optical fibre & nanotechnology

41
3 Optical Fibre 3.1 Introduction Communication means transfer of information from one point to another. There has always been a demand for increases capacity of transmission of information and scientists and engineers continuously pursue technological routes for achieving this goal. The conduction of light along transparent cylinders by multiple total internal reflections is a fairly old and well known phenomenon. However, the earliest recorded scientific demonstration of this phenomenon was given by John Tyndall at the Royal society in England in 1870. In this demonstration, Tyndalll used an illuminated vessel of water and showed that when a stream of water was allowed to flow through a hole in the side of the vessel, light was conducted along the curved path of the stream. When it is necessary to transmit information, such as speech, images, or data, over a distance, one generally uses the concept of carrier wave communication. In such a system, the information to be sent modulates an electromagnetic wave such as a radio wave, microwave, or light wave, which acts as a carrier. This modulated wave is then transmitted to the receiver through a channel and the receiver demodulates it to retrieve the imprinted signal. The carrier frequencies associated with TV broadcast ( 900 MHz) are much higher than those associated with AM radio broadcast ( 20 MHz). This is due to the fact that, in any communication system employing electromagnetic waves as the carrier, the amount of information that can be sent increases as the frequency of the carrier is increased. Obviously, TV broadcast has to carry much more information than AM broadcasts. Since optical beams have frequencies in the range of 10 14 to 10 15 Hz, the use of such beams as the carrier would imply a tremendously large increase in the information- transmission capacity of the system as compared to systems employing radio waves or microwaves. In a conventional telephone hookup, voice signals are converted into equivalent electrical signals by the microphone and are transmitted as electrical currents through metallic (copper or aluminum) wires to the local telephone exchange. Thereafter, these signals continue to travel as electric currents through metallic wire cable (or for long-distance transmission as radio/microwaves to another telephone exchange) usually with several repeaters in between. From the local area telephone exchange, at the receiving end, these signals travel via metallic wire pairs to the receiver telephone, where they are converted back into corresponding sound waves. Through such cabled wire-pair telecommunication systems, one can at most send 48 simultaneous telephone conversations intelligibly. On the other hand, in an optical communication system that uses glass fibers as the transmission medium and light waves as carrier waves, it is distinctly possible today to have 35,000 or more simultaneous telephone conversations (equivalent to a transmission speed of about 2.5 Gbit/s) through one glass fiber no thicker than a human hair. This large information-carrying capacity of a light beam is what generated interest among communication engineers and caused them to explore the possibility of developing a communication system using light waves as carrier waves. The idea of using light waves for communication can be traced as far back as 1880 when Alexander Graham Bell invented the photo phone (Figure 3.1) shortly after he invented the telephone in 1876. In this remarkable experiment, speech was transmitted by modulating a light beam, which traveled through air to the receiver. The flexible reflecting diaphragm (which could be activated by sound) was illuminated by sunlight. The reflected light was

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Communication means transfer of information from one point to another. There has always been a demand for increases capacity of transmission of information and scientists and engineers continuously pursue technological routes for achieving this goal. The conduction of light along transparent cylinders by multiple total internal reflections is a fairly old and well known phenomenon. However, the earliest recorded scientific demonstration of this phenomenon was given by John Tyndall at the Royal society in England in 1870. In this demonstration, Tyndalll used an illuminated vessel of water and showed that when a stream of water was allowed to flow through a hole in the side of the vessel, light was conducted along the curved path of the stream. When it is necessary to transmit information, such as speech, images, or data, over a distance, one generally uses the concept of carrier wave communication. In such a system, the information to be sent modulates an electromagnetic wave such as a radio wave, microwave, or light wave, which acts as a carrier. This modulated wave is then transmitted to the receiver through a channel and the receiver demodulates it to retrieve the imprinted signal. The carrier frequencies associated with TV broadcast ( 900 MHz) are much higher than those associated with AM radio broadcast ( 20 MHz). This is due to the fact that, in any communication system employing electromagnetic waves as the carrier, the amount of information that can be sent increases as the frequency of the carrier is increased. Obviously, TV broadcast has to carry much more information than AM broadcasts. Since optical beams have frequencies in the range of 1014 to 1015 Hz, the use of such beams as the carrier would imply a tremendously large increase in the information-transmission capacity of the system as compared to systems employing radio waves or microwaves.

TRANSCRIPT

Page 1: Optical Fibre & Nanotechnology

3

Optical Fibre

3.1 Introduction

Communication means transfer of information from one point to another. There has always

been a demand for increases capacity of transmission of information and scientists and

engineers continuously pursue technological routes for achieving this goal. The conduction of

light along transparent cylinders by multiple total internal reflections is a fairly old and well

known phenomenon. However, the earliest recorded scientific demonstration of this

phenomenon was given by John Tyndall at the Royal society in England in 1870. In this

demonstration, Tyndalll used an illuminated vessel of water and showed that when a stream

of water was allowed to flow through a hole in the side of the vessel, light was conducted

along the curved path of the stream. When it is necessary to transmit information, such as

speech, images, or data, over a distance, one generally uses the concept of carrier wave

communication. In such a system, the information to be sent modulates an electromagnetic

wave such as a radio wave, microwave, or light wave, which acts as a carrier. This modulated

wave is then transmitted to the receiver through a channel and the receiver demodulates it to

retrieve the imprinted signal. The carrier frequencies associated with TV broadcast

( 900 MHz) are much higher than those associated with AM radio broadcast ( 20 MHz).

This is due to the fact that, in any communication system employing electromagnetic waves

as the carrier, the amount of information that can be sent increases as the frequency of the

carrier is increased. Obviously, TV broadcast has to carry much more information than AM

broadcasts. Since optical beams have frequencies in the range of 1014

to 1015

Hz, the use of

such beams as the carrier would imply a tremendously large increase in the information-

transmission capacity of the system as compared to systems employing radio waves or

microwaves.

In a conventional telephone hookup, voice signals are converted into equivalent electrical

signals by the microphone and are transmitted as electrical currents through metallic (copper

or aluminum) wires to the local telephone exchange. Thereafter, these signals continue to

travel as electric currents through metallic wire cable (or for long-distance transmission as

radio/microwaves to another telephone exchange) usually with several repeaters in between.

From the local area telephone exchange, at the receiving end, these signals travel via metallic

wire pairs to the receiver telephone, where they are converted back into corresponding sound

waves. Through such cabled wire-pair telecommunication systems, one can at most send

48 simultaneous telephone conversations intelligibly. On the other hand, in an optical

communication system that uses glass fibers as the transmission medium and light waves as

carrier waves, it is distinctly possible today to have 35,000 or more simultaneous telephone

conversations (equivalent to a transmission speed of about 2.5 Gbit/s) through one glass fiber

no thicker than a human hair. This large information-carrying capacity of a light beam is what

generated interest among communication engineers and caused them to explore the

possibility of developing a communication system using light waves as carrier waves.

The idea of using light waves for communication can be traced as far back as 1880 when

Alexander Graham Bell invented the photo phone (Figure 3.1) shortly after he invented the

telephone in 1876. In this remarkable experiment, speech was transmitted by modulating a

light beam, which traveled through air to the receiver. The flexible reflecting diaphragm

(which could be activated by sound) was illuminated by sunlight. The reflected light was

Page 2: Optical Fibre & Nanotechnology

received by a parabolic reflector placed at a distance of about 200 m. The parabolic reflector

concentrated the light on a photo conducting selenium cell, which formed a part of a circuit

with a battery and a receiving earphone. Sound waves present in the vicinity of the diaphragm

vibrated the diaphragm, which led to a consequent variation of the light reflected by the

diaphragm. The variation of the light falling on the selenium cell changed the electrical

conductivity of the cell, which in turn changed the current in the electrical circuit. This

changing current reproduced the sound on the earphone.

Figure 3.1: Schematic of the photophone invented by Bell. In this system, sunlight was

modulated by a vibrating diaphragm and transmitted through a distance of about 200 meters in

air to a receiver containing a selenium cell connected to the earphone.

After succeeding in transmitting a voice signal over 200 meters using a light signal, Bell

wrote to his father: "I have heard a ray of light laugh and sing. We may talk by light to any

visible distance without any conducting wire." To quote from Maclean: "In 1880 he (Graham

Bell) produced his 'photophone' which, to the end of his life, he insisted was '...the greatest

invention I have ever made, greater than the telephone....' Unlike the telephone, though, it had

no commercial value."

The modern impetus for telecommunication with carrier waves at optical frequencies owes its

origin to the discovery of the laser in 1960. Earlier, no suitable light source was available that

could reliably be used as the information carrier. At around the same time,

telecommunication traffic was growing very rapidly. It was conceivable then that

conventional telecommunication systems based on, say, coaxial cables, radio and microwave

links, and wire-pair cable, could soon reach a saturation point. The advent of lasers

immediately triggered a great deal of investigation aimed at examining the possibility of

building optical analogues of conventional communication systems. The very first such

modern optical communication experiments involved laser beam transmission through the

atmosphere. However, it was soon realized that shorter-wavelength laser beams could not be

sent in open atmosphere through reasonably long distances to carry signals, unlike, for

example, the longer-wavelength microwave or radio systems. This is due to the fact that a

laser light beam (of wavelength about 1 m) is severely attenuated and distorted owing to

scattering and absorption by the atmosphere. Thus, for reliable light-wave communication

under terrestrial environments it would be necessary to provide a "guiding" medium that

could protect the signal-carrying light beam from the vagaries of the terrestrial atmosphere.

This guiding medium is the optical fiber, a hair-thin structure that guides the light beam from

one place to another as was shown in Figure 3.2.

Page 3: Optical Fibre & Nanotechnology

Figure 3.2: A typical fiber optic communication system: T, transmitter; C, connector; S, splice;

R, repeater; D, detector

In addition to the capability of carrying a huge amount of information, optical fibers

fabricated with recently developed technology are characterized by extremely low losses

(< 0.2 dB/km), as a consequence of which the distance between two consecutive repeaters

(used for amplifying and reshaping the attenuated signals) could be as large as 250 km. We

should perhaps mention here that it was the epoch-making paper of Kao and Hockham in

1966 that suggested that optical fibers based on silica glass could provide the necessary

transmission medium if metallic and other impurities could be removed. Indeed, this 1966

paper triggered the beginning of serious research in developing low-loss optical fibers. In

1970, Kapron, Keck, and Maurer (at Corning Glass in USA) were successful in producing

silica fibers with a loss of about 17 dB/km at a wavelength of 633 nm. (Kapron, Keck, and

Maurer) Since then, the technology has advanced with tremendous rapidity. By 1985 glass

fibers were routinely produced with extremely low losses (< 0.2 dB/km). Along the path of

the optical fiber are splices, which are permanent joints between sections of fibers, and

repeaters that boost the signal and correct any distortion that may have occurred along the

path of the fiber. At the end of the link, the light is detected by a photodetector and

electronically processed to retrieve the signal.

