DOC-20240218-WA0001.

RAJALAKSHMI ENGINEERING COLLEGE (AUTONOMOUS) THANDALAM, CHENNAI – 602105. PH23132 PHYSICS FOR INFORMATION SCIENCE Common to I semester CSE, CSE (CS), AIML, AI&DS & CSD and II semester- B.Tech – Information Technology Faculty of Physics 1 Department of Humanities and Sciences Subject Code Subject Name Category L T P C PHYSICS FOR INFORMATION SCIENCE PH23132 BS 3 0 2 4 For Common to –I sem B.E.-CSE, CSD, CSE (Cyber Security), AIML & AI&DS&II sem B.Tech.- IT Objectives:  To understand the principles of laser and fiber optics in engineering and technology.  To analyze the properties of magnetic and superconducting materials.  To understand the advanced concept of quantum theory and applications.  To become proficient in semiconductor applications  To become proficient in optoelectronic devices UNIT-I LASERS AND FIBER OPTICS 9 Lasers: Characteristics, Einstein’s A and B coefficients derivation – resonant cavity, optical amplification (qualitative) –Nd-YAG Laser, Semiconductor lasers: Homojunction and Heterojunction- Applications of Lasers. Fiber optics: principle, numerical aperture and acceptance angle - types of optical fibers (material, mode and refractive index) – losses associated with optical fibers -Fiber optic communication system - fiber optic sensors: pressure and displacement. UNIT-II MAGNETIC AND SUPERCONDUCTING MATERIALS 9 Magnetic dipole moment – atomic magnetic moments- magnetic permeability and susceptibility -Magnetic material classification: diamagnetism – paramagnetism – ferromagnetism – antiferromagnetism – ferrimagnetism – Domain Theory- M versus H behaviour – Hard and soft magnetic materials – examples and uses-– Magnetic principle in computer data storage. Superconductors: Properties - BCS theory (Qualitative)- Type-I and Type II superconductors - Magnetic levitation-SQUID-Cryotron. UNIT-III QUANTUM PHYSICS 9 Introduction- Quantum free electron theory-De Broglie’s concept-Schrodinger wave equation-Time independent and time dependent equations-Physical significance of wave function - Particle in a one dimensional box – electrons in metals -degenerate states – Fermi- Dirac statistics – Density of energy states -Size dependence of Fermi energy – Quantum confinement – Quantum wells, Quantum wires, Quantum dots and Quantum clusters - Band gap of nanomaterials. UNIT-IV SEMICONDUCTOR PHYSICS 9 Intrinsic Semiconductors – Energy band diagram – direct and indirect band gap semiconductors – Carrier concentration in intrinsic semiconductors – Band gap determination- extrinsic semiconductors (Qualitative)- Hall effect - determination of Hall co-efficient -Formation of P-N junction-Forward bias- Reverse bias -Ohmic contact- Schottky diode- Tunnel diode. UNIT-V OPTOELECTRONICS 9 Classification of optical materials – carrier generation and recombination processes – Absorption, emission and 2 scattering of light in metals, insulators and semiconductors (concepts only) – Photo electric effect-Photo current in a P- N diode – Photo transistor-solar cell - LED – Organic LED- Non Linear Optical materials-properties and applications. Contact Hours : 45 List of Experiments 1 Determine the wavelength of the laser using grating and size of the particle using diode laser. 2 Determine the numerical aperture and acceptance angle of optical fiber. 3 Study the permeability of the free space using Helmoltz coil. 4 Determine the hysteresis loss in the transformer core using B-H curve unit. 5 Determine the band gap of given semiconductor. 6 Determine the Hall coefficient of semiconducting material. 7 Determine specific resistance of the material of given wires using metre bridge. 8 Study the resonance frequency in series connected LCR circuits. 9 Determine the V-I characteristics of the solar cell. 10 Determine the thickness of the given specimen by using air wedge method. Contact Hours : 30 Total Contact Hours : 75 Course Outcomes: On completion of the course, the students will be able to  Use the concepts of Laser and Fiber optics in communication.  Use the properties of magnetic and superconducting materials in data storage devices.  Apply the concepts of electron transport in nanodevices.  Analyse the physics of semiconductor devices  Analyze the properties of optical materials for optoelectronic applications. Suggested Activities  Problem solving sessions Suggested Evaluation Methods  Quizzes  Class Presentation / Discussion Text Book(s): 3 1 Bhattacharya, D.K. & Poonam, T. “Engineering Physics”. Oxford University Press, 2015. 2 Jasprit Singh, “Semiconductor Devices: Basic Principles”, Wiley 2012. 3 Kasap, S.O. “Principles of Electronic Materials and Devices”, McGraw-Hill Education, 2007. Reference Books(s) / Web links: 1 S. O. Pillai, Solid state physics, New Age International, 2015. 2 Serway, R.A. & Jewett, J.W. “Physics for Scientists and Engineers”. Cengage Learning, 2010. 3 Hanson, G.W. “Fundamentals of Nanoelectronics”. Pearson Education, 2009. 4 S.No. UNITS 1 LASERS AND FIBRE OPTICS 2 MAGNETIC AND SUPERCONDUCTING MATERIALS 3 QUANTUM PHYSICS 4 SEMICONDUCTOR PHYSICS 5 OPTOELECTRONIC DEVICES 5 UNIT I LASERS AND FIBRE OPTICS LASER The word “LASER” is an acronym for “Light Amplification by Stimulated Emission of Radiation. Einstein in 1917 theoretically proved that the process of stimulated emission must exist. But only in the year 1954, a group of scientists at Columbia University headed by Charles H.Townes operated a microwave device for “Microwave Amplification by Stimulated Emission of Radiation (MASER)”. In 1960, T.H.Maiman of the Hughes Research Laboratories first achieved laser action at optical frequency in ruby. Since 1960 the development of lasers has been extremely rapid. Though it was called as “an invention in search of an application” at the time of its invention, the variety of lasers and the wealth of laser applications developed since 1960 is enormous. Characteristics of Laser 1. High Directionality (or) Low Divergence: Ordinary light spreads in all directions and its angular spread is 1 metre/metre. But in laser it is highly directional and its angular spread is 1mm/metre. For example the laser beam can be focused to very long distance with a few divergence or angular spread. Divergence or angular spread is given by φ = degrees Where d1 , d2 are any two distances for the laser source emitted and r 1, r2 are the radii of the beam spots at a distance d1 and d2 respectively as shown 2. High Intensity: The intensity of the laser beam is very high. If a person is allowed to observe an ordinary light, emitted by a 100 W bulb at a distance of 1 foot from the source, he can perceive only one thousandth watt of light. While if a person is allowed to the laser beam from the same distance, the entire laser beam penetrates through his eye. This show the high intensity of the laser beam. 6 3. Highly monochromatic: Laser beam is highly monochromatic i.e. the wavelength is single, whereas in ordinary light like mercury vapour lamp, many wavelengths of light are emitted. 4. Highly Coherent: It is an important characteristics of laser beam. In lasers the wave trains of same frequency are in phase i.e. the radiation given out is in mutual agreement not only in phase but also in the direction of emission. Thus it is a coherent beam. Due to high coherence it results in an extremely high power. PRINCIPLE OF SPONTANEOUS AND STIMULATED EMISSION-EINSTEIN’S QUANTUM THEORY OF RADIATION From the theory of radiation with matter, the working of laser can be studied. Consider an atom that has two energy levels, E 1 and E2. When light is absorbed by the atoms or molecules, then it goes from the lower energy level (E1) to the higher energy level (E2) called as upward transition (absorption) and during the transition from higher energy level (E2) to lower energy level (E1) the light is emitted from the atoms or molecules called as downward transition (emission).When it is exposed to radiation having a stream of photons, each with energy hν, three distinct processes can take place. (i) Absorption (ii) Spontaneous emission (iii) Stimulated emission Upward Transition (i) Absorption An atom in the lower energy level or ground state energy level E1 absorbs the incident photon radiation of energy hv and goes to the higher energy level or excited level E2 as shown in figure. This process is called absorption 7 If there are many numbers of atoms in the ground state then each atom will absorb the energy from the incident photon and goes to the excited state. then, The rate of absorption (R12) is proportional to the following factors. R12 α Energy density of the incident radiation (ρν) α Number of atoms in the ground state (N1) i.e. R12 α ρν N1 or R12 = B12 ρν N1 (1) where B12 is a constant which gives the probability of absorption transition per unit time. (12 represents the transition from energy level E1 to E2. Similarly 21 represents the transition from energy E2 to E1.) Downward transition Once the atoms are excited by stimulated absorption, they stay in the excited state for a short duration of time called the lifetime of the excited state. After their lifetime they move to their lower energy level spontaneously emitting photons energy E = hν. Such an emission takes place by one of the two methods. (ii) Spontaneous emission The atom in the excited state returns to the ground state by emitting a photon of energy E = (E2- E1) = hν, spontaneously without any external triggering as shown in figure. This process is known as spontaneous emission. Such an emission is random and independent of incident radiation. 