflection. This type of

ray is the simplest to describe while describing the fundamental properties of transmission.

There are other types of rays as well as we shall see in the following sections. The reason

why a cladding is need is two fold

It must be noted that the light transmission illustrated in fig 1.4 assumes a perfect Fiber with

no discontinuities or impurities at the core-cladding boundary, which would result in

refraction rather than total internal reflection leading to loss of ray into the cladding

1.7 Acceptance angle

Since only rays striking the core-cladding interface at angles greater than the critical angle are

propagated through the Fiber it is clear that not all rays entering the Fiber will continue to be

propagated through the Fiber.

The geometry of launching a ray into the Fiber is illustrated in fig 1.5 which shows a

Meridional ray BC incident at the critical angle θC, at the core cladding boundary. We see that

his ray enters the core at an angle θA to the Fiber axis and id refracted at the air-core interface

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OPTICAL FIBER

before being incident at θC at the core-cladding boundary. A ray entering the Fiber at an angle

greater than θ is shown with dotted line. We see that this ray strikes the core-

Cladding boundary at angle less than θC and hence is refracted into the cladding (does not

suffer total internal reflection).

Fig 1.5 Acceptance Angle/Cone

Cladding

Acceptance Cone θA Core

Hence for rays to be transmitted by TIR within the Fiber core they must be incident on the

Fiber core at angles less than θA. Thus θA is the maximum angle which a ray entering a Fiber

can make with the axis of the core in order to be transmitted wihin the core by TIR. θ A is

called Acceptance angle. From symmetry considerations it may be noted that the output

angle of the ray emerging from the Fiber w.r.t core axis will be equal to the input angle,

assuming the ray emerges into a medium of same refractive index from which it was input

( say air)

Acceptance Cone: The cone whose semi vertical angle is θA is called Acceptance cone. All

the rays within the acceptance cone are transmitted within the core by TIR

Expression for Acceptance angle

Let the ray enter the Fiber from a medium of refractive index nO (generally air for which nO =

1) at an angle θ less than the acceptance angle θA for the Fiber. Let the refractive index of the

core be n1 and that of the cladding be n2. Let the angle of refraction at be θ1 Assuming the

entrance face of the core is normal to the axis and considering refraction at the core face we

have from Snell’s law.

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Eventually lost by radiation

OPTICAL FIBER

Cladding n2 C θ B D Core Axis n1

A nO

nO Sin θ = n1 Sinθ1Considering the right angled triangle BCD we have the angle of incidence at the core

cladding interface α = (π/2) – θ1 Note that α > θC the critical angle for the core cladding

interface. Hence we have

nO Sin θ = n1 Sin (π/2 – α) = n1 Cos αnO Sin θ = n1 √1- Sin2α

When the limiting case is considered α becomes θC and θ becomes θA. In that case we have nO Sin θA = n1 √1- Sin2θCSubstituting for Sin θC = (n2/n1) and simplifying we get nO Sin θA = (n12 – n22)1/2 or Sin θA = {(n12 – n22)1/2}/nONumerical Aperture (NA): The quantity nO Sin θA is called the numerical Aperture of the

Fiber. Its square is a measure of the light gathering power of the system. Thus for a Fiber we

have

NA = (n12 – n2

2)1/2 ---------------------------------------------- (1)

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OPTICAL FIBER

Since SinθA cannot exceed 1 and in air nO ~ 1 it means the largest value of NA is 1.In this

case the acceptance angle is 90O and the Fiber totally internally reflects all the light entering

its face. Fibers with a wide variety of NA ranging from 0.2 to 1 are commercially available

Note: Generally n1 is only a few per cent greater than n2. Hence (n1 + n2) ≈ 2n1

Therefore we have nO SinθA = √n12 – n2

2 = √(n1 + n2)(n1 n2) = √2n1 (n1-n2)

N.A = √2n12 {(n1-n2)/n1} = n1√2 ∆ ------------------------------- (2)

Where ∆ = {(n1-n2)/n1} is known as the relative fractional refractive index. Both equation 1)

and (2) are very useful measure of the light gathering ability of the fiber.

