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INTRODUCTION TO OPTICAL FIBRE COMMUNICATIONS(Fibre Structure and Wavelength Fundamentals)

1.0 Introduction

An optical telegraph was built by Claude Chappe in 1790s in France. In 1870, John

Tyndall demonstrated the principle of guiding light through internal reflections. In 1880,

Alexander Graham Bell invented the photophone, which used unguided light to carry speech.

A major breakthrough leading to high capacity optical communications was achieved

with the invention of laser in 1960. The laser acted as a narrowband source of optical radiation

suitable for use as a carrier of information. In 1966, Charles K. Kao at Standard

Telecommunications Laboratories, England fabricated a low loss glass fibre, giving a loss of

1000 dB/km or so. Such a fibre could transmit light for a short distance only. But Kao suggested

that purer glass materials would permit the use of fibre for longer transmission lengths. Kao had

shown that it would be possible to transmit light signals over long distance using glass fibre and

modulated infrared light. In 1970 Corning glass works, U.S.A. developed a low loss fibre giving

a loss of 20dB/Km. This was the second major breakthrough to make optical communication a

practical reality. By 1972, losses were reduced to 4dB/km. Today, the best fibres have a loss of

< 0.2 dB/km.

The information travels from the transmitter to the receiver over the information channel.

There are basically two types of information channels: unguided or guided channels.

Atmosphere is an unguided type of channel over which waves can propagate. Guided channels

are those which guide the electromagnetic waves through them. Two wire lines, coaxial cable,

waveguide and optic fibre are the examples of Guided information channels. Guided channels

have the advantages of privacy, no weather dependence and the ability to convey messages

within, under and around physical structures.

An optical fiber is a thin strand of glass or plastic serving as the transmission medium

over which the information passes. The basic fiberoptic system is a link connecting optical

transmitter and receiver.

Transmitter

It converts an electrical signal into a light signal. The source is either a lightemitting

diode or laser diode which does the actual conversion. The drive circuitry changes the electrical

signal fed to the transmitter into a form suitable for the source.

FiberOptic Cable

It is the medium for carrying the light. The cable includes the fibers and its protective

coverings.

Receiver

It accepts the light and converts it back into an electrical signal. The generator amplifies,

reshapes the signal before passing it on.

The range of wavelengths in the visible region extends from 0.4 m to 0.7 m. Thevisible range is not suitable for light transmission through glass fiber. In this region, the waves

are attenuated to such an extent that only short transmission links are possible. Losses in the

ultraviolet region are even greater. It is the infrared region from 0.8 m to 1.6 m which is

used for fiber optic transmission.

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1.1Advantages of Fibers

1.1.1 Wide Bandwidth

The information carrying capacity which increases with the bandwidth of the

transmission medium, is very large in fibers. The bandwidth available on a pair of single mode

fibers is in the order of several GHz. Thus, thousands of circuits can be carried on the fibers

whether the information is voice, data or video or a combination of these.

1.1.2 Low Loss

Bandwidth is an effective indication of the rate at which information can be sent. Loss

indicates how far the information can be sent. As a signal travels along a transmission path the

signal loses strength. This loss of strength is known as attenuation. In a copper cable,

attenuation increases with the modulation frequency: the higher the frequency of the information

signal, the greater is the loss. In an optical fibre, attenuation is flat: loss is the same at any

signaling frequency until a very high frequency. Thus, the problem of loss is much more in a

copper cable as information carrying capacity increases.

Fig.1 shows the loss characteristics Vs the channel bandwidth for fibres, and coaxial

cable. Loss in coaxial cable increases with frequency, whereas loss in the optical cable remainsflat.

Fig. 1Attenuation versus Frequency (BW)

The loss at very high frequencies in the optical fibre does not result from additional

attenuation of the light by the fibre. The loss is caused by loss of information, not by optical

power, but due to the variation of the optical power. At very high frequencies, distortion causes

a reduction or loss of this information.