8 If N1 and N2 are the number of atoms in the ground state (E1 and excited state (E2) respectively, then The rate of spontaneous emission is R21(sp) α N2 Or R21 (sp) = A21N2 (2) Where A21 is a constant which gives the probability of spontaneous emission transitions per unit time. (i) Stimulated Emission The atoms in the excited state can also return to the ground state by external triggering (inducement of photon) thereby emitting a photon of energy equal to the energy of the incident photon known as stimulated emission. Thus results in two photons of same energy, phase difference and of same directionality as shown in figure. Therefore, the rate of stimulated emission is R21 (st) α ρν N2 Or R21 (st) = B21ρν N2 (3) Where B21 is a constant which gives the probability of stimulated emission transitions per unit time. Einstein’s Theory In 1917, Einstein proposed a mathematical expression for the existence of the stimulated emission of light. This expression is known as Einstein‘s expression. Einstein’s theory of absorption and emission of light by an atom is based on Planck’s theory of radiation. Also under thermal equilibrium, the population of energy levels obeys the Boltzmann distribution law 9 Under thermal equilibrium, upward and downward transition rates must be equal The rate of absorption = the rate of emission Therefore eq(1) = eq(2) + eq(3) B12 ρν N1 = A21N2 + B21ρν N2 ρν (B12N1 – B21N2) = A21N2 A21 N 2 Therefore ρν = B12 N1  B21 N 2 A21 Or ρν = (4) B12 ( N1 / N 2 )  B21 From Boltzmann distribution law N1 = N0e- E1/KBT Similarly N2 = N0e-E2/KBT Where KB is the Boltzmann Constant, T is the absolute temperature and N0 is the number of atoms at absolute zero. At equilibrium, the ratio of population levels is given by N1  e(E2- E1)/KBT N2 Since E2- E1 = hν, we have 10 N1  e h / K B T (5) N2 Substituting eq(5) in eq(4), A21 ρν = h / K BT B12 (e )  B21 A21 1 or ρν =. (6) B21 ( B12 / B21 )e h / K BT  1 This equation has a very good agreement with Planck’s energy distribution radiation law. 8h 3 1 i.e. ρν =. h / K BT (7) c 3 e 1 Comparing eq(6) and eq (7) it can be written as A21 8h 3 B12 = B21 = B and  (8) B21 c3 Taking A21 = A The constants A and B are called as Einstein Coefficients, which accounts for spontaneous and stimulated emission probabilities. Ratio of stimulated and spontaneous emission rates From equations 2) and 3) we have, R21 (St ) B21  N 2  R21 (Sp) A21 N 2 R21 ( St ) B21   (9) R21 ( Sp) A21 Rearranging eq 6), B21 1   A21 ( B12 / B21 )e h / K BT  1 Since B12 = B21, we have 1 B h / K B T  21  (10) e  1 A21 Comparing eq 9) and 10), 11 R21 ( St ) 1 B  h / K BT  21  (11) R21 ( Sp) e  1 A21 Or it can be written as B R  21  A21 From Eq (11), Einstein proved the existence of the stimulated emission of radiation. The spontaneous emission produces incoherent light, while the stimulated emission produces coherent light. In ordinary conventional light source, the spontaneous emission is dominant. For laser action, stimulated emission should be predominant over spontaneous emission and absorption. To achieve this, an artificial condition known as Population inversion is required. Population Inversion : Consider the ratio of stimulated emission rate to stimulated absorption rate. N 2  B21 Stimualated emission rate= = N2 / N1(as B21 = B12 ignoring degeneracy) N1  B12 Stimulated absorption rate At thermal equilibrium N2 / N1 N4. When flashtube or laser diode supplies light energy to the active medium (Nd:YAG crystal), the lower energy state (E1) electrons in theneodymium ions gains enough energy and moves to the pump state or higher energy state E4.The lifetime of pump state or higher energy state E4 is very small (230 microseconds) so the electrons in the energy state E4 do not stay for long period. After a short period, the electrons will fall into the next lower energy state or metastable state E3 by releasing non-radiation energy (releasing energy without emitting photons). The lifetime of metastable state E3 is high as compared to the lifetime of pump state E4. Therefore, the electrons reach E 3 much faster than they leave E3. This results in an increase in the number of electrons in the metastable E 3 and hence population inversion is achieved. After some period, the electrons in the metastable state E3 will fall into the next lower energy state E2 by releasing photons or light. The emission of photons in this manner is called spontaneous emission. The lifetime of energy state E2 is very small just like the energy state E 4. 16 Therefore, after a short period, the electrons in the energy state E 2 will fall back to the ground state E1 by releasing radiationless energy. When photon emitted due to spontaneous emission is interacted with the other metastable state electron, it stimulates that electron and makes it fall into the lower energy state by releasing the photon. As a result, two photons are released. The emission of photons in this manner is called stimulated emission of radiation.When these two photons again interacted with the metastable state electrons, four photons are released. Likewise, millions of photons are emitted. Thus, optical gain is achieved. Spontaneous emission is a natural process but stimulated emission is not a natural process. To achieve stimulated emission, we need to supply external photons or light to the active medium.The Nd:YAG active medium generates photons or light due to spontaneous emission. The light or photons generated in the active medium will bounce back and forth between the two mirrors. This stimulates other electrons to fall into the lower energy state by releasing photons or light. Likewise, millions of electrons are stimulated to emit photons. The light generated within the active medium is reflected many times between the mirrors before it escapes through the partially reflecting mirror. CHARACTERISTICS Type: It is a four level solid state laser. Active medium: The active medium is Nd: YAG laser. Pumping method: Optical pumping is employed for pumping action. Pumping source: Xenon or Krypton flash tube is used as pumping source. Optical resonator: Two ends of Nd: YAG rod is polished with silver (one end is fully silvered and the other is partially silvered) are used as optical resonator. Power output: The power output is approximately 70 watt. Nature of output: The nature of output is pulsed or continuous beam of light. Wavelength of the output: The wavelength of the output beam is 1.06μm(infra-red) ADVANTAGES  It has high energy output.  It has very high repetition rate operation  It is much easy to achieve population inversion  Low power consumption  The efficiency of Nd:YAG laser is very high as compared to the ruby laser. 17 DISADVANTAGES The electron energy level structure of Nd3+ in YAG is complicated. APPLICATIONS: Military Nd:YAG lasers are used in laser designators and laser rangefinders. A laser designator is a laser light source, which is used to target objects for attacking. A laser rangefinder is a rangefinder, which uses a laser light to determine the distance to an object. Medicine Nd: YAG lasers are used to correct posterior capsular opacification (a condition that may occur after a cataract surgery). Nd:YAG lasers are used to remove skin cancers. Manufacturing Nd:YAG lasers are used for etching or marking a variety of plastics and metals. Nd:YAG lasers are used for cutting and welding steel. Semiconductor laser A most important type of laser is semiconductor laser. Because of its miniature in size (in the order of μm), efficient, large gain spectral width, and less expensive these types of laser has wider application. There are two types of semiconductor laser 1. Homo junction semiconductor laser. 