In recent years it has become apparent that fiber-optics are steadily replacing copper wire as

an appropriate means of communication signal transmission. They span the long distances

between local phone systems as well as providing the backbone for many network systems.

Other system users include cable television services, university campuses, office buildings,

industrial plants, and electric utility companies.

A fiber-optic system is similar to the copper wire system that fiber-optics is replacing. The

difference is that fiber-optics use light pulses to transmit information down fiber lines instead

of using electronic pulses to transmit information down copper lines. Looking at the

components in a fiber-optic chain will give a better understanding of how the system works

in conjunction with wire based systems.

At one end of the system is a transmitter. This is the place of origin for information coming

on to fiber-optic lines. The transmitter accepts coded electronic pulse information coming

from copper wire. It then processes and translates that information into equivalently coded

light pulses. A light-emitting diode (LED) or an injection-laser diode (ILD) can be used for

generating the light pulses. Using a lens, the light pulses are funneled into the fiber-optic

medium where they travel down the cable. The light (near infrared) is most often 850nm for

shorter distances and 1,300nm for longer distances on Multi-mode fiber and 1300nm for

single-mode fiber and 1,500nm is used for longer distances.

3.2 Advantages Of Optical Fibres At the heart of an optical communication system is the optical fiber that acts as the

transmission channel carrying the light beam loaded with information. In the present time,

we have ultra low loss fibres (0.001 dB/km) so that the optical signals can be transmitted

through the fibre over a very long distances with low loss. Thus the optical fibres are

dielectric waveguides which transmit the optical signals or data through them with a very low

attenuation and very low dispersion. Thus one can achieve very high band width or high data

rate using fiber optic cables. Now a days, we have dispersion free and dispersion

compensation fibers.

Let us see the advantages of optical fiber communication over conventional communication

system.

Page 4: Optical Fibre & Nanotechnology

Enormous Bandwidths

The information carrying capacity of a transmission system is directly proportional to the

carrier frequency of the transmitted signals. The optical carrier frequency is in the range of

1014

Hz while the radio frequency is about 106

Hz. Thus the optical fibres have enormous

transmission bandwidths and high data rate. Using wavelength division multiplexing

operation, the data rate or information carrying capacity of optical fibres is enhanced to many

orders of magnitude.

Low transmission loss

Due to the usage of ultra low loss fibres and the erbium doped silica fibres as optical

amplifiers, one can achieve almost loss less transmission. Hence for long distance

communication fibres of 0.002 dB/km are used. Thus the repeater spacing is more than 100

km.

Immunity to cross talk

Since optical fibres are dielectric wave guides, they are free from any electromagnetic

interference (EMI) and radio frequency interference (RFI). Since optical interference among

different fibres is not possible, cross talk is negligble even many fibres are cabled together.

Electrical Isolation

Optical fibres are made from silica which is an electrical insulator. Therefore they do not

pick up any electromagnetic wave or any high current lightening. It is also suitable in

explosive environment.

Small size and weight

The size of the fiber ranges from 10 micrometres to 50 micrometres which is very very

small. The space occupied by the fiber cable is negligibly small compared to conventional

electrical cables. Optical fibers are light in weight. These advantages make them to use in

aircrafts and satellites more effectively.

Signal security

The transmitted signal through the fibre does not radiate. Unlike in copper cables, a

transmitted signal cannot be drawn from a fiber without tampering it. Thus, the optical fiber

communication provides 100% signal security.

Ruggedness and flexibility

The fibre cable can be easily bend or twisted without damaging it. Further the fiber cables

are superior than the copper cables in terms of handling, installation, stroage, transportation,

maintenance, strength and durability.

Low cost and availability

Since the fibres are made of silica which is available in abundance. Hence, there is no

shortage of material and optical fibers offer the potential for low cost communication.

Reliability

The optical fibres are made from silicon glass which does not undergo any chemical reaction

or corrosion. Its quality is not affected by external radiation. Further due to its negligible

attenuation and dispersion, optical fiber communication has high reliability. All the above

factors also tend to reduce the expenditure on its maintenance.

Page 5: Optical Fibre & Nanotechnology

3.3 Total internal reflection (TIR)

As mentioned earlier, the guidance of the light beam (through the optical fiber) takes place

because of the phenomenon of total internal reflection (TIR). Light pulses move easily down

the fiber-optic line because of a principle known as total internal reflection. "This principle of

total internal reflection states that when the angle of incidence exceeds a critical value, light

cannot get out of the glass; instead, the light bounces back in. When this principle is applied

to the construction of the fiber-optic strand, it is possible to transmit information down fiber

lines in the form of light pulses. To consider the propagation of light with in an optical fibre,

it is necessary to take account of the refractive index of the dielectric medium. The refractive

index of a medium is defined as the ratio of the velocity of light in vacuum to the velocity of

light in that medium.

A ray of light travels more slowly in an optically dense medium than in one that is less dense

and the refractive index gives the measure of this effect.

Snell’s law of refraction, which is derived from basic electromagnetic theory, states that

when light is incident on two homogeneous isotropic media that have a common plane

boundary, the bending of light at the interface is governed by the following expression

n1 sin 1 = n2 sin 2

Figure 3.3: (a) A ray of light incident on a denser medium (n 2 > n 1 ). (b) A ray incident on a

rarer medium (n 2 < n1 ). (c) For n 2 < n 1 , if the angle of incidence is greater than critical angle, it

will undergo total internal reflection.

As we know, when a ray of light is incident at the interface of two media (like air and glass),

the ray undergoes partial reflection and partial refraction as shown in Figure 3.3. The angles

1, 2, and r represent the angles that the incident ray, refracted ray, and reflected ray make

with the normal. Further, the incident ray, reflected ray, and refracted ray lie in the same

plane. In Figure 3.3 (a), since n2 > n1 we must have (from Snell's law) 2 < 1, i.e., the ray

will bend toward the normal. On the other hand, if a ray is incident at the interface of a rarer

medium (n2 < n1), the ray will bend away from the normal (see Figure 3.3b). The angle of

incidence, for which the angle of refraction is 90º, is known as the critical angle and is

denoted by c. Thus, when

-- (1)

2 = 90 . When the angle of incidence exceeds the critical angle (i.e., when 1 > c), there is

no refracted ray and we have total internal reflection (3.3c).

n1

n2

n1 n1

n2 n2

1

2

r

(a) (b) (c)

Page 6: Optical Fibre & Nanotechnology

Total internal refection confines light within optical fibers (similar to looking down a mirror

made in the shape of a long paper towel tube). Because the cladding has a lower refractive

index, light rays reflect back into the core if they encounter the cladding at a shallow angle. A

ray that exceeds a certain "critical" angle escapes from the fiber.

Example 3.1

For the glass-air interface, n1 = 1.501, n2 = 1.0, and the critical angle is given by

c = sin-1

=41.80

On the other hand, for the glass-water interface, n1 = 1.5, n2 = 1.336, and

c = sin-1

62.5º.

3.4 The Construction Of An Optical Fibre The structure of an optical fibre consists of a transparent core with a refractive index

n1 surrounded by a transparent cladding of slightly lower refractive index n2. The core must a

very clear and pure material for the light or in most cases near infrared light (850nm, 1300nm

and 1500nm). The core can be Plastic (used for very short distances) but most are made from

glass. Glass optical fibers are almost always made from pure silica, but some other materials,

such as fluorozirconate, fluoroaluminate, and chalcogenide glasses, are used for longer-

wavelength infrared applications.

Figure 3.4 (a)

Figure 3.4 (b)

Figure 3.4 (a) A glass fiber consists of a cylindrical central core clad by a material of slightly

lower refractive index. (b) Light rays impinging on the core-cladding interface at an angle

greater than the critical angle are trapped inside the core of the fiber.

Figure 3.4 shows an optical fiber, which consists of a (cylindrical) central dielectric core clad

by a material of slightly lower refractive index. The corresponding refractive index

distribution (in the transverse direction) is given by:

where n1 and n2 ( n1) represent respectively the refractive indices of core and cladding and a

represents the radius of the core. We define a parameter through the following equations.

When << 1 (as is indeed true for silica fibers where n1 is very nearly equal to n2) we may

write

Page 7: Optical Fibre & Nanotechnology

The cladding is usually pure silica while the core is usually silica doped with germanium.

Doping by germanium results in a typical increase of refractive index from n2 to n1.

3.5 Acceptance Angle

To understand the propagation of light in an optical fibre through total internal

reflection at the core cladding interface, it is useful to give more stress upon the geometric

optics approach with reference to the light rays entering the fibre. Since only rays with a

sufficient grazing angle at the core cladding interface are transmitted by the total internal

reflection, it is clear that not all rays entering the fibre core will continue to propagate down

the length of the optical fibre.

Now, for a ray entering the fiber core at its end, if the angle of incidence at the

internal core-cladding interface is greater than the critical angle c [= sin-1

(n2/n1)], the ray

will undergo TIR at that interface. Further, because of the cylindrical symmetry in the fiber

structure, this ray will suffer TIR at the lower interface also and therefore be guided through

the core by repeated total internal reflections.

Figure 3.5 : Acceptance angle layout

Figure 3.5 shows a number of light rays entering the optical fibre at left end (called

Launching End). Let no, n1, n2 be the refractive indices of surrounding, core and clad

respectively where n0 < n2 < n1. Let a ray of light (named as ray number 1) enters the fibre

making an angle θi with axis of fibre. It refracts into the core at angle θr and then travels along

path DA. At point A, it strikes core clad interface and angle of incidence at A is ¢. If ¢ is

greater than critical angle then ray will suffer total internal reflection and hence can propagate

through fibre.

Apply Snell's level at point D we get

ri nn sinsin 10

In right angled triangle AED, we have

090r

090r

Sin r = cos

substituting this in the above equation we get

cossin 10 nn i

We know that decreases as cos increase. Thus, i and hence sin i is maximum, when is

minimum. The minimum value of is equal to the critical angle c. so that the ray just suffer the total

internal reflection at the core cladding interface and the largest value of θi is θ0. Therefore,

imumc min

Page 8: Optical Fibre & Nanotechnology

imumi max0

cnn cossin 100

According to the Snell’s law the critical angle is given by

0

21 90sinsin nn c

That implies 1

2sinn

nc

cc

2sin1cos

=2

2

2

1

1

2

1

2

2 11 nn

nn

n

Substitute this value we get

2

2

2

100 sin nnn

2

2

2

1

0

0

1sin nn

n

2

2

2

1

0

1

0

1sin nn

n

Above Equation gives the maximum value of angle of incidence at the launching end of

the optical fibre, such that the ray can just propagated in the core of the fibre. This angle is

called acceptance angle. The light rays contained within a cone having semi vertical angle 0

are accepted or transmitted along the fibre. This cone is called Acceptance cone.

3.6 Numerical Aperture

On the basis of ray theory analysis it is possible to obtain a relationship between the

acceptance angle and the refractive indices of the three medium involved, namely the core,

cladding and air. This leads to the definition of the more generally used term, the numerical

aperture of an optical fibre. For an optical fibre the acceptance angle is the maximum angle of

incidence at the launching (input) end of the fibre so that the optical information can just

propagate with in the optical fibre. On the similar lines numerical aperture of an optical fibre

is defined as the light gathering ability of an optical fibre.