1.1.3 Electromagnetic Immunity

Optic fibres are insulators. No electric current flows through them, either due to the

transmitted signal or due to external radiation striking the fibre. For these reasons, fibres do not

radiate or pickup electromagnetic radiation as in copper cables. Any copper conductor acts like

an antenna, either transmitting or receiving energy.

Since fibers do not radiate or receive electromagnetic energy, they make an ideal

transmission medium. As a consequence to fibre's electromagnetic immunity, signals do not

become distorted by EMI. Fibres offer very high standards in error free transmission.

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1.1.4 Small Size

Fibres are hair thin in size. Fibers covered with protective coverings are still smaller than

the equivalent copper conductor. The small size of fibre optic cables makes them attractive for

applications where space is at a premium.

1.1.5 Light Weight

A glass fibre weighs considerably less than a copper conductor. A fibreoptic cable with

the same information carrying as a copper cable weighs less than the copper cable. Weight

savings are important in such applications as aircraft and automobiles.

1.1.6 Greater Safety

A fibre is a dielectric. It does not carry electricity. If the cable is damaged, it does not

present any spark or fire hazard, so it cannot cause explosions or fires as a faulty copper cable

can. Moreover, it does not attract lightning. The fiberoptic cable can be run through hazardous

areas.

1.1.7 Higher Security

Fibre optics is a highly secure transmission medium, because the fibres do not radiate

energy that can be received by a nearby antenna without getting detected. It is also extremelydifficult to tap a fibre.

2.0Basic Fibre Construction

2.1 An optical fibre has two concentric layers called the core and the cladding. The inner

core carries the light. The refractive index of core is slightly higher than the cladding.

The typical value of refractive index of core is between 1.48 to 1.5. The index of cladding

is 1% lower than that of the core; the typical values being 1.46 to 1.48. The difference in

index in core and cladding allows total internal reflection of light through the core.

Most fibres have an additional coating around the cladding. The primary function of

the additional coatings which are made of polymer is to protect the core and cladding from

shocks that might affect the optical or physical properties of the fiber. The coatings do not

have any optical property so as to affect light propagation within the fibre.

2.1.1 Light Propagation in Optical Fibres

The speed of light is actually the velocity of electromagnetic energy in a vacuum

such as space. The speed of light in other materials such as glass, plastic is less. The

speed of light changes when it travels from one material to another, resulting in light

changing its direction of travel. This deflection of light is called refraction. Furthermore

different wavelengths of light travel at different speeds in the same material.

2.1.2 The index of refraction denoted by n, is a dimensionless number expressing the

ratio of the velocity of light c in free space to its velocity v in a specific material :

n = c/v

The refractive indices of some selected materials are shown in Table 1 below. The index

of glass can be changed by controlling its composition.

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Table IRefractive Indices of Various Materials

Material Index (n) Light velocity(Km/s)

Vacuum 1.0 300,000

Air 1.0003 300,000

Water 1.33 225,000

Fused Quartz 1.46 205,000

Glass 1.5 200,000Diamond 2.0 150,000

Silicon 3.4 88,000

Gallium Arsenide 3.6 83,000

2.1.3 Even when light passes from one index to another, a small portion is always reflected

back into the first material. This reflection is known as Fresnel reflection. For light

passing from air to glass, reflection loss is about 0.17 dB.

The relationship between the incident and refracted ray is clearly brought out by Snell's

law which states:

n1 sin 1 = n2 sin 2

where n1, n2 are the refractive indices of the two materials and 1, 2 are the angles of

incidence and refraction respectively. Critical angle of incidence c where 2 = 90 is

c= arc Sin (n2/n1)

At angles greater than c the light is reflected back. These simple principles of reflection

and refraction form the basis of light propagation through the optical fibre. The amount

that a ray of light is refracted depends on the refractive indices of the two materials.

Light passing from a lower refractive index to a higher one is bent towards the normal,

an imaginary line perpendicular to the interface of the two materials. But light going froma higher index to a lower one refracts away from the normal, as shown in Fig.2.