2. Hetero junction semiconductor laser. 1. Homo Junction semiconductor laser It is a diode laser. When PN junction is formed with single crystalline material (ie., Either side of Junction has the same base material). Then it is called as Homo junction semiconductor laser Principle When P-N junction diode is in forward bias, at the junction holes and electron recombination occurs. Due to recombination photons are emitted. This emitted photon stimulate further recombination and hence a laser output obtained. 18 Electrode p type GaAs n type GaAs Electrode Fig.Schematic construction of Homojunction semiconductor diode laser Construction P-N junction diode laser is formed by heavily doped GaAs with Ge (P-type) and GaAs with T (n-type). The diode is extremely small in size with 500 μm long and about 100 μm wide and thick. The top and bottom face are provided with ohmic contact. The front and real faces are polished parallel to each other and perpendicular to the plane of the junction. This polished faces constitute an optical resonator. Working Since n-region and p-region are heavily doped, the fermi level of p-region lies within the valence band and fermi level of n-region lies within the conduction band. At junction, the fermi level is uniform as shown in figure above. When the p-n junction is forward bias, the holes in the p-type and electron in the n-type moves towards the junction. At junction recombination of holes and electron occurs with an emission of photon. These emitted photon travel to and fro between the polished face of the junction. These stimulate more electron-hole recombination. Thus the amplification occurs between the polished surfaces. The amplified radiation has enough energy to come out of the junction as laser of wavelength 8400 A°. 19 Fig.Energy level representation of semiconductor diode laser Characteristics of homo junction laser  Type → Semiconductor laser.  Active Medium → P – n junction.  Active Center → Recombination of electrons and holes.  Pumping Method → Direct conversion.  Optical Resonator → Polished end faces of P – n junctions.  Power Output → 1mwatt.  Output nature → Pulsed (or) Continuous.  Wavelength → 8400A°. 2. Hetero junction semiconductor laser When the junction are formed by different material i.e., one side of junction differs from that on the other side of the junction, then it is called as Hetero junction. Principle Here the charge carries (electron and holes) confined in a very narrow region and recombination takes place at this region. Due to recombination radiation are emitted. This emitted photon oscillate between the polished surfaces of junction and finally a laser is obtained from the diode. 20 Fig. Schematic construction of Homojunction semiconductor diode laser Construction Here p-GaAs layer is sandwiched between two layer of GaAlAs. The material GaAlAs (p type and n type) wider energy gap and lower refractive index. The thickness of the p-GaAs is very small and it has narrow energy gap with high refractive index. p-GaAs is the active region where the laser action take place. The front and rare face are polished parallel to each other and perpendicular to the plane of the junction. The polished face will act as a optical resonator. Fig.Ga-As Heterojunction Laser 21 Working When the junction is forward biased, the charge carriers (i.e.,Electron and holes) are injected into the active region (i.e to narrow band gap of P-GaAs) in high concentration. Thus the layer GaAs contains a large concentration of electron in conduction band and large number of holes within the valance band. Thus population inversion is achieved between the conduction band and valance band of p-GaAs. Recombination of electron-holes occurs at p-GaAs which leads to spontaneous emission of photon. This spontaneous photon will stimulate more electron to recombine with holes, thus a stimulated photon is emitted. This stimulated photon travel back and front between the polished surfaces. When the stimulated photons have enough strength, laser beam emerges from the diode with wavelength of 8000 A° Characteristics of Hetero junction laser.  Type → Semiconductor laser.  Active Medium → P – type GaAs.  Active Center → Recombination of electrons and holes.  Pumping Method → Direct conversion.  Optical Resonator → Polished end faces of P – n junctions.  Power Output → 1mW.  Output nature → Continuous.  Wavelength → 8000A°. FIBER OPTICS Introduction Optics is a branch of physics which helps us to understand the properties of light and how light reflects, refracts with the medium. Fiber optics is the propagation of light through an optical fiber either glass or plastics. John Tyndall explained about light conduction through stream of water and light signal could be bent through water in 1854. Light travels based on the principle of total internal reflection. Optical fiber based transmission in communication offers several advantages over ordinary wire transmission. Fiber optics science and technology is most interesting field in expecting electrical wiring even in our vehicles and houses soon. Fiber optic communication permits long range data transmission over long distances at higher bandwidths than wireless transmission. Audio signal, video signal, microwave signal and data from computer can be modulated and demodulated using optical fiber. Applications of fiber optics can also be extended to Fiber-optic sensors for temperature and strain measurements in buildings, oil pipelines, and wings of airplanes and medical field in the form of endoscopes. 22 Comparison of Optical Fibers with Electric Cables S.No Optical Fibers Electric Cables 1 The capacity of a fiber for optical data Less in capacity of transmission transmission is higher 2 Less in weight Heavier in weight 3 Transmission losses of a fiber can be Transmission loss will be high (greater than very low (well below 1 dB/km for the 1 dB/km) optimum wavelengths) 4 Large number of channels can be re- Re-amplification could not be carried out amplified in a single fiber amplifier 5 Fiber connections are immune to Electromagnetic interference affects human electromagnetic interference health 6 Fire explosions can be avoided Cannot be avoided Optical fiber’s disadvantages  Fiber connections are comparatively sensitive and difficult to handle, particularly when single-mode fibers are used. Precise alignment and high cleanliness are required. For such reasons, fiber connections are often only competitive if a high transmission bandwidth can be utilized.  Glass fibers may not be bent very tightly, because this can cause high bend losses or even breakage. This can be a problem e.g. in the context of fiber-to-the-home technologies. Note, however, that silica fibers are surprisingly robust against bending – much more than most other things made of glass. Structure of an Optical fiber Optical fiber consists of three parts: the core, the cladding, and the coating or buffer which is shown in below fig.The core is inner part of the fiber (whose maximum diameter around 50 µm) made up of glass dielectrics. Light can mainly propagate along the core of the fiber and conducts no electricity. The core is surrounded by a layer of material called the cladding whose diameter around 125-200 µm. Cladding is particularly made of glass or 23 plastic. Even though light will propagate along the fiber core without the layer of cladding material, the cladding does perform some necessary functions. Cladding is an intermediate layer which protects the fiber from absorbing surface contaminants also reduces scattering loss at the surface of core. Cladding is surrounded by a polymeric layer called the coating or buffer(diameter: upto 500 µm)which is used to protect an optical fiber from physical damage. The material used for a buffer is a type of plastic. The buffer is elastic in nature and prevents abrasions. Also, the buffer prevents the optical fiber from scattering losses caused by microbends. Microbends occur when an optical fiber is placed on a rough and distorted surface. Microbends are discussed later in this chapter. Fig. Structure of an optical fiber Principle and propagation of light through an optical fiber The optical fibers used in communications have a very simple structure. They consist of two sections: the glass core and the cladding layer (Figure). The core