1.8 Skew Rays – Alternate paths

There is another kind of ray that propagates through the fiber. This ray does not pass through

the axis the fiber. The ray gets reflected at the core-cladding boundary at such an angle that it

traces a helical path around the fibre. A possible path of propagation of skew rays is shown in

Fig 1.6 View A, provides an angled view and view B provides a front view. Skew rays

propagate without passing through the axis of the fiber. The acceptance angle for skew rays is

larger than the acceptance angle of Meridional rays. This condition explains why skew rays

outnumber Meridional rays. Skew rays are often used in the calculation of light acceptance in

an optical fiber. The addition of skew rays increases the amount of light capacity of a fiber. In

large NA fibers, the increase may be significant. The addition of skew rays also increases the

amount of loss in a fiber. Skew rays tend to propagate in the annular region near the edge of

the fiber core and do not fully utilize the core as a transmission medium. A class of skew

rays, known as leaky rays, loses energy to the cladding or the surrounding medium as they

travel along the fiber. Skew rays do not obey the mathematical formulas developed for

Meridional rays. For instance the NA for skew rays depends on the acceptance angle and the

angle γ between the skew ray and the radius of the fiber.

N. A = nO Sin θA Cos γThe above equation shows that the N.A for skew ray is actually larger than that of a Meridional ray. Light injected into a fiber outside of the normal acceptance angle may still propagate as a skew ray in the fiber.

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OPTICAL FIBER

Skew rays also offer an advantage when light exits the fiber. The angle that the skew ray leaves a fiber does not depend on the conditions under which it entered the fiber as it does with Meridional rays. Skew rays are

complimentary to the Meridional rays in the sense that if the light input to the fiber is non-

uniform, skew rays will tend to have a smoothing effect on the distribution of the light as it is

transmitted, giving a more uniform output.

Fig 1.6 (A)

Fig 1.6 (B) View from a plane normal to the fiber axis

1.9 Fiber Bundles:

In any practical application of Optical waveguide technology a number of fibers are bound

together in a Cable. The structure of the cable depends on the application to which it is put. It

also depends on a number of factors like whether the cable is used underground, within the

building, connected to outdoor poles, used underwater etc. However the basic structure is

common to most cables. The factors that should be considered in designing a fiber are

(1) The mechanical strength/ Maximum allowable axial load

(2) Strength and flexibility required.

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OPTICAL FIBER

(3) Room for stretching

(4) Brittleness/ Tolerance to impact

(5) Corrosion/ Lateral forces etc.

A typical fiber structure is shown below Fig 1.10. It shows standard configuration with

commonly used material. Individual fibers or modules of bundled fiber groupings and

optional copper wires for powering in-line equipment are wound closely around the central

buffered strength member. A cable wrapping tape and other strength members such as

Kevlar (High tensile Organic yarn) then encapsulate and bind these fiber groupings together.

Surrounding all these components crush resistance and handles the tensile stresses applied to

the cable. This ensures that the fibers inside are not crushed. The jacket also protects the

fibers inside is a tough polymer jacket that provide against abrasion, moisture, oil, solvents

and other contaminants Yarn Strength

material

PVC Jacket

Outer Sheath Basic Fiber Building Block

Buffered Strength material

Plastic Binding Tape

Fig 1.7 A typical Fiber Bundle

A large number of fibers are put together to form a bundle. A bundle consists of thousands of

individual fibers. The diameter of a bundle varies from 2 x 10-4cm to 1 x 10-3cm. If the

relative positions of the fibers at the input and output ends are the same, the bundle forms a

‘Coherent” bundle. These bundles are often used for direct transmission of images and find

application in Fiber optic Endoscope.

Fig 1.8 Coherent Bundle

1.10 Types of Optical Fibers

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OPTICAL FIBER

Optical fibers can be classified based on the material with which they are fabricated, the way

the Refractive index of the core varies across its cross section and the number of modes the

fiber can carry. Based on the material an optical fiber may have a glass core and a glass

cladding, a glass core and a plastic cladding or a plastic core and a plastic cladding.

Based on the variation of Refractive index of the core we have

(1) Step Index Fiber (2) Graded Index fiber

Step Index Fiber.

In this case the core has a constant refractive index surrounded by a cladding of lower

constant refractive index.

Graded Index Fiber

In graded index fibers the refractive index of the core varies radially outward being maximum

at the axis of the fiber and decreasing radially outwards reaching the value of the Cladding

index at the Core-Cladding boundary. The refractive index Profile of Step index and graded

index fibers are as shown in figure 1.11 (a) and 1.11 (b) respectively. The shape of the

Refractive index profile of graded index fiber can vary for different kinds of fiber depending

on the application.

Step Index Profile Graded Index fiber

n

fig 1.9 (a) fig 1.9 (b)

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OPTICAL FIBER

The refractive index profile in graded index fiber can vary depending on the requirement.