We return to Figure 3.5 and consider a ray that is incident on the entrance face of the fiber

core, making an angle i with the fiber axis. Let the refracted ray make an angle with the

same axis. Assuming the outside medium to have a refractive index n0 (which for most

practical cases is unity), we get

Obviously, if this refracted ray is to suffer total internal reflection at the core-cladding

interface, the angle of incidence must satisfy the equation,

Since

,

we will have

Let im represent the maximum half-angle of the acceptance cone for rays at the input end.

Applying Snell's law at the input end and using above Equations we must have i< im, where

Page 9: Optical Fibre & Nanotechnology

and we have assumed n0 = 1; i.e., the outside medium is assumed to be air. Thus, if a cone of

light is incident on one end of the fiber, it will be guided through it provided the half-angle of

the cone is less than im. This half-angle is a measure of the light-gathering power of the fiber.

We define the numerical aperture (NA) of the fiber by the following equation:

The numerical apertures for fibres used in short distance communication are in the range of

0.3 to 0.5. Where as for long distance transmission NA lies in the range 0.1 to 0.3.

Example 3.2

For a typical step-index (multimode) fiber with n1 1.45 and 0.01, we get

so that im 12 . Thus, all light entering the fiber must be within a cone of half-angle

12 .

Example 3.3

A silica optical fibre with core diameter large enough to be considered by ray theory

analysis has a core refractive index of 1.50 and a cladding refractive index of 1.47.

Determine (a) the critical angle at the core –cladding interface; (b) the NA of the

fibre; (c) The acceptance angle in air of the fibre.

Example 3.4

A typical relative refractive index difference for an optical fibre designed for long

distance communication is 1%. Estimate the NA and the solid acceptance angle in air

for the fibre when the core index is 1.46. Further, calculate the critical angle at the

core-cladding interface with in the fibre. It may be assumed that the concept of

geometric optics hold for the fibre.

3.7 Modes Of Propagation Of An Optical Fibre

3.7.1 Single Mode:

Single mode of propagation is a single stand (most applications use 2 fibers) of glass fiber

with a diameter of 8.3 to 10 microns that has one mode of transmission. Single Mode Fiber

with a relatively narrow diameter, through which only one mode will propagate typically

1310 or 1550nm. Carries higher bandwidth than multimode fiber, but requires a light source

with a narrow spectral width. Synonyms mono-mode optical fiber, single-mode fiber, single-

mode optical waveguide, uni-mode fiber.

Single Modem fiber is used in many applications where data is sent at multi-frequency

(WDM Wave-Division-Multiplexing) so only one cable is needed - (single-mode on one

single fiber)

Single-mode fiber gives you a higher transmission rate and up to 50 times more distance than

multimode, but it also costs more. Single-mode fiber has a much smaller core than

multimode. The small core and single light-wave virtually eliminate any distortion that could

result from overlapping light pulses, providing the least signal attenuation and the highest

transmission speeds of any fiber cable type.

Single-mode optical fiber is an optical fiber in which only the lowest order bound mode can

propagate at the wavelength of interest typically 1300 to 1320nm.

Page 10: Optical Fibre & Nanotechnology

Figure 3.6 Single mode propagation

3.7.2 Multi-Mode:

Multimode optical fibre has a little bit bigger diameter, with a common diameters in

the 50-to-100 micron range for the light carry component (in the US the most common size is

62.5um). Most applications in which Multi-mode fiber is used, 2 fibers are used (WDM is not

normally used on multi-mode fiber). POF is a newer plastic-based cable which promises

performance similar to glass cable on very short runs, but at a lower cost.

Multimode fiber gives you high bandwidth at high speeds (10 to 100MBS - Gigabit to 275m

to 2km) over medium distances. Light waves are dispersed into numerous paths, or modes, as

they travel through the cable's core typically 850 or 1300nm. Typical multimode fiber core

diameters are 50, 62.5, and 100 micrometers. However, in long cable runs (greater than 3000

feet [914.4 meters), multiple paths of light can cause signal distortion at the receiving end,

resulting in an unclear and incomplete data transmission so designers now call for single

mode fiber in new applications using Gigabit and beyond.

Figure 3.7 Multimode optical fibre

3.8 Types Of An Optical Fibre

3.8.1 Step-Index Optical Fiber The optical fibre with a core of constant refractive index n1 and a cladding of slightly

lower refractive index n2 is known as step index fibre. This is because the refractive index

profile for this type of fibre makes a step change at the core –cladding interface. The

refractive index profile may be defined as:

)(

)(

2

1

claddingarn

corearnrn

Page 11: Optical Fibre & Nanotechnology

Figure 3.8 index profile of step index optical fibre.

Example 3.5

A multimode step index fibre with a core diameter of 80 micro meter and a relative index

difference of 1.5 % is operating at a wavelength of 0.85 micro meter. If the core refractive

index is 1.48, estimate; (a) the normalized frequency of the fibre (b) the number of guided

modes.

Example 3.6

A graded index optical fibre has a core with a parabolic refractive index profile which has a

diameter of 50 micrometer. The fibre has a numerical aperture of 0.2. Estimate the total

number of guided modes propagating with in the fibre when it is operating at a wavelength of

1 micro meter.

3.8.2 Graded Index Optical Fiber It contains a core in which the refractive index diminishes gradually from the center

axis out toward the cladding. The higher refractive index at the center makes the light rays

moving down the axis advance more slowly than those near the cladding. Also, rather than

zigzagging off the cladding, light in the core curves helically because of the graded index,

reducing its travel distance. The shortened path and the higher speed allow light at the

periphery to arrive at a receiver at about the same time as the slow but straight rays in the

core axis. The result: a digital pulse suffers less dispersion. The refractive index of the core

changes with distance r from centre of the core according to the expression,

parameterindextheis

axistheatcoretheofindexrefractivetheisn

radiuscorea

n

nn

a

rnrn

)0(

)0(

)0(

21)0()(

1

1

21

11

Page 12: Optical Fibre & Nanotechnology

Figure 3.9 index profile of graded index optical fibre

Figure 3.10 propagation of optical signals in an graded index optical fibre

3.9 Attenuation in optical fibres

The transmission loss or attenuation of optical fibres is one of the most important factors in

bringing about their wide acceptance in telecommunications. Attenuation and pulse

dispersion represent the two most important characteristics of an optical fiber that determine

the information-carrying capacity of a fiber optic communication system. Obviously, the

lower the attenuation (and similarly, the lower the dispersion) the greater can be the required

repeater spacing and therefore the lower will be the cost of the communication system.

There are many reasons which can cause the loss of optical power as light propagates through

the fibre.

3.9.1 Material Loss: The fabrication of various types of fibres involves GeO2, P2O5 etc. as dopants in silica in

order to modify its refractive index. These dopants have property of observing light waves

corresponding to wavelength range 800 nm-1300nm. Since optical carrier wavelength fall in

this range thus, these materials cause loss of optical power by absorbing a part of it.

3.9.2 Rayleigh scattering Loss:

During the manufacturing process of the fibre a large number of inhomogeneites appear in

the material due to fluctuation in density and presence of impurity atoms. These in

Page 13: Optical Fibre & Nanotechnology

homogeneities act as scattering centres as their dimensions are comparable to the carrier

wavelength.

3.9.3 Absorption Loss:

The absorption of light by core material can take place via three different mechanisms

namely UV absorption, IR absorption and ion resonance. During the manufacturing process

minute quantities of water molecules are trapped in glass fibre. These water molecules

contribute OH-1

ions to the material. A concentration of OH-1

of 1part in billion can cause

1dB/km loss at 950 nm. So dehydration of the material during manufacturing can be

employed to keep OH-1

ions at minima.

3.9.4 Bending Loss:

It is not possible to make core uniform diameter. The diameter of core may be varying

slightly at certain locations. These locations are called as micro bends. When ray of light

strikes at this micro bend then by chance the angle of incidence may become less than the

critical angle. Hence, ray will leak into the cladding , this is called as microbending loss as in

figure 3.11 (a). If whole of the optical fibre is bent then it is called as macro bend and the loss

is due to failure of TIR [Figure 3.11(b)].

Similarly, radiation induced loss, temperature loss leaky mode etc. also contribute to the

attenuation of power in an optical fibre.

Figure 3.11: Bending Loss

The attenuation of an optical beam is usually measured in decibels (dB). If an input power P1

results in an output power P2, the power loss in decibels is given by

(dB) = 10 log10 (P1/P2)

Figure 3.12 shows the spectral dependence of fiber attenuation (i.e., loss coefficient per unit

length) as a function of wavelength of a typical silica optical fiber. The losses are caused by

various mechanisms such as Rayleigh scattering, absorption due to metallic impurities and

water in the fiber, and intrinsic absorption by the silica molecule itself. The Rayleigh

scattering loss varies as 1/ 04, i.e., shorter wavelengths scatter more than longer wavelengths.

Here 0 represents the free space wavelength. This is why the loss coefficient decreases up to

about 1550 nm. The two absorption peaks around 1240 nm and 1380 nm are primarily due to

traces of OH? ions and traces of metallic ions. For example, even 1 part per million (ppm) of

iron can cause a loss of about 0.68 dB/km at 1100 nm. Similarly, a concentration of 1 ppm of

OH- ion can cause a loss of 4 dB/km at 1380 nm. This shows the level of purity that is

required to achieve low-loss optical fibers. If these impurities are removed, the two

absorption peaks will disappear. For 0 > 1600 nm the increase in the loss coefficient is due

to the absorption of infrared light by silica molecules. This is an intrinsic property of silica,

and no amount of purification can remove this infrared absorption tail.

Page 14: Optical Fibre & Nanotechnology

Figure 3.12 :Typical wavelength dependence of attenuation for a silica fiber. Notice that the

lowest attenuation occurs at 1550 nm [adapted from Miya, Hasaka, and Miyashita].

As you see, there are two windows at which loss attains its minimum value. The first window

is around 1300 nm (with a typical loss coefficient of less than 1 dB/km) where, fortunately

the material dispersion is negligible. However, the loss attains its absolute minimum value of

about 0.2 dB/km around 1550 nm. The latter window has become extremely important in

view of the availability of erbium-doped fiber amplifiers.

Example 3.7

Let us assume that the input power of a 5-mW laser decreases to 30 W after

traversing through 40 km of an optical fiber. Find the attenuation of the fiber in

dB/km. [ 0.56 dB/km.]

Example 3.8

When the mean optical power launched in to an 8 km length of fibre is 120 microWatt, the

mean optical power at the fibre output is 3 microWatt. Deteremine;

(a) The overall signal attenuation or loss in decibles through the fibre assuming there are

no splicers and connectors.

(b) The signal attenuation per kilometer for the fibre

(c) The overall signal attenuation for a 10 km optical link using the same fibre with

splicing at 1 km interval, each giving an attenuation of 1 dB.