is a cylindrical structure, and the cladding is a cylinder without a core. Core and cladding have different refractive indices, with the core having a refractive index, n1, which is slightly higher than that of the cladding, n2. It is this difference in refractive indices that enables the fiber to guide the light. Because of this guiding property, the fiber is also referred to as an “optical waveguide.” As a minimum there is also a further layer known as the secondary cladding that does not participate in the propagation but gives the fiber a minimum level of protection. This second layer is referred to as a coating. Total internal reflection The basics of light propagation can be discussed with the use of geometric optics. The basic law of light guidance is Snell’s law (Fig.). Consider two dielectric media with different refractive indices and with n1> n2 and that are in perfect contact, as shown in figure. At the interface 24 between the two dielectrics, the incident and refracted rays satisfy Snell’s law of refraction that is, In addition to the refracted ray there is a small amount of reflected light in the medium with refractive index n1. Because then always >. As the angle of the incident ray increases there is an angle at which the refracted ray emerges parallel to the interface between the two dielectrics (Fig). This angle is referred to as the critical angle, , and from Snell’s law is given by Transmitted Transmitted Ray Ray n2 n2 Partially n1> n2 n1 n1 Reflected Incident Incident Ray Ray Ray (a) (b) Fig. Snell’s law lawla law Propagation of light through optical fiber For a ray to be launched into the fiber and propagated it must arrive at the interface between the two media (with different refractive indices) at an angle that is at minimum equal to and in general less than that. Fig. illustrates the geometry for the derivation of the acceptance angle. To satisfy the condition for total internal reflection, the ray arriving at the interface, between the fiber and outside medium, say air, must have an angle of incidence less than , otherwise the internal angle will not satisfy the condition for total reflection, and the energy of the ray will be lost in the cladding. 25 Core Cladding Fig Propagation of light through optical fiber Consider that a ray with an incident angle less than the , say , enters the fiber at the interface of the core (n1) and the outside medium, say air (n0), and the ray lies in the meridional plane. From Snell’s law at the interface we obtain (1) (2) (3) When (4) sin = (5) Substituting equation (5) in (4), we get (6) Equation (6) simplified when , 26 (7) This equation defines the angle within which the fiber can accept and propagate light and is referred to as the “Numerical Aperture” (NA). (8) This equation states that for all angles of incident where the inequality ≤ ≤ is satisfied the incident ray will propagate within the fiber. The parameter NA expresses the propensity of the fi ber to accept and propagate light within the solid cone defined by an angle. The equation for the NA can be also expressed in terms of the difference between the refractive indices of core and cladding—that is, Fractional index change (9) Further simplifications the NA can now be written as Numerical Aperture (10) Types of optical fibers Optical fibers Material Number of Refractive modes index profile Glass Plastic Single Multi- Step Graded fiber fiber mode mode index index fiber fiber fiber fiber Single Multimode mode Step Step index 27 index fiber fiber Fig. Optical fiber - Classification chart Material Based optical fibers The material based classification results to the following types: 1. Plastic made fibers. 2. Glass made fibers. Plastic made fibers Plastic fibers are manufactured from a polymer perform drawing into a fiber. The losses associated with this type of fiber are about 100s of dB. The operate at low temperature i.e. upto 125 degree celsius while glass fibers can be used upto 1000 degree celsius. These are used in sensors, process control and short distance communication. Features 1. High light gathering capacity 2. Large core area 3. Low cost components 4. Uses visible LEDs 5. Easy to connect or couple Example: Core: Polymethyl methacrylate cladding: Co-polymer Core: Polystyrene cladding: Methyl methacrylate Glass made fibers A fiber with glass core and plastic cladding is called as “plastic clad silica” or PCS fiber. They have following characteristics 1. High NA 2. Large core diameter 3. High attenuation 4. Low bandwidth Advantage of large core is the greater power coupling. The high value of NA permits use of less expensive surface emitting LED’s. Along with high attenuation and low bandwidth plastic fibers have poor mechanical strength and low maximum operating temperature. Example: Core: SiO2 cladding: P2O3 - SiO2 Based on modes of propagation of light through core, the types of optical fiber are identified areas 28 1. Single mode fibers 2. Multimode fibers Single mode fibers Single-mode fibers usually have a relatively small core (with a diameter of only a few micrometers) and can guide only a single spatial mode (disregarding the fact that there are two different polarization directions), the profile of which in most cases has roughly a Gaussian shape. Changing the launch conditions only affects the power launched into the guided mode, whereas the spatial distribution of the light exiting the fiber is fixed. Efficiently launching light into a single-mode fiber usually requires a laser source with good beam quality and precise alignment of the focusing optics in order to achieve mode matching. The mode radius of a single-mode fiber is often of the order of 5 μm, but there are also large mode area fibers with single-mode guidance. In the latter case, the alignment tolerances are lower in terms of position but higher in terms of angle. Multimode optical fibers Dimensions of a waveguide are much larger than the wavelength of input signal, which means that large number of modes can be guided. Constructive interferences between multiple reflections on the diopter between both materials is observed. A fiber-optic is a circular dielectric waveguide which is very probably multimode if the core, or in other words the central part where light propagates, has a diameter much larger than the wavelength. This diameter is approximately between 50 and 200 µm for silica fibers, and 0.5 and 1 mm for plastic fibers. We can then simply, but correctly, study propagation by geometric optics. We will see that a mode is characterized by its path and by the distribution of the electromagnetic field around it. We must insist on the fact that in a multimode guide, the different modes are on the same wavelength. Types of optical fibers can be classified based on the refractive index are 1. Step index fibers 2. Graded index fibers Step Index Single mode optical fibers The core diameter of this type of fiber is very small i.e. of the order of wavelength of light to be propagated through the fiber. The refractive index profile has step change in the refractive index from core to cladding as shown in Figure. 29 The main characteristics of step index single mode optical fibers are as follows: 1. Very small core diameter 2. Low numerical aperture 3.Low attenuation 4. Very high bandwidth In order to get single mode, with all other modes cut off, the diameter of the core must satisfy the relation Where λ is wavelength of light propagating through optical fiber NA is numerical aperture of the optical fiber Step Index multimode optical fibers The refractive index of multimode fiber is close to 1.5 for silica fibers. The simplest type of multimode fiber is a step-index fiber (see Figure), directly emerging from optical applications. In this fiber, the core (n1) is surrounded by a cladding (n2) having slightly lower refractive index. This cladding is an important region which plays an active role in guiding and is also surrounded by a coating. Practically, light emanating from any point source will have several paths with different angles of incidence at boundary layer. It may also contain different colors with different frequencies. It is called as step index multimode propagation as shown in Figure. Any other light wave which is meeting the core cladding interface at and above the critical value of θ c will also be totally reflected and hence will propagate along the core. However any light wave meeting the core cladding interface at an angle less than θc will pass into and be absorbed by