Most graded index fibers are designed to have a nearly quadratic decease of their refractive

index. These fibers are analysed by their α –profile, which is given by

n1[ 1 - ∆(r/a)α ] for r < a

n(r) =

n1(1 - ∆) = n2 for r≥ a

where a is the radius of the core. The parameter α determines the index profile. A step index

profile is approached in the limit of large α. A parabolic –index fiber corresponds to α =2

1.11 Modes in fibers.

As described earlier the propagation of light along a waveguide can be described in terms of a

set of guided EM waves called MODES of waveguide. These guided modes are referred to as

bound or trapped modes. Each guided mode is a pattern of Electric and Magnetic field lines

that is repeated along the fiber at intervals equal to the wavelength of the wave. Only certain

discrete number of modes is capable of propagating along a guide. These modes are those

that satisfy the homogeneous wave equation (Maxwell’s) in the fiber and the boundary

conditions at the waveguide.

Another method of studying the propagation characteristics of light in an optical fiber

is the Geometrical optics or ray approach as mentioned earlier. It is relatively accurate when

the number of modes is large, i.e Multimode fibers. The main advantage of this approach is

that it gives a more direct physical interpretation of light propagation characteristics in a fiber

Consider a step index fibre shown in figure 1.10. It shows the path of a Meridional ray

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OPTICAL FIBER

Fig1.10 A Step index fiber showing the path of a particular Meridional ray

There are however several paths that can be followed by the various rays that enter the fiber

through the acceptance angle. In the context of geometrical optic approximation, Modes refer

to the different path that light rays can take in passing through the fiber. Figure 1.11

Fig 1.11. A Step index fiber showing various paths (Modes) of Meridional rays

Based on the number of modes a fiber can carry optical fibers are classified into Single mode

and Multi- mode Fibers. The former carries only a single mode or has only one path for the

Meridional rays, while the latter carries many modes. Step index fibers are of both types

namely Single Mode Step index (SMF) and Multimode Step index fiber (MMF) while graded

index fibers are generally multimode - Graded index multimode fiber (GRIN).

Single mode step index fiber: Feature

1. The core diameter in this case ~ 10 µm surrounded by a cladding of diameter ~ 60-70µm.

2. ∆ ~ 0.22

3. Core – SiO2 + Ge Cladding – Si + P

4. It will transmit a single mode for all wavelengths longer than the cut off λC

Multi- mode Step index Fiber- Feature

1. Core diameter ~ 50 to 20 µm cladding diameter ~ 100 to 250µm

2. This has a large NA. Light passes in Zig- Zag mode

3. Allows many modes. Rays are continuously reflected off the core-cladding boundary at different angles towards the centre

4. Point source of light not required.

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OPTICAL FIBER

Step-index multimode fibers are mostly used for imaging and illumination. Graded-index

multimode fibers are used for data communications and networks carrying signals moderate

distances - typically no more than a couple of kilometres. The following table illustrates the

comparison between step index and Graded index fibers

Parameter Step Index Fiber Graded Index fiber

Data Rate Slow Fast

Coupling

Efficiency

High Low

Ray Path Reflection at the Core-Cladding

boundary

Reflection at other points as

well

Index Variation ∆ = (n1 – n2 )/2 ∆ = ( n12 - n2

2 )/2n12

N.A Constant Varies with distance from fiber

axis

Material Glass/Plastic Glass

BW efficiency 10~ 20 MHz/Km 1 GHz/Km

Pulse Spreading More Less

Attenuation 0.3dB/Km at 1.3µm 0.6~ 1dB/Km at 1.3µm

Typical Light

Source

LED LED/LASER

Application LAN & Subscriber Communication LAN/WAN

1.12 Attenuation (Losses) in Optical Fibers

Fiber losses is a limiting factor in the performance of a fiber because the reduce the signal

power reaching of receiver. As optical receivers need a certain minimum amount of power

for recovering the signal accurately, thus the transmission distance is inherently limited by

fiber losses. In fact, the use of silica fibers for optical communications became practical only

when losses were reduced to an acceptable level during the 1970s. With the advent of optical

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OPTICAL FIBER

amplifiers in 1990s, transmission distances can exceed several thousands of kilometres by

compensating the accumulated losses periodically. However low loss fibers are still required

since spacing among amplifiers are set by fiber losses.

Attenuation coefficient (α)

In general the rate of change in average optical power P of a bit stream propagating inside an optical fiber is governed by Beer’s Law

dPdZ

=−αP --------------------------------------------- (1)

where α is known as attenuation constant which is essentially a property of the material

∫Pi

PO dPdZ

=−α∫0

L

dL

ln (PO/Pi) = - αL

PO = Pi e- α L --------------------------------------- (2)

α = - (1/L) ln (PO/Pi) --------------------------------------- (3)

From equation (2) we may thus define α as the reciprocal of the length of a fiber for which

the output power PO reduces to (1/e) times the input power Pi. In this case the unit of α is m-1

as seen from equation (3).