(d) The numerical input/output ratio in (c).

3.10 Dispersion

In digital communication systems, information to be sent is first coded in the form of pulses

and these pulses of light are then transmitted from the transmitter to the receiver, where the

information is decoded. The larger the number of pulses that can be sent per unit time and

still be resolvable at the receiver end, the larger will be the transmission capacity of the

system. A pulse of light sent into a fiber broadens in time as it propagates through the fiber.

This phenomenon is known as pulse dispersion, and it occurs primarily because of the

following mechanisms:

1. Different rays take different times to propagate through a given length of the fiber.

We will discuss this for a step-index multimode fiber and for a parabolic-index fiber

in this and the following sections. In the language of wave optics, this is known as

intermodal dispersion because it arises due to different modes traveling with different

speeds.

2. Any given light source emits over a range of wavelengths, and, because of the

intrinsic property of the material of the fiber, different wavelengths take different

amounts of time to propagate along the same path. This is known as material

dispersion or intramodal dispersion

Page 15: Optical Fibre & Nanotechnology

3.10.1 Intermodal dispersion

This type of dispersion is also termed as modal dispersion. The dispersion arises due to the

difference in the time taken by the various modes to travel along given length of the fibre and

does not depend upon the wavelength of the light, but depends upon the angle at which the

ray of light strikes core clad interface.

Figure 3.13: Intermodal dispersion

Figure 14 shows a step index optical fibre of diameter d. Ray of light 1 travels along path AB

and strikes at angle of incidence (i) greater than the critical angle (ic) and therefore suffers

the total internal reflection. Let n1 and n2 be the refractive indices of the core and cladding

respectively.

AB=x=path traveled by the ray of light

In triangle ABD i

zxor

x

zi

sinsin

z is the linear distance traveled by the ray of light along the axis of the fibre. If L is the length

of the fibre, then the length of the path (x) traveled by ray of light is

i

Lxtotal

sin and xtotal will be maximum when I is minimum and minimum allowed

value of i is critical angle ic

Thus, ci

Lx

sinmax

2

1max

n

Lnx and xtotal will be minimum when I is maximum i.e. i= 90

0

LL

x0min

90sin

Thus, maximum difference between the two paths of rays reaching the other end of the fibre

is

1

12

1minmaxmax

L

n

nLxxx

If v is the velocity of the optical ray in the core then

iscwheren

cvorn

v

c

1

1 the speed of light in vacuum.

Thus maximum time delay between the highest and lowest mode is

)1(

1max

maxintc

Ln

v

xor

Page 16: Optical Fibre & Nanotechnology

This time delay is called as the dispersion delay and is the characteristic property of the fibre

and this type of delay is absent in single mode fibre.

Example 3.9

For a typical (multimoded) step-index fiber, if we assume n1 = 1.5, = 0.01, L = 1

km, find the dispersion time delay.

3.10.2 Material dispersion or intramodal dispersion

The pulse dispersion that occurs with in a single mode is called intramodal dispersion. This

type of dispersion is wavelength dependent. The refractive index of the material is different

for different wavelengths. Any light source emits light of different wavelengths. Thus,

different wavelength components of an optical pulse have different transit times. Therefore

the spectral components of the

However, a pulse travels with what is known as the group velocity, which is given by

vg = c/ng

where ng is known as the group index and, in most cases its value is slightly larger than n. We

define the material dispersion coefficient Dm, which is measured in ps/km-nm. Dm represents

the material dispersion in picoseconds per kilometer length of the fiber per nanometer

spectral width of the source. At a particular wavelength, the value of Dm is a characteristic of

the material and is (almost) the same for all silica fibers. The values of Dm for different

wavelengths. A negative Dm implies that the longer wavelengths travel faster; similarly, a

positive value of Dm implies that shorter wavelengths travel faster. However, in calculating

the pulse broadening, only the magnitude should be considered.

3.11 V- Number or The Waveguide parameter

While discussing step-index fibers, we considered light propagation inside the fiber as a set

of many rays bouncing back and forth at the core-cladding interface. There the angle could

take a continuum of values lying between 0 and cos-1

(n2/n1), i.e,

0 < < cos-1

(n2/n1)

Now, when the core radius (or the quantity ) becomes very small, ray optics does not remain

valid and one has to use the more accurate wave theory based on Maxwell's equations. In

wave theory, one introduces the parameter

where has been defined earlier and n1

~ n2 . The quantity V is often referred to as the "V-

number" or the "waveguide parameter" of the fiber.

Example 3.10

Consider a step-index fiber (operating at 1300 nm) with n2 = 1.447, = 0.003, and a

= 4.2 m. Thus,

Thus the fiber will be single moded and the corresponding value of will be about

= 3.1º. It may be mentioned that for the given fiber we may write

Thus, for

0 > 2.958/2.4045 = 1.23 m

which guarantees that V < 2.4045, the fiber will be single moded. The wavelength for

which V = 2.4045 is known as the cutoff wavelength and is denoted by c. In this

example, c = 1.23 m and the fiber will be single moded for 0 > 1.23 m.

Page 17: Optical Fibre & Nanotechnology

Example 3.11

For reasons that will be discussed later, the fibers used in current optical

communication systems (operating at 1.55 m) have a small value of core radius and

a large value of . A typical fiber (operating at 0 1.55 m) has n2 = 1.444,

= 0.0075, and a = 2.3 m. Thus, at 0 = 1.55 m, the V-number is,

The fiber will be single moded (at 1.55 m) with = 5.9

0. Further, for the given fiber

we may write

and therefore the cutoff wavelength will be c = 2.556/2.4045 = 1.06 m.

3.12 Applications Of Optical Fibres

(A) Fibre Optics In Medicine:

The initial effort in fibre optics concered the fabrication of aligned flexible fibre bundles in

endoscopy for visualization of internal portions of the human body. Subsequent

developments in the field of fibre optics have made possible the application of flexible

fibrescopes not only to gastroscopy, but also to the other areas of endoscopy. Furthermore,

recent developments have shown that other configuration of rigid, straight and curved

optical fibres can be used in medicine such as a rigid endoscope and ahypodermic probe to

allow visualization of regions under the skin. Also a remote spectrophotometer that consists

of an optical fibre allows the determination of the constituents of blood, such as oxygen

saturation, dye flow etc. recent application of laser in the field of retinal coagulation have

pointed to the possibility of combining the laser with fibre optics for the coagulation of

remote tissues. This would extend the application of from diagnostic to therapeutic

techniques.

(b) Fibre Optics In photoelectronics

A photoelectronic system is capable of converting incident photons into electrons that are

accelerated and multiplied before they are converted in to an electrical or optical signal.

Photomultipliers, cathode ray tubes, image converters, image intensifies are the examples

of photoelectronic systems. Fibre optics provides an efficient means of transporting an

image. One important application of optical fibre in photoelectronics lies in the coupling of

the image intensifier stages.

(c) Fibre Optics as sensors

Although the most important application of optical fibers is in the field of transmission of

information, optical fibers capable of sensing various physical parameters and generating

information are also finding widespread use. The use of optical fibers for such applications

offers the same advantages as in the field of communication: lower cost, smaller size, more

accuracy, greater flexibility, and greater reliability. As compared to conventional electrical

sensors, fiber optic sensors are immune to external electromagnetic interference and can be

used in hazardous and explosive environments. A very important attribute of fiber optic

sensors is the possibility of having distributed or quasi-distributed sensing geometries, which

would otherwise be too expensive or complicated using conventional sensors. With fiber

optic sensors it is possible to measure pressure, temperature, electric current, rotation, strain,

and chemical and biological parameters with greater precision and speed. These advantages

are leading to increased integration of such sensors in civil structures such as bridges and

tunnels, process industries, medical instruments, aircraft, missiles, and even cars.

Fiber optic sensors can be broadly classified into two categories: extrinsic and intrinsic. In

the case of extrinsic sensors, the optical fiber simply acts as a device to transmit and collect

Page 18: Optical Fibre & Nanotechnology

light from a sensing element, which is external to the fiber. The sensing element responds to

the external perturbation, and the change in the characteristics of the sensing element is

transmitted by the return fiber for analysis. The optical fiber here plays no role other than that

of transmitting the light beam. On the other hand, in the case of intrinsic sensors, the physical

parameter to be sensed directly alters the properties of the optical fiber, which in turn leads to

changes in a characteristic such as intensity, polarization, or phase of the light beam

propagating in the fiber.

A large variety of fiber optic sensors has been demonstrated in the laboratory, and some are

already being installed in real systems.

(d) Millatary And Aerospace Applications:

In military optical fibres find their use in guided weapons and submarine war fare

nets, nuclear testing and fixed plant installations etc. in aerospace, optical fibres are widely

used because their low weight and small size and further more these fibres provide full signal

security.

(e) In Communication:

Due to their small size and light weight and enormous bandwidth optical fibres are

widely used in communication.

Page 19: Optical Fibre & Nanotechnology

Questions

1. Consider a step index optical fibre for which n1=1.475, n2=1.460 and a=25 micro

meter. What is the maximum value of theta for which the rays will be guided through

the fibre? (b) corresponding to the maximum value of theta calculate the number of

reflections that would take place in transversing a kilometer length of the fibre.

Ans. 8.2, 2.88 million reflections/km

2. In the above problem assume a loss of only 0.01 % of power at each reflection at the

core cladding interface. Calculate the corresponding loss in dB/km.

Ans. 1234 dB.

3. Repeat the calculations in the above two problems for a bare silica fibre for which

n1=1.46, n2=1 and a=25 micro meter.

Ans. 46.8 degree, 21 millions/km, 9150 dB/km

4. Consider a bare fibre consisting of a core of refractive index 1.48 and having air as

cladding. What is its numerical aperature? What is the maximum incident angle upto

which light can be guided by the fibre? Ans. 1.09, pi/2.

5. Consider a fibre with n1 =1.48, n2=1.46 and with its end placed in water, what is the

maximum angle of incidence for guidance? Ans. 10.5 degree.

6. Polymer optical fibres with high purity polymethyle methacrylate core and florinatted

cladding are commercially available with a numerical aperture of 0.50. What is the

corresponding maximum angle of acceptance? Ans. 60 degree.

7. An optical fibre has a numerical aperture of 0.5 and a cladding refractive index of

1.46. Find

a) the acceptance angle for the fibre in water which has a refractive index of 1.33

b) the critical angle at the core – cladding interface?

8. A step index fibre has a relative refractive index difference of 0.85%. calculate the

critical angle at the core – cladding interface, when the core – index is 1.59. Also

findthe numerical aperture, if the source to fibre medium is air.

9. In an optical fibre, the core material has refractive index 1.546 and refractive index of

clad material is 1.378. What is the value of critical angle? Also find the numerical

aperture and the value of angle of acceptance cone.

10. Optical power of 1.5mW is launched into an optical fibre of length 98m. If the power

emerging from the other end is 0.45 mW, find out the fibre attenuation.