Fig. 2Principles of Refraction

As the angle of incidence (the angle between the incident ray and the normal) increases,

the angle of refraction approaches 90 to the normal. The angle of incidence that yields

an angle of refraction (angle between the refracted ray and the normal) as 90 is known

as critical angle. If the angle of incidence increases further (beyond critical angle), thelight is totally reflected back into the first material so that it does not enter the second

material. The angles of incidence and reflection are equal.

The fibre uses a circular configuration such that n2 surrounds n1.

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2.1.4 Figure 3 shows the propagation of light through a circular fibre with refractive indices of

core and cladding being n1, n2 respectively and n1>n2. There are three possibilities of

ray striking the corecladding interface.

(a) Light ray 1 injected into the fibre and striking the coretocladding interface at an

angle greater than the critical angle. This is totally reflected back into the core.

Since the angles of incidence and reflection are equal, the reflected light will

again be reflected. The light will continue zigzagging down the length of the fibre.

(b) Light ray 2 strikes the core cladding interface at an angle less than the critical

angle. Such a ray continues travelling to cladding. It then strikes the outer

surface of the cladding at an angle greater than the critical angle of incidence, so

it is reflected back into the cladding. It will then reenter the core, pass through

the cladding on the opposite side and is reflected again into the cladding and

then to core. The cladding is usually inefficient as a light carrier, and the light in

the cladding becomes attenuated fairly rapidly. Such a ray does not contribute to

the light energy travelling to the distant end, and it is lost over distance.

(c) Light ray 3 strikes the core cladding interface at an angle less than the critical

angle, so it is refracted into the cladding, where it meets the claddingair

interface at angle less than the critical angle of incidence for claddingair. This

ray escapes into air and does not contribute to light propagation in the fibre.

Fig. 3

Light Propagation through Fibre

In the aforesaid analysis, it is made clear that the injected light should meet the

coretocladding interface at angles greater than the critical angle so that light is

totally reflected internally and travels down the length of the fibre. The

propagation of light is governed by the indices of the core and cladding and by

Snell's law. This analysis has considered only meridional rays those that pass

through the fibre axis each time they are reflected. Other rays, called Skew rays,

travel down the fibre without passing through the axis. The path of a Skew ray is

typically helical, wrapping around and around the central axis. Such a ray is

ignored.

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2.2 Optical Fibre Classification

2.2.1 The optical fibres can be classified in three ways :

Material

Size (or Mode)

Refractive Index

2.2.2 Material Classification

One way of classifying the fibres is by their material make up.

Glass fibres have a glass core and glass cladding. They are most widely used. The

glass used in fibres is ultrapure, ultratransparent silicon dioxide or fused quartz.

Impurities such as germanium, phosphorus, boron or fluorine are added to the pure

glass to achieve the desired refractive index.

Plasticclad Silica (PCS) fibres have a glass core and plastic cladding. The performance

of this type of fibre is not as good as all glass fibres.

Plastic fibres have a plastic core and plastic cladding. Plastic fibres have high lossesand very low bandwidths but are inexpensive. Plastic and PCS fibres do not have

protective coatings surrounding the cladding.

2.2.3 Classification According to Size (or Mode)

The second way to classify fibres is by the size (core diameter) or modes in fibre. Mode

is a mathematical and physical concept describing the propagation of electromagnetic

waves through media. Mode theory derives from Maxwell's equations. For the purpose

of understanding the concept we shall define the mode simply as a path that a light

ray can follow in travelling down a fibre. The number of modes supported by a fibre

ranges from 1 to over 1,00,000. Thus, an optical fibre provides a path of travels for one

or thousands of light rays depending on its size and properties.

Multimode Fibre is characterized by relatively large core diameters. Typical values of

core diameters are 50, 62.5, 80, 100 micrometers. A multimode fibre supports more

than one propagating mode.

Single Mode Fibre supports only a single propagating mode. It is characterized by

small core diameters ranging from 4 to 10 micrometers.

Fig.4 shows crosssection of the core and cladding diameters of four commonly used

single and multimode fibres.

Fig. 4

Typical Core and Cladding Diameters

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2.2.4 Classification According to Refractive Index Profile

The refractive index profile describes the relationship between the indices of the core

and cladding. There are two main relationships existing in fibre optics: Step Index and Graded

Index. The stepindex fibre is characterized by a uniform index throughout the core material.