the cladding. Thus the various light waves travelling along the core will have different propagation paths of different path lengths. Hence they will meet at the other end of the fiber at different time instants. This causes dispersion of signal called as transit time dispersion. This dispersion sets an upper limit on the rate at which the light can be modulated by analog or digital electrical signal. As a result of this distortion the variations of successive pulses may overlap into each other and 30 Fig. Types of optical fiber based on refractive index causes distortion of the information being carried. However this defect can be minimized by making the core diameter of the same order as the wavelength of the light wave to be propagated. The resultant propagation is a single light wave, explained earlier in single mode step index optical fiber. This type of fiber has very high capacity and large bandwidth. Graded Index optical fibers From the figure it is quite clear that light waves or rays with large angle of incidence travel more path lengths than those with smaller angles. But we know that the decrease of refractive index allow a higher velocity of light energy propagation. Thus all waves will reach a given point along the fiber at virtually same time. As a result the transit time dispersion is reduced. This type of light propagation is referred as graded index multimode propagation through optical fiber. Fiber Modes – Single-mode versus MultimodeFibers An optical fiber can support one or several (sometimes even many) guided modes, the intensity distributions of which are located at or immediately around the fiber core, although some of the intensity may propagate within the fiber cladding. In addition, there is a multitude of cladding modes, which are not restricted to the core region. The optical power in cladding modes is usually lost after some moderate distance of propagation, but can in some cases propagate over longer distances. Outside the cladding, there is typically a protective polymer coating, which gives the fiber improved mechanical strength and protection against moisture, and also determines the losses for cladding modes. Such buffer coatings may consist of acrylate, silicone or polyimide, for example. At the fiber ends, the coating often has to be stripped off. S.NO Single mode fiber Multimode fiber 1 Only a single mode propagates Many modes propagate through fiber through fiber 2 Diameter is much less than Diameter much larger than single mode fiber multimode fiber < 10 µm 3 Largest transmission bandwidth Transmission bandwidth is small compared to single mode fiber 4 Exhibits low loss Comparatively more lossy 5 Superior transmission quality due Lesser transmission quality than single mode to absence of modal noise fiber S.NO Step index optical fiber Graded index optical fiber 31 1 Bandwidth: 50MHz Bandwidth: 200,600 MHz 2 Modal dispersion is more Modal dispersion is lower 3 NA: 0.2 to 0.5 (for 12dB/km loss) NA: 0.16 to 0.2(for 5 to 12dB/km loss) 4 Refractive indices of core and Refractive indices of core varies gradually and cladding vary step by step cladding is constant 5 Attenuation loss is high Attenuation loss is low Losses in optical fibers The optical fiber does not experience the loss in terms of intensity of light. However, the presence of impurities, scattering at the edges, geometry of structure and dispersion of light causes some losses. Transmission loss/attenuation (α) If the intensity of light at the second end of the optical fiber be pout and intensity at first end be pin Attenuation: Attenuation is the loss of optical energy as it travels through the fiber; this loss is measured in dB/km.Attenuation is a transmission loss that can be measured as a difference between the output signal power and the input signal power. It can be expressed in dB as Attenuation loss α = 10 log10 (Pin/ Pout) dB The attenuation loss of fiber in dB/km is then expressed as α = 10 log10 (Pin/ Pout) /L dB/km Attenuation is a measure of the loss of signal strength or light power that occurs as light pulses propagate through a run of multimode or single-mode fiber. Attenuation in fiber optics, also known as transmission loss, is the reduction in intensity of the light beam (or signal) with respect to distance traveled through a transmission medium. Causes of Attenuation: Empirical research has shown that attenuation in optical fiber is caused primarily by both scattering and absorption. Attenuation depends on a) Attenuation depends on wavelength used (i.e. frequency used). The most common peak wavelengths are 780 nm, 850 nm, 1310 nm, 1550 nm, and 1625 nm. b) Attenuation depends on light intensity i.e input light power. c) Attenuation depends on diameter of optical fiber (diameter of core mainly). For single/mono mode attenuation is minimum since lesser the traversed distance lesser the power loss. 32 d) Attenuation definitely depends on distance. Distance between optical source and repeater/detector. Possible losses in optical fiber The possible losses are absorption, scattering, radiation losses and geometric losses. The absorption loss The absorption losses appears as  Extrinsic losses  Intrinsic losses  Atomic defect losses Extrinsic losses: The extrinsic loss appears due to presence of impurities which absorb the light. The impurities may be due to presence of Fe, Cr, Co and Cu in the core material. The impurities could absorb the energy that may reemit the absorbed energy during the de excitation in different wavelength which causes loss of intensity to original light of specific wavelength. Intrinsic loss: Since, the fiber core itself absorbs some quantity of energy which is known as intrinsic loss. Scattering and radiation losses: Since, optic fiber contains glass as core, where impurities are present, the scattering of light at these impurities causes Rayleigh scattering where the energy of scattered waves is directly proportional to the 4th power (E 4) of wavelength. The loss of energy at couplers and interfaces are known as radiative losses. Geometrical loss Due to bending of optical fibers there are 2 types of losses from macroscopic bending and microscopic bending. If the fiber be rounded as big circle of known radius of curvature, the loss may be less called macroscopic bending loss. For small bending of fiber the loss of energy in microscopic bending is larger. Sometime the irregularities in the dimensions cause geometrical losses. Dispersion loss Dispersion is the spreading out of a light pulse in time as it propagates down the fiber. Dispersion in optical fiber includes model dispersion, material dispersion and waveguide dispersion. Each type is discussed in detail below. Inter modal dispersion Material dispersion Waveguide dispersion 33 Fig Different dispersion losses in optical fiber Intermodal dispersion The optical power in the pulsed wave distribution over the mode of light through the fiber decreases during the propagation, these changes are known as intermodal dispersion. Multimode fibers can guide many different light modes since they have much larger core size. This is shown in above figure. Each mode enters the fiber at a different angle and thus travels at different paths in the fiber. Since each mode ray travels a different distance as it propagates, the ray arrive at different times at the fiber output. So the light pulse spreads out in time which can cause signal overlapping so seriously that you cannot distinguish them anymore. Model dispersion is not a problem in single mode fibers since there is only one mode that can travel in the fiber. Material dispersion The refractive index of core causes the changes in the wavelength/frequency called material dispersion. If narrow pulse passes throughfiber, causes broadening of pulse width due to material property. It can be overcome by highly monochromatic source of light. The single mode fiber could reduce the material dispersion to maximum extent. Material dispersion is the result of the finite line width of the light source and the dependence of refractive index of the material on wavelength, which is shown in fig. Material dispersion is a type of chromatic dispersion. Chromatic dispersion is the pulse spreading that arises because the velocity of light through a fiber depends on its wavelength. Waveguide dispersion The optical fiber can be considered as circular wave guide where refractive index varies with modes of propagation with wavelength causes wave guide dispersion. Waveguide dispersion is only important in single mode fibers. It is caused by the fact that some light travels in the fiber cladding compared to most light travels in the fiber core. It is shown picture. Since fiber cladding has lower refractive index than fiber core, light ray that travels in the cladding travels faster than that in the core. Waveguide dispersion is also a type of 34 chromatic dispersion. It is a function of fiber core size, V-number, wavelength and light source line width. FIBRE OPTIC COMMUNICATION SYSTEM(Block diagram) The optical fiber consists of three main elements: 1. Transmitter: An electric signal is applied to the optical transmitter. The optical transmitter consists of driver circuit, light source and fiber flylead.  