Page 20: Optical Fibre & Nanotechnology

4

Superconductivity and Nanotechnology

____________________________________

4.1 Introduction

Superconductivity is a fascinating and challenging field of physics. Scientists and engineers

throughout the world have been striving to develop an understanding of this remarkable

phenomenon for many years. For nearly 75 years superconductivity has been a relatively

obscure subject. If mercury is cooled below 4.1 K, it loses all electric resistance. This

phenomenon of losing electrical resistance by certain metals was first discovered in 1911 by

Dutch physicist H. Kammerlingh Onnes in Leiden. It was observed that the electrical

resistance of mercury continuously decreased from its melting point (233 K) to 4.2 K and

then, within some hundredths of a degree. Various other metals such as Pb, Sn and In also

show superconductivity. Superconductivity is being applied to many diverse areas such as:

medicine, theoretical and experimental science, the military, transportation, power

production, electronics, as well as many other areas.

Figure 4.1: Temperature dependence of a superconductor like Hg

In 1911, Onnes began to investigate the electrical properties of metals in extremely cold

temperatures. It had been known for many years that the resistance of metals fell when cooled

below room temperature, but it was not known what limiting value the resistance would

approach, if the temperature were reduced to very close to 0 K. Some scientists, such as

William Kelvin, believed that electrons flowing through a conductor would come to a

complete halt as the temperature approached absolute zero. Other scientists, including Onnes,

felt that a cold wire's resistance would dissipate. This suggested that there would be a steady

decrease in electrical resistance, allowing for better conduction of electricity. At some very

low temperature point, scientists felt that there would be a leveling off as the resistance

reached some ill-defined minimum value allowing the current to flow with little or no

resistance. Onnes passed a current through a very pure mercury wire and measured its

resistance as he steadily lowered the temperature. Much to his surprise there was no leveling

off of resistance, let alone the stopping of electrons as suggested by Kelvin. At 4.2 K the

resistance suddenly vanished. Current was flowing through the mercury wire and nothing was

Page 21: Optical Fibre & Nanotechnology

stopping it, the resistance was zero. Figure (4.1) is a graph of resistance versus temperature in

mercury wire as measured by Onnes. According to Onnes, "Mercury has passed into a new

state, which on account of its extraordinary electrical properties may be called the

superconductive state". The experiment left no doubt about the disappearance of the

resistance of a mercury wire. Kamerlingh Onnes called this newly discovered state,

Superconductivity.

Figure 4.2: Temperature dependence of a normal metal and a superconductor

Onnes recognized the importance of his discovery to the scientific community as well as its

commercial potential. An electrical conductor with no resistance could carry current any

distance with no losses. Figure (4.2) shows the temperature dependence of a normal metal

and a superconductor.

In one of Onnes experiments, he started a current flowing through a loop of lead wire

cooled to 4 K. A year later the current was still flowing without significant current loss.

Onnes found that the superconductor exhibited what he called persistent currents, electric

currents that continued to flow without an electric potential driving them. Onnes had

discovered superconductivity, and was awarded the Nobel Prize in 1913. The next great

milestone in understanding how matter behaves at extreme cold temperatures occurred in

1933. German researchers Walter Meissner and Robert Ochsenfeld discovered that a

superconducting material will repel a magnetic field. In subsequent decades other

superconducting metals, alloys and compounds were discovered. In 1941 niobium-nitride was

found to superconduct at 16 K. In 1953 vanadium-silicon displayed superconductive

properties at 17.5 K. And, in 1962 scientists at Westinghouse developed the first commercial

superconducting wire, an alloy of niobium and titanium (NbTi). High-energy, particle-

accelerator electromagnets made of copper-clad niobium-titanium were then developed in the

1960s at the Rutherford-Appleton Laboratory in the UK, and were first employed in a

superconducting accelerator at the Fermilab Tevatron in the US in 1987.In 1987, a ceramic

superconductor of the composition YBa2Cu3O7 was discovered which showed Tc equal to 90

K. In 1988, the value of Tc further shot up to about 125 K for thallium cuplates.

4.2 Meissner Effect

A superconductor is fundamentally different from our imaginary 'perfect' conductor. Contrary

to popular belief, Faraday's Law of induction alone does not explain magnetic repulsion by a

superconductor. At a temperature below its Critical Temperature, Tc, a superconductor will

not allow any magnetic field to freely enter it. This is because microscopic magnetic dipoles

are induced in the superconductor that opposes the applied field. This induced field then

repels the source of the applied field, and will consequently repel the magnet associated with

Page 22: Optical Fibre & Nanotechnology

that field. This implies that if a magnet was placed on top of the superconductor when the

superconductor was above its Critical Temperature, and then it was cooled down to below Tc,

the superconductor would then exclude the magnetic field of the magnet. This can be seen

quite clearly since magnet itself is repelled, and thus is levitated above the superconductor. It thus follows that the diamagnetic behaviour of a superconductor is independent of its history

as illustrated by the Figure (4.3).For this experiment to be successful, the force of repulsion

must exceed the magnet's weight. This is indeed the case for the powerful rare earth magnets

supplied with our kits. One must keep in mind that these phenomena will occur only if the

strength of the applied magnetic field does not exceed the value of the Critical Magnetic

Field, Hc for that superconductor material. This magnetic repulsion phenomenon is called the

Meissner Effect and is named after the person who first discovered it in 1933. German researchers Walter Meissner and Robert Ochsenfeld in 1933 that a superconductor

expelled the magnetic flux as the former were cooled below Tc in an external magnetic field i.

e. it behaved as a perfect dimagnet. This phenomenon is known as Meissner effect.

Figure 4.3: Magnetic behaviour of a perfect superconductor

Figure (4.8) differentiates a conductor and superconductor when placed in a magnetic field.

0)(0 MHB

MH Therefore, the susceptibility is given by

1H

M (4.1)

which is a perfect diamagnet.

Since the resistivity ( ) is zero for a perfect conductor, the application of Ohm’s law

( JE ) indicates that no electric field can exist inside the perfect conductor. Using

Maxwell’s equation

tE

B

Hence B= constant

Thus magnetic flux density passing through a perfect conductor becomes constant.

This means that when a perfect conductor is cooled in the magnetic field until its resistance

becomes zero, the magnetic field of the material gets frozen in and cannot change

subsequently irrespective of the applied field. This is in contradiction to Meissner effect.

Page 23: Optical Fibre & Nanotechnology

Hence the two mutually independent properties defining the superconductor state are the zero

resistivity and perfect diamagnetism.

4.3 Critical Field and Critical Temperature for Superconductors

The value of magnetic field at which the superconductivity vanishes is called threshold or the

critical field, Hc. Its value is few hundred oersteds for most of pure superconductors. The

critical temperature for superconductors is the temperature at which the electrical resistivity

of a metal drops to zero. The transition is so sudden and complete that it appears to be a

transition to a different phase of matter; this superconducting phase is described by the BCS

theory.

Table 4.1: Critical temperature for various Superconductors

Material T-Critical

Gallium 1.1 K

Aluminum 1.2 K

Indium 3.4 K

Tin 3.7 K

Mercury 4.2 K

Lead 7.2 K

Niobium 9.3 K

Niobium-Tin 17.9 K

La-Ba-Cu-oxide 30 K

Y-Ba-Cu-oxide 92 K

Tl-Ba-Cu-oxide 125 K

Several materials exhibit superconducting phase transitions at low temperatures. The highest

critical temperature was about 23 K until the discovery in 1986 of some high temperature

superconductors. Materials with critical temperatures in the range 120 K have received a

great deal of attention because they can be maintained in the superconducting state with

liquid nitrogen (77 K).The magnetic field is expressed by the relation. A typical plot of

critical magnetic field versus temperature for lead is shown in the figure (4.4). Such a plot is

also referred as the magnetic phase diagram. These types of cures are almost parabolic and

can be expressed by the relation

2

2

1)0(c

ccT

THH (4.2)

Where Hc (0) is the critical field at 0 K. Thus, at the critical temperature, the critical field

becomes zero, i.e.,

0)( cc TH

Page 24: Optical Fibre & Nanotechnology

Figure 4.4: Variation of magnetic field with temperature

4.3.1 Type I or Soft Superconductors

The superconductors which exhibit zero resistivity at low temperatures and have the property

of excluding magnetic fields from the interior of the superconductor (Meissner effect). They

are called Type I superconductors. The superconductivity exists only below their critical

temperatures and below a critical magnetic field strength. Type I superconductors are well

described by the BCS theory. These materials give away their superconductivity at lower

field strengths and are referred as soft superconductors. Figure (4.5) describes the behavior of

Lead, a type –I superconductor. These superconductor exhibit perfect diamagnetism below a

critical field Hc which for most of the cases is 0.1 tesla.

Figure 4.5: Type I Superconductor (Induced Magnetic Field Vs. Applied Magnetic

Field)

The Type 1 category of superconductors is mainly comprised of metals and metalloids that

show some conductivity at room temperature. They require incredible cold to slow down

molecular vibrations sufficiently to facilitate unimpeded electron flow in accordance with

what is known as BCS theory. BCS theory suggests that electrons team up in "Cooper pairs"

in order to help each other overcome molecular obstacles - much like race cars on a track

Page 25: Optical Fibre & Nanotechnology

drafting each other in order to go faster. Scientists call this process phonon-mediated

coupling because of the sound packets generated by the flexing of the crystal lattice.

Type 1 superconductors - characterized as the "soft" superconductors - were discovered

first and require the coldest temperatures to become superconductive. They exhibit a very

sharp transition to a superconducting state and "perfect" diamagnetism - the ability to repel a

magnetic field completely. Table 4.2 shows various Type 1 superconductors along with the

critical transition temperature (known as Tc) below which each superconducts. The 3rd

column gives the lattice structure of the solid that produced the noted Tc.

QUIZ I :

Surprisingly, copper, silver and gold, three of the best metallic conductors, do not rank

among the superconductive elements. Why is this? Because for superconductivity to take

place free electrons should be more for making copper pairs but in these metals there is only

one free electron in outer shell. Moreover these have FCC structure and the atoms are so

tightly packed that there is no electron - phonon interactions.

Table 4.2: Critical temperature for various Type I Superconductors with Crystal

Structure

Superconductor Temperature Lattice Lead (Pb) 7.196 K FCC Lanthanum (La) 4.88 K HEX Tantalum (Ta) 4.47 K BCC Mercury (Hg) 4.15 K RHL Tin (Sn) 3.72 K TET

Gallium (Ga) 1.083 K BCC Cadmium (Cd) 0.517 K HEX Platinum (Pt) 0.0019 K BCC Ruthenium (Ru) 0.49 K HEX Lithium (Li) 0.0004 K FCC Platinum (Pt) 0.0019 K BCC Titanium (Ti) 0.40 K ORC

Many additional elements can be coaxed into a superconductive state with the application of

high pressure. For example, phosphorus appears to be the Type 1 element with the highest

Tc. But, it requires compression pressures of 2.5 Mbar to reach a Tc of 14-22 K. The above

list is for elements at normal (ambient) atmospheric pressure.