It is customary however to express α in units of dB/Km by using the relation

α (in dB/Km) = - (10/L) log10(PO/Pi) -------------------------- (4)

and refer to it as Fiber loss parameter. Note L must be substituted in Km in equation (4)

We can show that α (in dB/Km) ≈ 4.343 α (in m-1) { Try it }

There are several factors that contribute to overall losses. We shall describe some of them.

Material Absorption

Loss of signal can occur due to absorption of light by the material.

Intrinsic absorption losses correspond to absorption by fused silica ( the material used to

make the fiber). This occurs at specific wavelengths corresponding to electronic and

vibrational resonances associated with the molecules. For Silica(SiO2) molecules, electronic

resonances occur in the UV region ( λ < 0.4µm) whereas vibrational resonances occur in the

IR region(λ >7µm). Because of the amorphous nature of the silica these resonances are in the

form of absorption bands which extends into the visible region. It turns out that this

absorbtion is minimum in the wavelength band 1.3µm to 1.6µm( < 0.03 dB/Km)

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OPTICAL FIBER

Extrinsic absorption results from the presence of impurities. Transition- metal impurities

such as Fe, Cu, Co, Ni, Mn and Cr absorb strongly in the wavelength range 0.6 to 1.6µm.

Their amounts should be reduced to below 1 part per billion to obtain a loss level below

1dB/Km. The main source of extrinsic absorbtion is the presence of water vapour. A

vibrational resonance of the OH ion occurs near 2.73µm. Its harmonic and combination

overtones with silica produce absorbtion at the 1.39, 1.24 and 0.94µm. Even a concentration

of 1 part per million can cause a loss of 50dB/Km at 1.39µm. In modern fibers the

concentration of OH ions has been reduced to less than 10-8 to overcome this (known as Dry

Fiber)

Rayleigh scattering: This is a fundamental loss mechanism arising from local microscopic

fluctuations in density. Silica molecules move randomly in molten state and freeze in place

during fiber fabrication. Density fluctuations lead to random fluctuations of the refractive

index on a scale smaller than the optical wavelength λ. Light scattering in such a medium is

at λ = 1.5µmintrinsic loss of silica fibers from Rayleigh scattering cans be written as αR =

c/λ4, where c is a constant in the range 0.7 to 0.9 (dB/Km)-µm4 depending on the core

material. This range of c translates to a value of αR ≈ 0.12 to 0.16 dB/Km. The contribution

from Rayleigh scattering can be reduced to less than 0.01dB/Km for wavelength longer than

3µm, but fibers cannot be used in this wavelength since infrared absorbtions starts to

dominate the fiber loss beyond 1.6µm.e

Waveguide Imperfections: An ideal single – mode fiber with perfect cylindrical geometry

guides the optical mode without energy leakage into cladding layers. In practice,

imperfections at the core cladding interface (due to random core radius variations) can lead to

additional losses. The physical process behind such losses is due to Mie Scattering, which

occurs due to inhomogeneities on a scale longer than the optical wavelength. Care has to be

taken to ensure that the core radius does not vary significantly along the fiber during

manufacture. If such variations can be kept below 1% the resulting scattering loss is typically

below 0.03dB/Km

Bends in Fibers. This is another source of scattering loss in fiber. We can understand this

using the ray picture. Normally a guided ray hits the core-cladding interface a an angle

greater than the critical angle to be totally internally reflected. However the angle of

incidence decreases near a bend and may become smaller than the critical angle for tight

bends. The ray would then escape out of the fiber, In the ray picture a part of the mode

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OPTICAL FIBER

energy is scattered and escapes into the cladding. It can be shown that the bending loss is

proportional to exp (-R/RC), where R is the radius of curvature of the fiber bend and

RC = a/n12 – n2

2) {a = radius of core} . For single mode fibers RC = 0.2 to 0.4 µm typically

and hence the bending loss is negligible (< 0.01dB/Km) for a bend radius R > 5 mm.

However since most macroscopic bends exceed R = 5mm, Macro bending

Random Axial Distortion: Another major source of fiber loss, particularly in fiber cables is

related to random axial distortions that occur (almost always) during cabling when the fiber

is pressed against a surface that is not smooth. Such losses are called Micro Bending losses.

This can be a major source of loss both in multi mode and single mode fibers (~100dB/Km!)

For single mode fibers, micro bending losses can be minimised by choosing V parameter

(See Appendix below) as close to cut off value of 2.405 as possible so that the mode energy

is confined mainly to the core.