The profile shows a sharp step at the junction of the core and cladding. In contrast, the graded

index has a nonuniform core. The index is highest at the centre and it gradually decreases

until it matches that of the cladding.

There are basically three types of fibres according to above classification:

1. Multimode stepindex or simply stepindex fibre.

2. Multimode gradedindex or gradedindex fibre.

3. Singlemode stepindex fibre (commonly called singlemode fibre).

2.2.5 Step Index Fibre

The multimode stepindex fibre is the simplest type. The core diameter ranges from

100 to 970 micrometers. It includes all glass, PCS and all plastic constructions. This type of

fibre is the most wide ranging but it is inefficient from the point of view of information carrying

capacity.

The fibre propagates a number of modes. The path lengths of different modes are

different as different rays take a shorter or longer time to travel the length of the fibre depending

on their angle with the fibreguided axis. The ray that travels straight down the center of the

core without reflecting arrives at the other end first, other rays arrive later. Thus, though all the

rays enter the fibre at the same time but arrive at the distant end at different times. This results

into spreading of light in time or simply pulse spreading.

This spreading of light is called modal dispersion. Modal dispersion results from the

varying modal path lengths in the fibre. Typical values of modal dispersion in multimode step

index fibres range from 15 to 30 ns/km, length of fibre. Modal dispersion is the main limiting

factor for transmitting higher data rates on step index fibres.

2.2.6 Graded Index Fibre

The modal dispersion can be reduced by using gradedindex fibre. The gradedindex

(or GRIN) fibre has a core material whose refractive index varies with distance from the fibre

axis. The structure is illustrated in Fig.8.

Fig. 5GRIN Fibre

Index is maximum at the core center and decreases gradually towards the core

cladding interface. The light travels faster in a medium of lower index of refraction (v = c/n). So

the farther the light ray is from the core axis, the greater is its speed. Because the index is

Minimum density

Maximum density

Minimum density

End view Side view Index profile

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continuously changing across the axis, the light ray is bent or continually redirected towards the

fibre axis in an almost sinusoidal fashion as shown in Fig.6.Fig. 6

Ray Paths along a GRIN fibre

Those rays that follow the longest path by travelling near the outside of the core have a

faster average velocity. The light travelling near the axis of the core has the slowest average

velocity. As a result of this, all rays tend to reach the end of the fibre at the same time. The

typical value of modal dispersion for GRIN fibre is 1 ns/km or less.

Typical sizes of multimode GRIN fibres are 50/125, 62.5/125 and 85/125. This type of

fibre has wide applications requiring wide bandwidths.

2.2.7 Single Mode Fibre

One way of reducing the modal dispersion by using a GRIN fibre. Another way in which

modal dispersion is completely eliminated is by reducing the core diameter until the fibre

propagates only one more efficiently. This type of fibre is known as mono or more popularly

single mode fibre. The single mode fibre has a very small core diameter of only 4 to 10

micrometer. The cladding diameter is standardized at 125 micrometer, as in GRIN fibres.

The point at which a singlemode fibre propagates only one mode depends on the

wavelengths of light carried. Different fibre designs have a specific wavelength, called the cutoff

wavelength, above which it carries only one mode. A fibre designed for singlemode operation

at 1300 nm has a cutoff wavelength of around 1200 nm.

The operation of the singlemode fibre is quite complex. In singlemode fibre the optical

energy is not confined to the core alone. Some of the optical energy of the mode travels in the

cladding as shown in Fig.7.

Fig. 7Light through (Multi & Single Mode Fibres

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The diameter of the light appearing at the end of the fibre is larger than the core

diameter. This diameter is known as Mode Field Diameter. Since the optical energy in a

singlemode fibre travels in the cladding as well as in the core, the cladding need to be more

efficient to carry light energy unlike the multimode fibres where the flow of energy in cladding is

undesirable. The singlemode fibres have a very large bandwidth of the several gigahertz and

allow transmission up to tens of kilometers.