4.3.2 Type II or Hard Superconductors

The Type 2 category of superconductors is comprised of metallic compounds and alloys. The

recently-discovered superconducting "perovskites" (metal-oxide ceramics that normally have

a ratio of 2 metal atoms to every 3 oxygen atoms) belong to this Type 2 group. They achieve

higher Tc's than Type 1 superconductors by a mechanism that is still not completely

understood. The first superconducting Type 2 compound, an alloy of lead and bismuth, was

fabricated in 1930 by W. de Haas and J. Voogd, but was recognized after the Meissner effect

had been discovered. This new category of superconductors was identified by L.V.

Shubnikov at the Kharkov Institute of Science and Technology in the Ukraine in 1936 found

Page 26: Optical Fibre & Nanotechnology

two distinct critical magnetic fields (known as Hc1 and Hc2) in PbTl2. The first of the oxide

superconductors was created in 1973 by DuPont researcher Art Sleight when Ba(Pb,Bi)O3

was found to have a Tc of 13K. The superconducting oxocuprates followed in 1986. Table

4.2 shows the critical temperature for arious Type II superconductors with crystal structure.

Type 2 superconductors - also known as the "hard" superconductors - differ from

Type 1 in that their transition from a normal to a superconducting state is gradual across a

region of "mixed state" behavior. Since a Type 2 will allow some penetration by an external

magnetic field into its surface, this creates some rather novel mesoscopic phenomena like

superconducting "stripes" and "flux-lattice vortices". Figure (4.7) shows the comparison

between Type I and Type II superconductor.

Figure 4.6: Type II Superconductor (Induced Magnetic Field Vs. Applied Magnetic

Field)

Fig 4.6 describes the magnetization curve of Pb – Bi alloy. It follows from the curve that for

fields less than Hc1, the material behaves as perfect diamagnetic and no flux penetration

takes place. Thus for H< Hc1, the material exists in the superconducting state. As the field

exceeds Hc1, the flux begins to penetrate the specimen and for H= Hc2 the complete

penetration occurs and the material becomes normal conductor. The fields Hc1 and Hc2 are

called as lower and upper critical fields respectively. In the region between Hc1 and Hc2, the

diamagnetic behaviour of the material vanishes gradually and then the flux density B inside

the specimen remains non zero.

Page 27: Optical Fibre & Nanotechnology

Table 4.2: Critical temperature for various Type I Superconductors with Crystal

Structure

Material Temperature Lattice

Sn6Ba4Ca2Cu10Oy

200 K TET

Tl2Ba2Ca2Cu3O10 127-128 K TET

TlBa2CaCu2O7+ 103 K TET

Sn3Ba8Ca4Cu11Ox 109 K ORTH

Bi1.6Pb0.6Sr2Ca2Sb0.1Cu3Oy 115 K ORTH

Sn2Ba2(Y0.5Tm0.5)Cu3O8+

96 K ORTH

Figure 4.7: Type I and Type II Superconductor (Induced Magnetic Field Vs. Applied

Magnetic Field)

Page 28: Optical Fibre & Nanotechnology

Figure 4.8: Diagrammatic differentiation of a conductor and a superconductor

4.4 Isotope Effect

It was observed in the year 1950 that the transition temperatures of a superconductor

varies with its isotopic mass M as

2

1

MT c (4.3)

Thus larger the isotopic mass, lower is the transition temperature. For example, the transition

temperature of mercury changes fro 4.185 K to 4.146 K when its isotopic mass is changed

from 199.5 to 203.4 amu.

Page 29: Optical Fibre & Nanotechnology

Now it is known that the mean square amplitude of atomic or lattice variations at low

temperatures is proportional to 2

1

M and the Debye temperature, D , of the phonon spectrum

is related to M as

tConsMD tan2

1

(4.4)

From Equation (4.3) and (4.4)

tConsT

D

c tan or (4.5)

2

1

MT Dc (4.6)

The equations (4.5) and (4.6) indicate that the lattice variations are likely to be

involved in causing superconductivity. This led Frohlich to show that two electrons in a metal

can effectively attract each other.

4.5 BCS Theory

Many theories for the explanation of the phenomenon of superconductivity were

proposed e.g. by London and London, by Giznburg and London. But the BCS theory

proposed by Bardeen, Cooper, and Schrieffer in 1957 is most successful and is most widely

acceptable. They received the Nobel Prize in Physics in 1972 for this theory. BCS theory

starts from the assumption that there is some attraction between electrons, which can

overcome the Coulomb repulsion. In most materials (in low temperature superconductors),

this attraction is brought about indirectly by the coupling of electrons to the crystal lattice (as

explained above). However, the results of BCS theory do not depend on the origin of the

attractive interaction. The original results of BCS (discussed below) described an "s-wave"

superconducting state, which is the rule among low-temperature superconductors but is not

realized in many "unconventional superconductors", such as the "d-wave" high-temperature

superconductors. Extensions of BCS theory exist to describe these other cases, although they

are insufficient to completely describe the observed features of high-temperature

superconductivity

(i) Electron – phonon – Electron interaction

The electron – phonon interaction is the basis of the BCS theory. This was originally

suggested by Frohlich in 1950, but he could not explain superconductivity. When an electron

passes away near by adjacent ion, both interact electrostatically (means coulomb attraction

takes place). In this way momentum is imparted to ions which cause them to move together

due to elastic behaviour of lattice. This slight movement together increases the positive

charge density then propagates as a wave, which carries momentum through the lattice. In

this way the electron has emitted a phonon, the momentum carried by phonon has been

supplied by the electron, whose momentum changes when the phonon was emitted.

If now at this stage a second electron passes by the moving region of increased

positive density, it will experience an attractive coulomb interaction, and there by it can

absorb all the momentum, the moving region carries. Thus the second electron will absorb the

momentum supplied by the first electron. The result of this is that two electrons have

exchanged momentum through an interaction involving a phonon. This interaction of two

electrons via phonons exceeds the coulomb’s repulsions. The pair of these two electrons is

known as Copper Pairs.

Page 30: Optical Fibre & Nanotechnology

Figure 4.9 : Electron - Electron interaction in a superconducting material

(ii) Copper Pair

Copper Pair is produced when the two electrons interact each other via phonon

attractively and by overcoming the repulsive forces. The binding energy of a copper

pair is called energy gap Eg, which is of the order of 10-3

eV(less than the energy of

unbounded electrons).

Figure 4.10: Electron – electron interaction via a phonon and formation of Copper pair

of a superconductor

Since superconductivity phenomenon is due to these copper pairs, which have binding

energy only of 10 kelvin, hence superconductivity is a low- temperature

phenomenon.

Two electrons are bound in a Copper pair but they are weakly bound and are in

continuous process of breaking and making new pairs with new patterns. The

electrons in a copper pair have opposite spins and the total spin of the pair is zero. As

a result the pairs behave as bosons (instead of fermions in conductors) and hence they

follow Bose –Einstein statistics. When there is no current in the superconductor, the

linear momentum of each electron of the copper pair is equal and opposite, to make

the sum zero. If all the pairs have same constant total momentum, then there will be

no inhibition to the unavoidable process of old pairs breaking up and new pairs

reforming. Thus a large number of pairs are present. All the pairs in same ground state

and form a single large giant system. The current in a superconductor involves this

whole system of pairs, each pair is now having non-zero momentum.

(iii) BCS ground state and existence of energy-gap

The BCS ground state is different from the normal ground state. In the normal

conductors the electron does not interact with each other but in case of

superconductivity the electrons interact and form copper pairs which are responsible

for the phenomenon of superconductivity. In case of non-interacting fermi gas all the

energy states above the fermi surface are vacant and below it, all the states are filled.

This filled state below fermi surface is the ground state of normal conductors. To

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form an excited state, very small energy is required as the first excited state is just

above the fermi surface.

In case of superconductivity the electrons interact with each other attractively and

phonons mediate this interaction. This interacting fermi gas forms the BCS ground

state. This ground state is separated from lowest excited state by energy-gap Eg,

which is binding energy of copper pair. This energy gap is a function of temperature

unlike the energy-gap of semiconductors and insulators. The maximum energy-gap in

superconducting state occurs at 0 K, where pairing is complete and vanishes at T = Tc

where pairing also vanishes.

4.6 Applications

i. Superconductors as conductors - the most obvious application of being as very

efficient conductors; if the national grid were made of superconductors rather

than aluminium, then the savings would be enormous - there would be no need to

transform the electricity to a higher voltage (this lowers the current, which reduces

energy loss to heat) and then back down again.

ii. Superconductors as generator: Electric generators made with superconducting

wire are far more efficient than conventional generators wound with copper wire.

In fact, their efficiency is above 99% and their size about half that of conventional

generators. These facts make them very lucrative ventures for power utilities.

General Electric has estimated the potential worldwide market for

superconducting generators in the next decade at around $20-30 billion dollars.

Late in 2002 GE Power Systems received $12.3 million in funding from the U.S.

Department of Energy to move high-temperature superconducting generator

technology toward full commercialization.

iii. MRI: MRI is a technique developed in the 1940s that allows doctors to see what

is happening inside the body without directly performing surgery. The

development of superconductors has improved the field of MRI as the

superconducting magnet can be smaller and more efficient than an equivalent

conventional magnet.

iv. Superconducting memory cell: A close superconducting circuit, in which

persistent currents can be induced, can work as a memory cell. When the

superconductor is in normal state, there is no current and it is called ‘0’ state. In

the Superconducting state the circuit will have a current and it is called ‘1’ state.

The capacity of a such a memory cell s upto billion bits and the speed is in the

order of 10-6 to 10-7 sec.

v. Superconducting bearings: The Meisner effect is made use of in bearings. The

mutual repulsion between two superconductors due to he repulsion between

magnetic fields they generate can be embodied in bearings and would operate

without power loss.

vi. Superconducting Magnets: Type II superconductors such as niobium-tin and

niobium-titanium are used to make the coil windings for superconducting

magnets. These two materials can be fabricated into wires and can withstand high

magnetic fields. Typical construction of the coils is to embed a large number of

fine filaments ( 20 micrometers diameter) in a copper matrix. The solid copper

gives mechanical stability and provides a path for the large currents in case the

superconducting state is lost. These superconducting magnets must be cooled with

liquid helium.

vii. Superconductor in Particle Accelarator: Most high energy accelerators now use

superconducting magnets. The proton accelerator at Fermilab uses 774

superconducting magnets in a ring of circumference 6.2 kilometers.