Driver circuit drives the light source.  Light source converts electrical signal to optical signal.  Fiber connector is used to connect optical signal to optical fiber. 2. Transmission channel: It consists of a cable that provides mechanical and environmental protection to the optical fibers contained inside. Each optical fiber acts as an individual channel.  Optical splice is used to permanently join two individual optical fibers.  Optical connector is for temporary non-fixed joints between two individual optical fibers.  Optical coupler or splitter provides signal to other devices. 35  Repeater converts the optical signal into electrical signal using optical receiver and passes it to electronic circuit where it is reshaped and amplified as it gets attenuated and distorted with increasing distance because of scattering, absorption and dispersion in waveguides, and this signal is then again converted into optical signal by the optical transmitter. 3. Receiver: Optical signal is applied to the optical receiver. It consists of photo detector, amplifier and signal restorer.  Photo detector converts the optical signal to electrical signal.  Signal restorers and amplifiers are used to improve signal to noise ratio of the signal as there are chances of noise to be introduced in the signal due to the use of photo detectors.  For short distance communication only main elements are required. Source- LED Fiber- Multimode step index fiber Detector- PIN detector  For long distance communication along with the main elements there is need for couplers, beam splitters, repeaters, optical amplifiers. Source- LASER diode Fiber- single mode fiber Detector- Avalanche photo diode (APD) FIBER OPTIC TRANSMITTERS A fiber optic transmitter is a hybrid electro-optic device. It converts electrical signals into optical signals and launches the optical signals into an optical fiber. A fiber optic transmitter consists of an interface circuit, a source drive circuit, and an optical source. The interface circuit accepts the incoming electrical signal and processes it to make it compatible with the source drive circuit. The source drive circuit intensity modulates the optical source by varying the current through it. The optical signal is coupled into an optical fiber through the transmitter output interface. Although semiconductor LEDs and LDs have many similarities, unique transmitter designs result from differences between LED and LD sources. Transmitter designs compensate for differences in optical output power, response time, linearity, and thermal behavior between LEDs and LDs to ensure proper system operation. Nonlinearities caused by junction heating in LEDs and mode instabilities in LDs necessitate the use of linearizing circuits within the transmitter in some cases. 36 A schematic diagram of a point-to-point fiber optic data link. FIBER OPTIC RECEIVERS In fiber optic communications systems, optical signals that reach fiber optic receivers are generally attenuated and distorted (see figure below). The fiber optic receiver must convert the input and amplify the resulting electrical signal without distorting it to a point that other circuitry cannot use it. Attenuated and distorted optical signals. OPTICAL DETECTORS A transducer is a device that converts input energy of one form into output energy of another. An optical detector is a transducer that converts an optical signal into an electrical signal. It does this by generating an electrical current proportional to the intensity of incident optical radiation. The relationship between the input optical radiation and the output electrical current is given by the detector responsivity. OPTICAL DETECTOR PROPERTIES Fiber optic communications systems require that optical detectors meet specific performance and compatibility requirements. Many of the requirements are similar to those of an optical source. Fiber optic systems require that optical detectors: Be compatible in size to low-loss optical fibers to allow for efficient coupling and easy packaging. Have a high sensitivity at the operating wavelength of the optical source. Have a sufficiently short response time (sufficiently wide bandwidth) to handle the system's data rate. Contribute low amounts of noise to the system. 37 Maintain stable operation in changing environmental conditions, such as temperature. FIBER OPTIC SENSORS Fiber optic sensors are fiber-based devices that use optical fibers to detect certain entities such as mechanical strain or temperature, concentrations of chemical species, acceleration, rotations, pressure, vibrations and displacements. These sensors are mainly used in remote sensing applications. Most of the fiber optic sensors are multiplexed along the length of a fiber by using light wavelength shift for each sensor or by determining the time delay as light passes along the fiber. Measurand Source Electronic Transducer Detector Processing ercccccer Fig. Block Diagram of Fiber Optic Sensor The general block diagram of fiber-optic sensor is shown above. The block diagram consists of optical source (Light Emitting Diode, LASER, and Laser diode), optical fiber, sensing element, optical detector and end-processing devices (optical-spectrum analyzer, oscilloscope). These sensors are classified into three categories based on the operating principles, sensor location and application. Benefits of Fiber Optic Sensors Fiber optic sensors are small and light weight. Resistant to high temperature and explosive environments, they possess electrically insulating material which also make them suitable for use in applications subject to high voltages and there are no risks of electrical sparks. In addition to this fiber optic sensors are very resistant to electromagnetic and radio frequency interference. They are highly sensitive, have excellent range and resolution and multiplexing capabilities. Types of Fiber-Optic Sensor Systems These sensors can be classified and explained in the following manner: 38 1. Based on the sensor location, the fiber optic sensors are classified into two types:  Intrinsic Fiber-Optic Sensors or Active Sensors  Extrinsic Fiber-Optic Sensor or Passive Sensors Intrinsic Type Fiber Optic Sensors In this type of sensors, sensing takes place within the fiber itself. The sensors depend on the properties of the optical fiber itself to convert an environmental action into a modulation of the light beam passing through it. Here, one of the physical properties of light signal may be in the form of frequency, phase, polarization, intensity. The most useful feature of the intrinsic fiber optic sensor is, it provides distributed sensing over long range distances. The basic concept of the intrinsic fiber optic sensor is shown in the following figure. Fig. Intrinsic Type Fiber Optic Sensor Extrinsic Type Fiber optic Sensors In extrinsic type fiber optic sensors, the fiber may be used as information carriers that show the way to a black box. It generates a light signal depending on the information arrived at the black box. The black box may be made of mirrors, gas or any other mechanisms that generates an optical signal. These sensors are used to measure rotation, vibration velocity, displacement, twisting, torque and acceleration. The major benefit of these sensors is their ability to reach places which are otherwise unreachable. 