2.3 Advanced Single Mode Fibres

Apart from step profile in ordinary single mode fibre, more complex index profiles are

being used to obtain lower losses and lower dispersion in the fibres. Fig.8 shows refractive

index profiles of advanced singlemode fibres.

2.3.1 Modes in StepIndex Fibres

We have seen that the modal dispersion causes pulse spreading and overlapping. As a

result, it limits the data rate or information carrying capacity that a fibre can support. We will see

later that the modal dispersion depends on wavelength and core diameter. At this junction, we

will introduce a parameter V number. The V number is a fibre parameter that takes into account

the core diameter, wavelength propagated, and fibre numerical aperture (commonly known as

NA to be defined later). It is also called the normalized frequency.

Fig. 8Refractive Index Profiles of Advanced SingleMode Fibres

For a multimode stepindex fibre, the number of modes

N = V2/2

For a GRIN fibre, the number of modes is approximately

N = V2/4

For large values of V, many modes will propagate. Large V corresponds to a relatively

large core radius. The number of modes in a gradedindex fibre is about half that of a step

index fibre having the same core diameter and NA. A fibre with a 50 micrometer core supports

over 1000 modes.

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2.3.2 Fiber Comparisons

The performance of the fibre depends on its type. Here, the term performance means

higher bandwidth, higher information carrying capacity, and lower losses. Though it is common

to stress on high performance, i.e. low losses and high bandwidth of fibres, but one has to

choose the fibre depending on the application.

2.4 Numerical Aperture

3.0Characteristics of Optical Fibres - IntroductionLike any other medium such as the VF pair, coaxial cable or the free space in the case

of microwave systems, the optical fibre also its own transmission characteristics such as

Numerical Aperture, Modal and Material Dispersion, etc.

Numerical Aperture

Numerical aperture is defined as the "lightgathering ability" of a fibre. When an optical

ray in a medium of refractive index 'n' falls on the lateral surface of the core of optical fibre at a

maximum angle so that it can traverse throughout the fibre core length due to total internal

reflection, then n sin is called the Numerical Aperture (NA) of the fibre.

Only light injected into the fibre at angles greater than the critical angle will be propagated.

In Fig.9, a meridional ray is shown entering the end face of the core at an angle .

Fig. 9Meridional Ray in a Core

The ray will be refracted into the core at an offaxis angle. It strikes the core

cladding interface at an angle i and is totally reflected if i > c (c = Critical angle).

Numerical Aperture is a unitless quantity. We can also define the angles at which

rays will be propagated by the fibre. These angles form a cone that gives the maximumangle of light acceptance. The acceptance angle is related to the NA. A ray not falling

within the acceptance cone is lost by radiation.

Fig. 10Numerical Aperture

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The numerical aperture of a fibre is important because it gives an indication as to

how the fibre accepts and propagates light; a fibre with a low NA requires highly

directional light. Numerical apertures and acceptance angles for fibres representative of

Allglass, PCS and allplastic constructions are listed in Table 2.

Table 2Typical Numerical Apertures and Acceptance Angles

Construction n1 n2 NA Acceptance Angle

Allglass 1.48 1.46 0.24 13.9o

PCS 1.46 1.40 0.41 24.2o

Allplastic 1.49 1.41 0.48 29.0o

In general, fibres with a large bandwidth have a lower NA. They thus allow fewer

modes. Fewer modes means less dispersion and, hence, greater bandwidth. A large NA

promotes more modal dispersion, since more paths for the rays are provided.

In GRIN fibres, the NA is maximum at the centre (NA = 0.26). The NA drops off to

zero at the edge of the core. Only a ray perfectly parallel to the fibre axis will be guided if

it enters the waveguide at this point.

NA for singlemode fiber is only about 0.11. Light in a singlemode fibre is not

reflected or refracted, so it does not exit the fibre at angles. Similarly, the fibre does not

accept light rays at angles within the NA and propagates them by total internal reflection.