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viii. Josephson Junction: The theoretical basis for the SQUID was discovered in

1962 by Brian D. Josephson, a research student at the University of Cambridge,

who also was awarded a Nobel prize for his work. (It seems likely that the

connection between significant discoveries in superconductivity and Nobel prizes

has not gone unnoticed by researchers in the field.) Josephson's work was focused

on what would happen if two layers of superconductors were separated by a thin

layer of insulating material. Such a structure would later be known as a

"Josephson junction". The SQUID magnetometer can detect magnetic field less

than 10 -4

Am-1

and is used for testing new ceramic superconductors.

ix. The high-Tc oxide superconductors with Tc >77 K have advantages over low -Tc

superconductors in the sense that liquid nitrogen serves as a coolant which greatly

reduces the cost. These SQUIDS fabricated using these superconductors find

applications in medical diagnostics, submarine detection and undersea

communications.

x. Magnetic-levitation: Magnetic-levitation is an application where superconductors

perform extremely well. Transport vehicles such as trains can be made to "float"

on strong superconducting magnets, virtually eliminating friction between the

train and its tracks. Not only would conventional electromagnets waste much of

the electrical energy as heat, they would have to be physically much larger than

superconducting magnets. A landmark for the commercial use of MAGLEV

technology occurred in 1990 when it gained the status of a nationally-funded

project in Japan. The Minister of Transport authorized construction of the

Yamanashi Maglev Test Line which opened on April 3, 1997. In December 2003,

the MLX01 test vehicle (shown above) attained an incredible speed of 361 mph

(581 kph).

A SQUID

4.7 Introduction to Nanotechnology

Nanotechnology, which is sometimes shortened to "Nanotech", refers to a field whose

theme is the control of matter on an atomic and molecular scale. Generally nanotechnology

deals with structures of the size 100 nanometers or smaller, and involves developing

materials or devices within that size. Nanotechnology is extremely diverse, ranging from

novel extensions of conventional device physics, to completely new approaches based upon

molecular self-assembly, to developing new materials with dimensions on the nanoscale,

even to speculation on whether we can directly control matter on the atomic scale.

Nanotechnology has the potential to create many new materials and devices with wide-

ranging applications, such as in medicine, electronics, and energy production. On the other

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hand, nanotechnology raises many of the same issues as with any introduction of new

technology, including concerns about the toxicity and environmental impact of

nanomaterials, and their potential effects on global economics, as well as speculation about

various doomsday scenarios.

The first use of the concepts in 'nano-technology' (but predating use of that name) was in

"There's Plenty of Room at the Bottom," a talk given by physicist Richard Feynman at an

American Physical Society meeting at Caltech on December 29, 1959. Feynman described a

process by which the ability to manipulate individual atoms and molecules might be

developed, using one set of precise tools to build and operate another proportionally smaller

set, so on down to the needed scale. In the course of this, he noted, scaling issues would arise

from the changing magnitude of various physical phenomena: gravity would become less

important, surface tension and Van der Waals attraction would become more important, etc.

This basic idea appears plausible, and exponential assembly enhances it with parallelism to

produce a useful quantity of end products.

The term "nanotechnology" was defined by Tokyo Science University Professor Norio

Taniguchi in a 1974 paper as follows: "'Nano-technology' mainly consists of the processing

of, separation, consolidation, and deformation of materials by one atom or by one molecule."

In the 1980s the basic idea of this definition was explored in much more depth by Dr. K. Eric

Drexler, who promoted the technological significance of nano-scale phenomena and devices

through speeches and the books Engines of Creation: The Coming Era of Nanotechnology

(1986) and Nanosystems: Molecular Machinery, Manufacturing, and Computation, and so

the term acquired its current sense.

Engines of Creation: The Coming Era of Nanotechnology is considered the first book on the

topic of nanotechnology. Nanotechnology and nanoscience got started in the early 1980s with

two major developments; the birth of cluster science and the invention of the scanning

tunneling microscope (STM). This development led to the discovery of fullerenes in 1986

and carbon nanotubes a few years later. In another development, the synthesis and properties

of semiconductor nanocrystals was studied. This led to a fast increasing number of metal

oxide nanoparticles of quantum dots. The atomic force microscope was invented six years

after the STM was invented. In 2000, the United States National Nanotechnology Initiative

was founded to coordinate Federal nanotechnology research and development.

4.8 Fundamental concepts

One nanometer (nm) is one billionth, or 10-9

, of a meter. By comparison, typical carbon-

carbon bond lengths, or the spacing between these atoms in a molecule, are in the range 0.12-

0.15 nm, and a DNA double-helix has a diameter around 2 nm. The comparative size of a

nanometer to a meter is the same as that of a marble to the size of the earth.

Two main approaches are used in nanotechnology.

1. "Bottom-up" approach

2. "Top-down" approach

In the "bottom-up" approach, materials and devices are built from molecular components

which assemble themselves chemically by principles of molecular recognition. Top-down

approaches seek to create smaller devices by using larger ones to direct their assembly.

4.9 Nanowire

A nanowire is a nanostructure, with the diameter of the order of a nanometer (10−9

meters).

Alternatively, nanowires can be defined as structures that have a lateral size constrained to

tens of nanometers or less and an unconstrained longitudinal size. At these scales, quantum

Page 34: Optical Fibre & Nanotechnology

mechanical effects are important — hence such wires are also known as "quantum wires".

Many different types of nanowires exist, including metallic (e.g., Ni, Pt, Au), semiconducting

(e.g., Si, InP, GaN, etc.), and insulating (e.g., SiO2,TiO2). Molecular nanowires are composed

of repeating molecular units either organic (e.g. DNA) or inorganic (e.g. Mo6S9-xIx).

4.9.1 Synthesis of Nanowires

Nanowire structures are grown through several common laboratory techniques including

suspension, deposition (electrochemical or otherwise), and VLS growth.

1. Suspension

A suspended nanowire is a wire produced in a high-vacuum chamber held at the longitudinal

extremities. Suspended nanowires can be produced by:

1) The chemical etching or bombardment (typically with highly energetic ions) of a larger

wire.

2) Indenting the tip of a STM in the surface of a metal near its melting point, and then

retracting it.

2. Deposition

A common technique for creating a nanowire is the Vapor-Liquid-Solid (VLS) synthesis

method. This technique uses as source material either laser ablated particles or a feed gas

(such as silane). The source is then exposed to a catalyst. For nanowires, the best catalysts are

liquid metal (such as gold) nanoclusters, which can either be purchased in colloidal form and

deposited on a substrate or self-assembled from a thin film by dewetting. This process can

often produce crystalline nanowires in the case of semiconductor materials.

The source enters these nanoclusters and begins to saturate it. Once supersaturation is

reached, the source solidifies and grows outward from the nanocluster. The final product's

length can be adjusted by simply turning off the source. Compound nanowires with super-

lattices of alternating materials can be created by switching sources while still in the growth

phase. Inorganic nanowires such as Mo6S9-xIx(which are alternatively viewed as cluster

polymers) are synthesised in a single-step vapour phase reaction at elevated temperature.

Figure 4.11 A SEM image of a 15 micron nickel wire

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4.9.2 Uses of nanowires

Nanowires still belong to the experimental world of laboratories. However, they may

complement or replace carbon nanotubes in some applications.

i. Nanowires can be used to build the next generation of computing devices.

ii. Nanowires are used to create active electronic elements. The first key step is to

chemically dope a semiconductor nanowire. This has already been done to

individual nanowires to create p-type and n-type semiconductors. The next step

was to find a way to create a p-n junction, one of the simplest electronic devices.

This was achieved in two ways. The first way was to physically cross a p-type

wire over an n-type wire. The second method involved chemically doping a single

wire with different dopants along the length. This method created a p-n junction

with only one wire. After p-n junctions were built with nanowires, the next logical

step was to build logic gates. By connecting several p-n junctions together,

researchers have been able to create the basis of all logic circuits: the AND, OR,

and NOT gates have all been built from semiconductor nanowire crossings.

Semiconductor nanowire crossings are important to the future of digital

computing.

iii. Nanowires are being studied for use as photon ballistic waveguides as

interconnects in quantum dot/quantum effect well photon logic arrays. Photons

travel inside the tube, electrons travel on the outside shell. When two nanowires

acting as photon waveguides cross each other the juncture acts as a quantum dot.

iv. Dispersions of conducing nanowires in different polymers are being investigated

for use as transparent electrodes for flexible flat-screen displays.

v. Due to their high Young's moduli, their use in mechanically enhancing composites

is being investigated. Because nanowires appear in bundles, they may be used as

tribological additives to improve friction characteristics and reliability of

electronic transducers and actuators.

4.10 Carbon Nanotubes

Carbon nanotubes (CNTs) are allotropes of carbon with a nanostructure that can have a

length-to-diameter ratio greater than 10,000,000 and as high as 40,000,000 as of 2004. These

cylindrical carbon molecules have novel properties that make them potentially useful in many

applications in nanotechnology, electronics, optics and other fields of materials science, as

well as potential uses in architectural fields. They exhibit extraordinary strength and unique

electrical properties, and are efficient conductors of heat. Their final usage, however, may be

limited by their potential toxicity.Nanotubes are members of the fullerene structural family,

which also includes the spherical buckyballs. The cylindrical nanotube usually has at least

one end capped with a hemisphere of the buckyball structure. Their name is derived from

their size, since the diameter of a nanotube is in the order of a few nanometers

(approximately 1/50,000th of the width of a human hair), while they can be up to several

millimeters in length (as of 2008). Nanotubes are categorized as single-walled nanotubes

(SWNTs) and multi-walled nanotubes (MWNTs). The nature of the bonding of a nanotube is

described by applied quantum chemistry, specifically, orbital hybridization. The chemical

bonding of nanotubes is composed entirely of sp2 bonds, similar to those of graphite. This

bonding structure, which is stronger than the sp3 bonds found in diamonds, provides the

molecules with their unique strength. Nanotubes naturally align themselves into "ropes" held

together by Van der Waals forces. Under high pressure, nanotubes can merge together,

trading some sp² bonds for sp³ bonds, giving the possibility of producing strong, unlimited-

length wires through high-pressure nanotube linking.

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4.10.1 Types of carbon nanotubes and related structures

Single-walled

armchair

(n, n)

the chiral vector is bent,

while the translation vector

stays straight

graphene nanoribbon

the chiral vector is bent,

while the translation vector

stays straight

zigzag

(n,0)

chiral (n, m)

n and m can be

counted at the end of

the tube

graphene nanoribbon

Most single-walled nanotubes (SWNT) have a diameter of close to 1 nanometer, with a tube

length that can be many thousands of times longer. The structure of a SWNT can be

conceptualized by wrapping a one-atom-thick layer of graphite called graphene into a

seamless cylinder. The way the graphene sheet is wrapped is represented by a pair of indices

(n,m) called the chiral vector. The integers n and m denote the number of unit vectors along

two directions in the honeycomb crystal lattice of graphene. If m=0, the nanotubes are called

"zigzag". If n=m, the nanotubes are called "armchair". Otherwise, when n is not equal to m,

they are called "chiral". Single-walled nanotubes are a very important variety of carbon

nanotube because they exhibit important electric properties that are not shared by the multi-

walled carbon nanotube (MWNT) variants.