***********************************************

Appendix

Review of Reflection and Refraction

To understand Ray theory let us start with some basic definitions and review of fundamentals

of geometric optics.

Refractive Index of an optical medium: The ratio of the speed of light in the medium to its

speed in vacuum or free space is known a Refractive index (n).

Mathematically n = (C/V). If V1 and V2 are the speed of light in two optical media such that

V1 < V2 then it follows that n1 > n2. The medium in which light travels with lesser speed is

relatively Denser while the medium in which it travels faster is known as Rarer. Clearly a

denser medium has a greater refractive index than that of a relatively rarer medium.

Ray: In geometrical optics a ray denotes the path along which light energy flows.

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In a Homogeneous, isotropic medium rays are straight lines. In the discussions that follow we

shall be considering all media to be homogeneous and isotropic unless otherwise specified.

Reflection of Light: When light energy strikes an interface between two optical media, a part

it bounces back into the first medium. This is known as reflection of light. Reflection is

governed by the following two laws.

(i) The incident ray (PQ), the reflected ray(QS) and the normal(QR) drawn at the point of

incidence are coplanar (ii) The angle of incidence (i) is equal to the angle of reflection(r).

Fig A1. Reflection of light

P Interface

S Medium1 Medium 2

Refraction of light: When light energy strikes the interface between two homogeneous

isotropic media a part of the light energy is transmitted into the second medium and

propagates in it. The direction along which light travels in the second medium is different

from its initial direction. In other words we say a ray of light bends at the interface when it

moves from one homogeneous, isotropic medium to another. This is known as Refraction of

light. Refraction is due to light having different speed in different media. Refraction of light

is governed by the following two laws.

(i) The incident ray (PQ), the refracted (MQN) and the normal(QR) drawn at the point of

incidence are coplanar. (ii) Snell’s Law: For a given wavelength of light and a given pair of

media the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a

constant.

P Refraction of light

Interface

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M Q N

Medium 1( n1) Medium 2 ( n2) R

Mathematically we write

n1 Sin i = n2 Sin r or (Sini/ Sinr ) = (n2 /n1) = Constant

We note the following if light travels from a rarer to a denser medium (n1 < n2) Sin i > Sin r and hence i > r. The ray bends towards the normal.

On the other hand if light travels from a denser to a rarer medium (n1 > n2) Sin i < Sin r and hence i < r. The ray bends away the normal.

Total Internal reflection

Critical Angle θC

n2 n2

r 90O

n1 i n1 θc

Fig A2 Total Internal Reflection of light

n2

n1 i >θC

We note that the refracted ray bends away from the normal. That is r > i . In addition we also

note that there is weak reflection. It is found that as the angle of incidence is increased

(1) The angle of refraction also increases, that is the refracted ray bend further away

from the normal

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OPTICAL FIBER

(2) The intensity of the refracted ray deceases while that of the reflected ray increases.

At a particular angle of incidence known as critical angle (θC) the refracted ray grazes the

interface between the two media. i.e. r = 90O.

If the angle of incidence increases beyond the critical angle (i.e. i > θC) there is no refracted

ray. The entire incident energy is reflected back into the first (denser) medium. This

phenomena is known as Total Internal Reflection

Definition and expression for Critical angle

When a ray of light passes from an optical denser medium to a arer medium, the angle of

incidence for which the angle of refraction is 90O( or for which the refracted ray grazes the

interface between the two media ) is called Critical angle.

Consider a ray of light passing from a denser medium of refractive index n1 to a rarer medium

of refractive index n2. Let the angle of incidence critical angle θC, then according to Snell’s

law

n1 SinθC = n2 Sin 90O = n2

or SinθC = (n2/n1) ……. θC = Sin -1 (n2/n1)

Note on Multi mode Transmission (More elaborate discussion in the next chapter).

A complete understanding of multimode propagation is possible only by solving Maxwell’s

Equation for transmission of EM waves in a dielectric cylinder subject to cylindrical

boundary conditions at the interface between the core and the cladding. It can be shown that

for a particular mode to be confined in the fiber and remain guided the propagation factor β

(product of refractive index and propagation constant k = 2π/λ) must satisfy the condition

n2k < β < n1k. (λ is the free space wavelength of the wave)

In other words only those waves whose β falls between the limits indicated by the above

equation can be guided. (Note that k defines the direction of a ray) An important factor

connected with the above cut-off condition is the Normalized Frequency or V number given

by V = (2πa/λ) √n12 –n22 = (2πa/λ) N.A where a is the radius of the core.

The V number is related to the number of modes M in a multimode fiber as M = V2/2

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