3.2 Dispersion

Dispersion is a phenomenon which spreads a light pulse as it travels down the

length of an optical fibre. Dispersion is undesirable as it limits the bandwidth or

informationcarrying capacity of a fibre. The bit rate must be low enough to ensure that

pulses do not overlap. The pulse broadening increases as the square root of thedistance of transmission. The duration that must be allotted between pulses to avoid

inter-symbol interference is proportional to the length of the fibre.

There are three classes of dispersion.

1. Modal or intermodal dispersion.

2. Material dispersion.

3. Waveguide dispersion.

3.2.1 Modal Dispersion

This type of dispersion is dominant in multimode fibres. It arises due to different

velocities of different modes. Singlemode fibres are not subject to intermodal

dispersion. Gradedindex fibres greatly reduce intermodal dispersion. Phase velocity of

light in the core will be same in any direction for a S.I. fibre. A ray travelling along the

fibre axis will travel the shortest distance. A ray having an angle i with the axis which is

equal to the critical angle (i = c), will be travelling the longest path. Most S.I. glass

fibres have measured pulse spreads around 1050 ns/km. The discrepancy arise due to

mode mixing and preferential attenuation.

Mode mixing is the exchange of power between modes. Rays in one mode are

deflected (by scattering and at bends and splices) into the paths of other modes. Rays

may move from higher to lowerorder modes, and vice versa. The result of continued

mode mixing is that energy launched in any one mode travels a total zigzag path length

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that is somewhere between the shortest (axialmode) path and the longest (critical

angle) path. All rays travel nearly the same total length, reducing multimode pulse

spreading considerably. The mode mixing is not perfect, so modal distortion is the main

cause of spreading in S.I. fibres. Although mode mixing reduces the pulse spread, it is

not altogether desirable. Deflections will also direct some rays into paths at less than the

critical angle. The light will be lost, increasing the fibre attenuation.

The second source of pulse spread reduction is the greater attenuation suffered

by higher ordered modes which penetrate more deeply into the cladding, thereby

contributing less to the received pulse compared to lowerorder modes. Pulse spread

will be smaller due to negligible amplitude of higherorder modes in the received pulse.

But it is undesirable as total signal attenuation increases. It is important to note that

modal dispersion does not depend on the source wavelength or on the source

bandwidth. GRIN fibres produce much less multimode distortion than S.I. fibres.

3.2.2 Material Dispersion

It is caused due to the variation of velocity with wavelength (colour). Different

wavelengths travel at different velocities through a fibre even when all the light followsthe same path. The velocity variation caused by some property of the material gives rise

to the effect which is called material dispersion.

We know that n = c/v, where c is the speed of light in a vacuum and v the speed of

the same wavelength in the material. The index of refraction changes according to the

wavelengths. As a result each wavelength travels at a different speed through the

material. The pulses travel at different velocities, reaching the end of the fibre at slightly

different times. When summed at the output, the pulses add together, yielding an output

that is lengthened or spread relative to the input signal. This illustrates how dispersion

creates pulse distortion. The farther the pulse travels, the greater the spreading.

Distortion caused by material dispersion can be reduced by using sources with

smaller bandwidths or line widths. Optical sources radiative over a range of wavelengths

instead of the desired single wavelength or single frequency. This range is known as

line width or spectra width. The smaller the line or spectral width, the more coherent

the source emits light at a single wavelength; thus it has zero line width and is perfectly

monochromatic. Typical line widths of common sources are listed in Table 3.

Table 2Typical Source Spectral Widths

Source Line width ()Lightemitting diode (semiconductor) 20100 nm

Laser Diode (semiconductor) 15 nm

Nd : YAG laser (solid state) 0.1 nm

HeNe laser 0.002 nm

At 1.3 micrometer, the material dispersion is zero. Pulse spreading due to

material dispersion disappears at this wavelength. M is positive at wavelengths below

1.3 micrometer. M is negative and pulse spreading is positive at wavelengths about 1.3

micrometers. Material dispersion is of greater concern in singlemode fibres. In a

multimode fibre, the modal dispersion is dominant and material dispersion is of no

consequence. For SM fibres material dispersion is large in the range of 0.8 to 0.9

micrometer. Pulse spread becomes smaller for longer wavelengths and narrower source

linewidths.