39 Fig. Extrinsic Type Fiber optic Sensors The best example of this sensor is the inside temperature measurement of the aircraft jet engine that uses a fiber to transmit a radiation into a radiation pyrometer, which is located outside of the engine. In the same way, these sensors can also be used to measure the internal temperature of the transformers. These sensors provide excellent protection of measurement signals against noise corruption. Figure shows the basic concept of the extrinsic fiber optic sensor. Pressure /Temperature sensor (INTRINSIC SENSOR) A form of Mach-Zehnderfiber optic pressure/ temperature sensors can be made using single-mode optical fibers for the two arms as shown in Fig. If the optical path lengths of the two arms are nearly equal (to within the coherence length of the source), the light from the two fibers interferes to form a series of bright and dark fringes. A change in the relative phase of the light from one fiber with respect to the other is observed as a displacement of the fringe pattern, a phase change of 2π radian causing a displacement of one fringe. The phase of the light leaving a fiber can be changed by dimensional and index of refraction changes in the fiber. Thus, if one fiber is subject to a different strain, pressure, temperature, etc. than the other, this difference appears as a displacement of the fringes and can be measured by this displacement. This is the basic principle of the fiber-optic strain gauge system. In this type we analyze the sensitivity of this device for pressure and temperature measurement. 40 Fig. Fiber optic Pressure / Temperature sensor Displacement sensor (Active Sensor) The main attractions of this technique for distance sensing are its simplicity and low price and the ability to measure distance at fast repetition rates (typically up to hundreds of kilohertz). Commercially available intensity sensors are offered for various probing distances, from a few millimeters up to about 50 mm, with possible methods for extensions. The resolution on the back slope can be 1 µm. However, the technique suffers from a number of limitations:  Precalibration for all target objects is necessary.  Since the distance is derived from the measured signal intensity, any change in the signal intensity will be interpreted as a distance change. Thus illumination intensity variations, optical connection losses, variations of the target reflectivity, dust, dirt, etc. will be interpreted by default to be distance changes.  The measured signal can be very sensitive to tilt of the target object—for example, consider a highly reflective object such as a mirror. It is easily seen (Fig.4.27) that more light will be collected from an “optimally” tilted target than for the target at normal incidence. Furthermore the tilt effect is different at each distance and for each tilt axis. 41 Fig. Fiber optic Displacement sensor Applications of Fiber Optic Sensors Fiber optic sensors are used in a number of different applications. In mechanical properties testing, fiber optical sensors are used to measure mechanical strain. They can also be used to measure acceleration, velocity, pressure, temperature and displacement. In heritage structures, fiber optic sensors can be used to evaluate post-seismic damage, analyze cracks, monitor restoration and monitor displacement. Similarly in dams they can detect and monitor leakages, foundation defects and measure spatial displacement. Hence Fiber optic sensors are used in a varied range of applications such as  Measurement of physical properties such as temperature, displacement, velocity, strain in structures of any size or any shape.  In real time, monitoring the physical structure of health.  Buildings and bridges, tunnels, Dams, heritage structures.  Night vision camera, electronic security systems, Partial discharge detection and measuring wheel loads of vehicles. Thus, an overview of fiber optic sensors and applications has been discussed. There are many advantages of using fiber optic sensors for long distance communication that include small in size, light in weight, compactness, high sensitivity, wide bandwidth, etc. All these characteristics make the best use of fiber optic as a sensor. 42 UNIT 1 SOLVED PROBLEMS 1. At room temperature the ground state and the first excited state of Ruby are separated by 1.8 eV. Calculate the ratio of the number of atoms in the excited state to that in the ground state. Given Eg = 1.8 eV = J ; k = 1.38 Formula: Calculation: (Ans. ) 2. Find the ratio of the probability of spontaneous emission to stimulated emission at 300 K for (a) microwave photons (.) and (b) optical photons ( Given: and Formula: Ratio of spontaneous to stimulated emission = Calculation: Ratio of Spontaneous to stimulated i) For microwave =3.96 ii) For optical photon 43 3. Calculate the numerical aperture, acceptance angle and the critical angle of a fiber having refractive index = 1.5 and a cladding refractive index = 1.45. Solution: 4. Calculate the numerical aperture, acceptance angle of a fiber with a core index of 1.54 and cladding index of 1.50 when the fiber is inside water of refractive index 1.33. Solution: 44 5. A certain optical fibre has an attenuation of 3.5 dB/km at 850 mm. If 0.5 mW of optical power is initially launched into the fibre, what is the power level in mW after 4 km. Attenuation α = 3.5 dB/km. Initial power level, Pi = 0.5 mW. Length of the cable, L = 4 km. Solution: Attenuation loss α = ( ) log10 ( ) dB (10) log10 ( ) dB=(3.5 dB/km) (4 km) = 14 dB P0ut = ( = 19.9 µW. 6. An optical signal has lost 85% its power after traversing 500 m of fibre. What is the loss in dB/km of this fibre? Solution: Let the initial power be PI = 1 mW PO = 85% Pi = 0.85 mW L = 500 m = 0.5 km. Attenuation loss α = ( ) log10 ( ) dB = ( ) log10 ( ) dB = 1.41 dB/km 7. Calculate the refractive indices of core and cladding material of an optical fiber if its numerical aperture is 0.22 and relative refractive indices is 0.012. Solution: 45 NA = n1 Given NA = 0.22 𝚫= 0.012 n1 = = = 1.42 n1- n2 = 𝚫 n1 n2 = n1 - 𝚫 n1 n1 (1- 𝚫) = 1.42 (1- 0.012) = 1.403 Hence n2 = 1.42 and n2 = 1.403 46 UNIT 2 MAGNETIC AND SUPERCONDUCTING MATERIALS MAGNETIC MATERIALS Magnetism in materials It arises from the magnetic moment or magnetic dipole of the magnetic materials. When an electron revolves around the positive nucleus, orbital magnetic moment arises. Similarly when the electron spins, spin magnetic moment arises. Similarly when the electron spins, spin magnetic moment arises. Materials which can be magnetized by an external magnetic field are called magnetic materials. When these materials are kept in external magnetic field, they will create a permanent magnetic moment in it. Basic terms involved in magnetism 1. Magnetic flux (ϕ) It is the total number of magnetic lines of force passing through a surface. Its unit is weber (Wb) 2. Magnetic flux density or magnetic induction (B) Magnetic flux density at any point in a magnetic field passing normally through unit area of cross section (A) at that point. It is denoted by the symbol B andits unit is weber / metre 2 or tesla.  B = weber / metre2 or tesla. A 3. Magnetic field intensity (or) strength (H) Magnetic field intensity at any point in a magnetic field is the force experienced by unit north pole placed at that point. It is denoted by H and its unit is Newton per weber or ampere turns per metre (A/m). 4. Magnetic permeability (μ) Magnetic permeability of a substance measure the degree to which the magnetic field can penetrate through the substance. It is found that magnetic flux density (B) is directly proportional to the magnetic field strength (H) 47 B α H B = μ H Where μ is a constant of proportionality and it is known as permeability or absolute permeability of the medium. B μ = H Hence, the permeability of a substance is the ratio of the magnetic flux density (B) inside the substance to the magnetic field intensity (H). Absolute permeability Absolute permeability of a medium or material is defined as the product of permeability of free space (μ0) and the relative permeability of the medium (μr) μ = μ 0 x μr Relative permeability of medium (μr) Relative permeability of a medium is defined as the ratio between absolute permeability of a medium to the permeability of a free space μr = μ / μ0 5. Intensity of magnetization (I) The term magnetization means the process of converting non-magnetic material on magnetic material. The intensity of magnetisation (I) is the measure of the magnetisation of a magnetized specimen. It is defined as the magnetic moment per unit volume. M I = weber / metre2 V 6. Magnetic susceptibility (χ) Magnetic susceptibility (χ) of a specimen is a measure of how easily a specimen can be magnetized in a magnetic field. It is the ratio of intensity of magnetisation (I) induced in it to the magnetizing field (H). I χ = H Relation between susceptibility (χ ) and Relative permeability ( μr) When a current is supplied