4.10.2 Applications of Carbon Nanotubes

The special nature of carbon combines with the molecular perfection of buckytubes (single-

wall carbon nanotubes) to endow them with exceptionally high material properties such as

electrical and thermal conductivity, strength, stiffness, and toughness. No other element in the

periodic table bonds to itself in an extended network with the strength of the carbon-carbon

bond. The delocalised pi-electron donated by each atom is free to move about the entire

structure, rather than stay home with its donor atom, giving rise to the first molecule with

metallic-type electrical conductivity. The high-frequency carbon-carbon bond vibrations

provide an intrinsic thermal conductivity higher than even diamond.In most materials,

however, the actual observed material properties - strength, electrical conductivity, etc. - are

degraded very substantially by the occurrence of defects in their structure. For example, high

strength steel typically fails at about 1% of its theoretical breaking strength. Buckytubes,

however, achieve values very close to their theoretical limits because of their perfection of

structure - their molecular perfection. This aspect is part of the unique story of buckytubes.

Buckytubes are an example of true nanotechnology: only a nanometer in diameter, but

molecules that can be manipulated chemically and physically. They open incredible

applications in materials, electronics, chemical processing and energy management.

(i)Field Emission

Buckytubes are the best known field emitters of any material. This is understandable, given

their high electrical conductivity, and the unbeatable sharpness of their tip (the sharper the

tip, the more concentrated will be an electric field, leading to field emission; this is the same

reason lightening rods are sharp). The sharpness of the tip also means that they emit at

Page 37: Optical Fibre & Nanotechnology

especially low voltage, an important fact for building electrical devices that utilize this

feature. Buckytubes can carry an astonishingly high current density, possibly as high as 1013

A/cm2. An immediate application of this behaviour receiving considerable interest is in field-

emission flat-panel displays. Instead of a single electron gun, as in a traditional cathode ray

tube display, here there is a separate electron gun (or many) for each pixel in the display. The

high current density, low turn-on and operating voltage, and steady, long-lived behaviour

make buckytubes attract field emitters to enable this application. Other applications utilising

the field-emission characteristics of buckytubes include: general cold-cathode lighting

sources, lightning arrestors, and electron microscope sources.

(ii) Conductive Plastics

Much of the history of plastics over the last half century has been as a replacement for metal.

For structural applications, plastics have made tremendous headway, but not where electrical

conductivity is required, plastics being famously good electrical insulators. This deficiency is

overcome by loading plastics up with conductive fillers, such as carbon black and graphite

fibres (the larger ones used to make golf clubs and tennis racquets). The loading required to

provide the necessary conductivity is typically high, however, resulting in heavy parts, and

more importantly, plastic parts whose structural properties are highly degraded. It is well

established that the higher aspect ratio of filler, the lower loading required to achieve a given

level of conductivity. Buckytubes are ideal in this sense, since they have the highest aspect

ratio of any carbon fibre. In addition, their natural tendency to form ropes provides inherently

very long conductive pathways even at ultra-low loadings. Applications that exploit this

behaviour of buckytubes include EMI/RFI shielding composites and coatings for enclosures,

gaskets, and other uses; electrostatic dissipation (ESD), and antistatic materials and (even

transparent!) coatings; and radar-absorbing materials.

(iii)Energy Storage

Buckytubes have the intrinsic characteristics desired in material used as electrodes in

batteries and capacitors, two technologies of rapidly increasing importance. Buckytubes have

a tremendously high surface area (~1000 m2/g), good electrical conductivity, and very

importantly, their linear geometry makes their surface highly accessible to the electrolyte

.Research has shown that buckytubes have the highest reversible capacity of any carbon

material for use in lithium-ion batteries In addition, buckytubes are outstanding materials for

supercapacitor electrodes and are now being marketed.

Buckytubes also have applications in a variety of fuel cell components. They have a number

of properties including high surface area and thermal conductivity that make them useful as

electrode catalyst supports in PEM fuel cells. They may also be used in gas diffusion layers

as well as current collectors because of their high electrical conductivity. Buckytubes' high

strength and toughness to weight characteristics may also prove valuable as part of composite

components in fuel cells that are deployed in transport applications where durability is

extremely important.

(iv)Molecular Electronics

The idea of building electronic circuits out of the essential building blocks of materials -

molecules - has seen a revival the past five years, and is a key component of nanotechnology.

In any electronic circuit, but particularly as dimensions shrink to the nanoscale, the

interconnections between switches and other active devices become increasingly important.

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Their geometry, electrical conductivity, and ability to be precisely derived, make buckytubes

the ideal candidates for the connections in molecular electronics. In addition, they have been

demonstrated as switches themselves.

(v)Fibres and Fabrics

Fibres spun of pure buckytubes have recently been demonstrated [R.H. Baughman, Science

290, 1310 (2000)] and are undergoing rapid development, along with buckytube composite

fibres. Such super strong fibres will have applications including body and vehicle armour,

transmission line cables, woven fabrics and textiles.

(vi)Catalyst Supports

Buckytubes have an intrinsically high surface area; in fact, every atom is not just on a surface

- each atom is on two surfaces, the inside and outside! Combined with the ability to attach

essentially any chemical species to their sidewalls provides an opportunity for unique catalyst

supports. Their electrical conductivity may also be exploited in the search for new catalysts

and catalytic behaviour.

(vii)Biomedical Applications

The exploration of buckytubes in biomedical applications is just underway, but has

significant potential. Cells have been shown to grow on buckytubes, so they appear to have

no toxic effect. The cells also do not adhere to the buckytubes, potentially giving rise to

applications such as coatings for prosthetics and anti-fouling coatings for ships.The ability to

chemically modify the sidewalls of buckytubes also leads to biomedical applications such as

vascular stents, and neuron growth and regeneration.

(viii)Other Applications

There is a wealth of other potential applications for buckytubes, such as solar collection;

nanoporous filters; catalyst supports; and coatings of all sorts. There are almost certainly

many unanticipated applications for this remarkable material that will come to light in the

years ahead and which may prove to be the most important and valuable of all.

4.11 Nanocrystals

Fahlman, B. D. has described a nanocrystal as any nanomaterial with at least one dimension

≤ 100nm and that is singlecrystalline. More properly, any material with a dimension of less

than 1 micrometre, i.e., 1000 nanometers, should be referred to as a nanoparticle, not a

nanocrystal. For example, any particle which exhibits regions of crystallinity should be

termed nanoparticle or nanocluster based on dimensions. These materials are of huge

technological interest since many of their electrical and thermodynamic properties show

strong size dependence and can therefore be controlled through careful manufacturing

processes. Crystalline nanoparticles are also of interest because they often provide single-

domain crystalline systems that can be studied to provide information that can help explain

the behaviour of macroscopic samples of similar materials, without the complicating presence

of grain boundaries and other defects. Semiconductor nanocrystals in the sub-10nm size

range are often referred to as quantum dots. Crystalline nanoparticles made with zeolite are

used as a filter to turn crude oil onto diesel fuel at an ExxonMobil oil refinery in Louisiana, a

method cheaper than the conventional way. A layer of crystalline nanoparticles is used in a

new type of solar panel named SolarPly made by Nanosolar. It is cheaper than other solar

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panels, more flexible, and claims 12% efficiency. (Conventionally inexpensive organic solar

panels convert 9% of the sun's energy into electricity.) Crystal tetrapods 40 nanometers wide

convert photons into electricity, but only have 3% efficiency. (Source: National Geographic

June 2006)

The term NanoCrystal is a registered trademark of Elan Pharma International Limited

(Ireland) used in relation to Elan’s proprietary milling process and nanoparticulate drug

formulations.

4.11.1 Quantum Dots

Quantum Dots, also known as nanocrystals, are a non-traditional type of semiconductor with

limitless applications as an enabling material across many industries. Each of Evident

Technologies' quantum dot product lines have a specified, unique composition and size that

give them novel quantum properties waiting to be exploited.

Shortcomings of Traditional Semiconductors

Traditional semiconductors have a shortcoming that they lack versatility. Their optical and

electronic qualities are costly to adjust, because their bandgap cannot be easily changed.

Their emission frequencies cannot be easily manipulated by engineering. EviDots exist in a

quantum world, one where properties are specified by our customers. Evident's unique

technology allows us to make semiconductors with tunable bandgaps, allowing for unique

optical and electronic properties and a broad range of emission frequencies limited only by

our imagination, not by cost.

Evident Technologies Quantum Dots - Versatile and Flexible in Form

Quantum dots are unparalleled in versatility and flexible in form. As small crystals, they can

be mixed into liquid solution, making them ideal for fluorescent tagging in biological

applications. As quantum dust, they perform as an innovative security taggant, adhering

invisibly to trespassers while emitting an infrared signal giving law enforcement the edge. In

bead form, they can be blended into ink, making for an excellent anti-counterfeiting pigment.

EviDots can be made into a film possessing legendary non-linear performance for

applications such as photonic switching, optical signal conditioning, and mode-locking lasers.

When drawn into fibers, they may serve as Homeland Security devices, detecting radiation

and helping fight terrorism.

Page 40: Optical Fibre & Nanotechnology

Questions

1. The actual energy gap at 0K in lead is 4.37 × 10-22

J. a) What is the critical

temperature according to BCS theory? B) radiation of what maximum wavelength

could break apart cooper pairs in lead at 0K? Ans: ( (a) 8.96 K (b) 4.545 x 10 -

4m)

2. The critical temperature for mercury with isotopic mass when its critical temperature

changes to 4.15K Ans: (202.7)

3. Lead in a superconducting state has critical temperature of 6.2K at zero magnetic field

and critical field 1064.00 MAmHC at 0K. Calculate the critical field at a) 2K, b)

2.5K & c) 3K. Discuss the result. Ans: ( (a) 2 K (b) 2.5 K (c)0.049 )

4. The area of a coil of 25 turns is 1.6cm2. This coil is inserted in 0.3s in a magnetic field

of 1.8T such that its plane is perpendicular to the flux lines of the field. Calculate the

emf induced in the coil. Also, calculate the total charge that passes through the wire, if

its resistance is 10Ω. Ans: (2.4 x 10 -2

V, 7.2x 10 -4

C)

5. A parallel plate capacitor of plate separation 0.25cm is connected in an electric circuit

having source voltage 250V. What is the value of the displacement current for 100ns

if the plate area is 100cm2. Ans: (0.0885 A)

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References:

1. David J. Griffiths, Introduction to Electrodynamics, Prentice Hall of India, 1999.

2. Nicola A. Spaldin , Magnetic Materials Fundamentals and Device Applications,

Cambridge University Press 2008.

3. Charles Kittel, Introduction to Solid Sate Physics, 8th

ed., John Willey and Sons 2005.

4. N. S. Kapany, Fibre Optics Principles and Applications, Academic Press, 1967.

5. Ajoy Ghatak and K Thyagarajan, Introduction to Fibre Opticcs, Cambridge University

Press, 1998.

6. Detlef Gloge, Optical fibre technology, IEEE Press 1976.

7. http://superconductors.org

8. http://hypaerphysics.phy-astr.gsu.edu

9. Ratner, Nanotechnology, Pearson Education 2008.