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3.2.3 Waveguide Dispersion

Waveguide dispersion results from the guiding structure and is important in

singlemode fibres. It occurs because guided optical energy is divided between the core

and the cladding. The energy travels at slightly different velocities in the core and

cladding because of the slightly different refractive indices of the materials.

Waveguide and material dispersions depend on the source's spectral width as

well as the length of the fibre. Waveguide dispersion is much less than material

dispersion in the range of 0.80.9 micrometer. At 1.3 micrometer, wavelength material

dispersion disappears, waveguide dispersion is significant. Just beyond this wavelength,

M becomes negative while M' stays positive. Cancellation occurs, leaving zero pulse

spread at a wavelength that is still close to 1.3 micrometer.

In SM fibre attenuation is lowest at 1550 nm, while the dispersion is lowest at

wavelength close to 1300 nm. To take advantage of lowest attenuation as well as low

dispersion at 1550 nm, singlemode fibre is constructed with a triangularshaped

refractive index variation. Such a fibre is known as dispersion shifted fibre. In order to

obtain uniformly low dispersion over a wide range of wavelengths in the region 1300 to

1600 nm, dispersion flattened fibres are used. The dispersion-flattened fibre is

constructed by appropriately tailoring the refractive index variation of the fibre. For this

depressedcladding fibre, where the core index is surrounded by a thin inner cladding

whose index is low and an outer cladding whose index is a bit higher is used.

3.2.4 Length Dependence of the Pulse Spread

The pulse broadening increases linearly with fibre length. Experiments with

multimode fibres have shown that this is true for short lengths (usually less than 1 km),

but for longer lengths, the broadening is proportional to the square root of the length.

A good fibre has little mode mixing, so equilibrium is established only after travelover a long distance. A fibre with no mode mixing would have infinite Le, and its pulse

spread would increase linearly with length. A poor fibre has a lot of mode mixing due to

scattering, micro-bends and in-homogeneities. For this fibre Le is relatively short.

Although the poor fibre has improved bandwidth, its attenuation will be much higher than

that of good fibres.

Material and waveguide dispersions are independent of mode coupling. Pulse

broadening by material and waveguide mechanisms increases linearly with path length.

3.2.5 Total Pulse Spread

The total pulse spread of a multimode fibre is determined, by the sum of the modal

distortion and the material plus waveguide (negligible) dispersions. The way in which

these two contributions are added to find the total effect, depends upon the pulse

shapes in question and the degree of precision required.

3.3 Band width

The bandwidth (BW) is defined to be the frequency at which the fibres base band

frequency response is down by 3 dB (in optical power). It is the 3 dB bandwidth of a fibre

which corresponds to reduction in modulated optic power by half. It is important to note

that optic 1.5 dB bandwidth equals the electrical 3 dB bandwidth.

f1.5dB (optic) = f3dB (electrical)

f1.5dB (optic) = 0.71 f3dB (optic)

hence, f3dB (electrical) = 0.71 f3dB (optic)

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The fibre bandwidth is generally specified as the bandwidth length product given

in megahertz or gigahertz kilometers. A bandwidth of 400 MHzkm. means that a 400

MHz signal can be transmitted for 1 km. It also means that the product of the frequency

and the length must be 400 or less (BW X L = 400). A lower frequency can be sent for a

longer distance. Conversely a higher frequency can be sent shorter distance.

3.4 Attenuation

Signal attenuation is a major factor in the design of any communication system. In anoptic system, the loss of power takes place at several points. These are the coupler,

splices and connectors and within the fibre itself. In this section, we will study the losses

associated with the fibre. Attenuation varies with the wavelength of light. The attenuation

curve of a typical fibre is shown in Fig.11.

Fig. 11Spectral Attenuation for Allglass Fibre

It can be seen that the fibre exhibits minimum attenuation at wavelength slots of around

850 nm, 1300 nm and 1550 nm. These slots are also called first window, second

window, and the third window, respectively. A typical singlemode fibre offers

attenuation of 2.02.5 dB/km. at 850 nm and 0.40.5 dB at 1300 nm and 0.250.30 at1550 nm. The operating wavelengths are so chosen as to avoid high loss regions of the

fibre attenuation curve.

