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 informationtransmission 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

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.

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.

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.

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 2

n2

n2

n1 1

n2

n1 n1

r

(a)

(c)

(b)

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

c),

there is

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 = 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 longerwavelength infrared applications. c

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 write

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

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 n0 sin i n1 sin r In right angled triangle AED, we have 900 r 90 0 r Sin r = cos substituting this in the above equation we get n0 sin i n1 cos 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, c

min imum

i

max imum

0

n0 sin

n1 cos

0

c

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

n1 sin That implies

sin

c

cos

c

n2 sin 900

c

n2 n1 1 sin 2

c

n22 n12

= 1

1 n12 n1

n22

Substitute this value we get

n0 sin sin

n12

0

1 n0

0

n12

n22 n22

1 n12 n22 n0 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. 0

sin

1

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

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, singlemode 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.

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: n1 r a (core) nr n2 r a (cladding)

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, n1 (r ) n1 (0) 1 2

r a

n1 (0) n 2 n1 (0) a

core radius

n1 (0) is the refractive index of the core at the axis is the index parameter

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

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.

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

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 z z In triangle ABD sin i or x x sin i 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 L and xtotal will be maximum when I is minimum and minimum allowed xtotal sin i value of i is critical angle ic L Thus, x max sin ic Ln1 x max and xtotal will be minimum when I is maximum i.e. i= 900 n2 L xmin L sin 900 Thus, maximum difference between the two paths of rays reaching the other end of the fibre is n L x max xmax xmin L 1 1 n2 1 If v is the velocity of the optical ray in the core then c c n1 or v where c is the speed of light in vacuum. v n1 Thus maximum time delay between the highest and lowest mode is x max Ln1 int or max v c(1 )

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

will be about

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.

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 we may write

and therefore the cutoff wavelength will be

c

= 5.90. Further, for the given fiber

= 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

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.

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.

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

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, particleaccelerator 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

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.

B M) 0 0 (H H M Therefore, the susceptibility is given by

M H

1

(4.1)

which is a perfect diamagnet. Since the resistivity ( ) is zero for a perfect conductor, the application of Ohm’s law (E J ) indicates that no electric field can exist inside the perfect conductor. Using Maxwell’s equation B E t 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.

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

Hc

T2 H c (0) 1 Tc2

(4.2)

Where Hc (0) is the critical field at 0 K. Thus, at the critical temperature, the critical field becomes zero, i.e., H c (Tc ) 0

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

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) Lanthanum (La) Tantalum (Ta) Mercury (Hg) Tin (Sn) Gallium (Ga) Cadmium (Cd) Platinum (Pt) Ruthenium (Ru) Lithium (Li) Platinum (Pt) Titanium (Ti)

7.196 K 4.88 K 4.47 K 4.15 K 3.72 K 1.083 K 0.517 K 0.0019 K 0.49 K 0.0004 K 0.0019 K 0.40 K

FCC HEX BCC RHL TET BCC HEX BCC HEX FCC BCC 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

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.

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

Material Sn6Ba4Ca2Cu10Oy

Temperature 200 K

Lattice TET

Tl2Ba2Ca2Cu3O10 TlBa2CaCu2O7+ Sn3Ba8Ca4Cu11Ox

127-128 K 103 K 109 K

TET TET ORTH

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

ORTH

Sn2Ba2(Y0.5Tm0.5)Cu3O8+

ORTH

96 K

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

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 1 2

Tc M (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.

Now it is known that the mean square amplitude of atomic or lattice variations at low temperatures is proportional to M is related to M as 1 2

1 2

and the Debye temperature,

M Cons tan t From Equation (4.3) and (4.4) D

Tc

Cons tan t or

D

, of the phonon spectrum (4.4)

(4.5)

D 1 2

Tc D M (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.

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

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.

ii.

iii.

iv.

v.

vi.

vii.

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. 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. 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. 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. 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. 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. 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.

viii.

ix.

x.

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

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 carboncarbon bond lengths, or the spacing between these atoms in a molecule, are in the range 0.120.15 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

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 superlattices 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

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. ii.

iii.

iv. v.

Nanowires can be used to build the next generation of computing devices. 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. 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. Dispersions of conducing nanowires in different polymers are being investigated for use as transparent electrodes for flexible flat-screen displays. 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, unlimitedlength wires through high-pressure nanotube linking.

4.10.1 Types of carbon nanotubes and related structures Single-walled

the chiral vector is bent, the chiral vector is bent, armchair while the translation vector graphene nanoribbon while the translation vector (n, n) stays straight stays straight

zigzag (n,0)

chiral (n, m)

n and m can be counted at the end of graphene nanoribbon the tube

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 multiwalled carbon nanotube (MWNT) variants. 4.10.2 Applications of Carbon Nanotubes The special nature of carbon combines with the molecular perfection of buckytubes (singlewall 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

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 fieldemission 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.

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 singledomain 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

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.

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 4 m) 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 H C 0 0.064MAm 1 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)

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.