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3.4.1 Sources of Loss in Fibres

The losses occurring in glass fibres can be attributed to three main causes:

1. Absorption

2. Scattering

3. Geometric effects.

3.4.2 Absorption

The losses due to absorption can be divided further in two categories:(a) Intrinsic absorption

(b) Absorption due to impurities

The intrinsic absorption is a natural property of glass itself. Even the purest

glass will absorb heavily within specific wavelength regions. Intrinsic absorption is very

strong in shortwavelength ultraviolet portion of the electromagnetic spectrum. This

absorption is due to strong electronic and molecular transition bands. Fortunately, the

operating region of the fibre is far removed from UV region. Apart from UV absorption

loss, glass absorbs light in the infrared region also. The infrared absorption peaks

occur between 7 and 12 micrometer for typical glass composition, far from the region of

interest. The IR loss is associated with vibrations of chemical bonds such as the silicon

oxygen bond. Thermal energy causes the atoms to be moving constantly, so the SiO

bond is continually stretching and contracting. This vibration has a resonant frequency in

the infrared range. IR absorption contributes a small loss at the upper limit of our

range, 1.6 micrometer. In fact, IR absorption prohibits the use of silica fibres beyond 1.6

micrometer wavelength. Impurities are a major source of loss in any practical fibre. In

general, two types of impurities are particularly troublesome:

(a) Metal ions

(b) Hydroxyl ion (OH)

Metal impurities causing absorption include ions of iron, copper, cobalt, vanadium,

nickel, manganese and chromium. To maintain low losses, the level of these ions must

be less than one part per billion.

The hydroxyl ion (OH) is another most important contributor to the loss. Though

the peak OH ion absorption lies at 2.73 micrometer (outside the band of interest), the

overtones and combination bands of this peak lie within the range of interest. The most

significant OH losses occur at 1.38, 1.24 and 0.94 micrometer. Fig.11 indicates OH

absorption peaks. OH impurity is kept to less than a few parts per million during theglass fibre manufacture.

3.4.3 Scattering

Scattering is the loss of optical energy due to imperfections in the fibre and from

the basic structure of the fibre. Due to scattering, the light is scattered in all directions

which causes the loss of power in the forward direction. This loss is known as Rayleigh

scattering loss.

Rayleigh scattering takes palce due to variations in the density and composition of

glass material in the fibre. Density and compositional variations take place during

manufacture itself. Material in-homogeneities unintentionally introduced into the glass

during manufacture also cause scattering losses.

Rayleigh scattering is inversely proportional to the fourth power of the wavelength

(1/4) and it diminishes rapidly at longer wavelengths.

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3.4.4 Geometric Effects

Bending a fibre causes attenuation. Two types of bends are :

(a) Micro-bending

(b) Macro-bending

Microscope bending loss is caused due to determination of the fibre axis during

cabling process. When a fibre is sheathed within a protective cable, it sets up stresses

which cause small axial distortion (micro-bends) to appear randomly along the fibre.

Micro-bends cause some of the light to couple out of the fibre. This effect can be

eliminated by using loosetube cable construction.

Excessive bending of the cable or fibre may result in loss known as Macro-bend

loss. This loss may occur when wrapping the fibre on a spool or pulling the fibre cable

around a corner. Fibres can be bent with radius of curvature as small as 10 cm. with

negligible loss. Typically, breaking will not occur unless the bend radius is less than 150

times the fibre diameter. For example, if the diameter is 125 micrometer, the bend radius

before breaking is as little as 1.9 cm. Fig.12 illustrates Micro-bend and Macro-bend

losses. A minimum bend radius should be maintained to avoid losses. As a rule of

thumb, the minimum bend radius is five times the cable diameter for an

unstressed cable and ten times the diameter for a stressed cable. The total

attenuation of the fibre is the combination of all the loss phenomena.

Fig. 12Radiation due to Micro-bending and Macro-bending