through a coil, magnetic field is developed. When a magnetic material is placed inside an external magnetic field, the magnetic flux density (B) arises due to applied magnetic field (H) and also due to the induced magnetization (I). i.e., the total flux density, 48 B = μ0 (H+I) 1) We know that, μ = B  μH 2) H Equating eq. 1) and 2) we get, μH = μ0 (H+I) Since μ = μ0μr we have I μ0μrH= μ0H (1+ ) H I But =χ H  μr = 1+ χ Origin of Magnetic moment-Bohr Magneton Whenever a charged particle has an angular momentum, it contribute to the permanent dipole moment. In general, there are three contributions to the angular momentum of an atom. i) Orbital angular momentum of the electrons: This corresponds to permanent orbital angular magnetic dipole moments. ii) Electron spin angular momentum: This corresponds to electron spin magnetic moments. iii) Nuclear spin angular momentum: This corresponds to nuclear magnetic moments. i) Orbital angular magnetic dipole moment: Consider an electron describing a circular orbit of radius r with a stationary nucleus at the centre as shown in figure 1. Let the electron rotate with a constant angular velocity w 0 radians per second. Electrons revolving in any orbit may be considered as current carrying circular coil producing magnetic field perpendicular to its plane. Thus the electronic orbits are associated with a magnetic moment. The orbital magnetic moment of an electron in an atom can be expressed in terms of atomic unit of magnetic moment is called Bohr magneton. 1 Bohr magnetonμB= = 9.27 x 10-24 Am2 49 Fig. 1 orbital angular magnetic dipole moment ii) Electron spin magnetic moment In addition to the orbital rotation, the electron rotates about its own axis called spin. This angular momentum of the electron produces a magnetic dipole moment. According to quantum theory, the spin angular momentum along a given directions is either +h/4π or –h/4π. Hence the spin dipole moment components along an external field are + = +1 Bohr magneton or - = -1 Bohr magneton iii) Nuclear magnetic moment The angular momentum associated with the nuclear spin is also measure in unt is of h/2π. The mass of the nucleus is larger than that of an electron by a factor of the order of 103. Hence nuclear spin magnetic moment is of the order of 10 -3 Bohr magnetons. TYPES OF MAGNETIC MATERIALS The magnetic materials are classified according to the presence or absence of the permanent magnetic dipoles.  The materials without permanent magnetic moment Example: Diamagnetic materials.  The materials with permanent magnetic moment. Example Paramagnetic materials Ferromagnetic materials Anti-Ferromagnetic materials Ferrimagnetic materials. 50 DIFFERENT TYPES OF MAGNETIC MATERIALS DIAMAGNETIC MATERIALS Diamagnetism is exhibited by all the materials. The atoms in the diamagnetic materials do not possess permanent magnetic moment. However, when a material is placed in a magnetic field, the electrons in the atomic orbits tend to counteract the external magnetic field and the atoms acquire an induced magnetic moment. As a result, the material becomes magnetized. The direction of the induced dipole moment is opposite to that of externally applied magnetic field. Due to this effect, the material gets very weakly repelled, in the magnetic field. This phenomenon is known as diamagnetism. When a magnetic field Ho is applied in the direction shown in figure the atoms acquire an induced magnetic moment in the opposite direction to that of the field. The strength of the induced magnetic moment is proportional to the applied field and hence magnetization of the material varies directly with the strength of the magnetic field. The induced dipoles and magnetization vanish as soon as the applied field is removed. Properties of diamagnetic material o They repel the magnetic lines of force, if placed in a magnetic field as shown in figure. o The susceptibility is negative and it is independent of temperature and applied field strength. ( χ = –ve). o The permeability is less than one. o There is no permanent dipole moment. o When the temperature is greater than the critical temperature diamagnetic becomes normal material. o It has superconducting property. 51 Examples : Gold, germanium, silicon, antimony, bismuth, silver, lead, copper, hydrogen, Water and alcohol. Fig. 2 Diamagnetic material PARAMAGNETIC MATERIALS In certain materials, each atom or molecule possesses a net permanent magnetic moment (due to orbital and spin magnetic moment) even in the absence of an external magnetic field. The magnetic moments are randomly oriented in the absence of external magnetic field. Therefore the net magnetic moment is zero, and hence the magnetization of the material is zero. But, when an external magnetic field is applied, the magnetic dipoles tend to align themselves in the direction of the magnetic field and the material becomes magnetized as shown in fig. This effect is known as paramagnetism. Thermal agitation disturbs the alignment of the magnetic moments. With an increase in temperature, the increase in thermal agitation tends to randomize the dipole direction thus leading to a decrease in magnetization. This indicates that the paramagnetic susceptibility decreases with increases in temperature. It is noted that the paramagnetic susceptibility varies inversely with temperature. χ χ = This is known as Curie law of paramagnetism and C is a constant called Curie constant 52 Properties of paramagnetic materials o Paramagnetic materials attract magnetic lines of force. o They possess permanent dipole moment. o The susceptibility is positive and depend on temperature is given by χ = o Permeability is greater than one. o When the temperature is less than Curie temperature, paramagnetic materials become diamagnetic material. The spin alignment is shown in fig. Examples:Manganese sulphate, ferric oxide, ferrous sulphate, nickel sulphate, etc. FERROMAGNETIC MATERIALS Certain materials like iron, cobalt, nickel and certain alloys exhibit high degree of magnetization. These materials show spontaneous magnetization. (i.e) they have small amount of magnetization even in the absence of external magnetic field. This indicates that there is strong internal field within the material which makes atomic magnetic moments with each other. This phenomenon is known as ferromagnetism. Properties of ferromagnetic materials: o All the dipoles are aligned parallel to each other due to the magnetic interaction between the two dipoles. o They have permanent dipole moment. They are strongly attracted by the magnetic field. o They exhibit magnetization even in the absence of magnetic field. This property of ferromagnetic material is called as spontaneous magnetization. o They exhibit hysteresis curve. o On heating, they lose their magnetization slowly. The dipole alignment is shown in fig. o Permeability is very much greater than 1. 53 o The susceptibility is very high and depends on the temperature. It is given by χ = (for T>θ) paramagnetic behaviour (for TTN χ T when TTN o Spin alignment is antiparallel of different magnitudes as shown fig. o Mechanically it has pure iron character. o They have high permeability and resistivity. o They have low eddy current losses and low hysteresis losses. o Examples: Nickel ferrite, Ferrous Ferrite, Ni-Zn ferrite. Applications of Ferrites Transformer cores Inductors Permanent magnet Magnetic tapes and films Radio receivers Radar absorbing coating Ferrite core memories Bubble memories DOMAIN THEORY OF FERROMAGNETISM We can observe that ferromagnetic materials such as iron does not have magnetization unless they have been previously placed in an external magnetic field. But according to Weiss theory, the molecular magnets in the ferromagnetic material are said to be aligned in such way that, they exhibit magnetization even in the absence of external magnetic field. This is called spontaneous magnetization. (i.e) it should have some internal magnetization due to quantum exchange energy. 56 According to Weiss hypothesis, a single crystal of ferromagnetic material is divided into large number of small regions called domains. These domains have spontaneous magnetization due to the parallel alignment of spin magnetic moments in each atom. But the direction of spontaneous magnetization varies from domain to domain and is oriented in such way that the net magnetization of the specimen is zero The boundaries separating the domains are called domain walls. These domain walls are analogous to the grain boundaries in a polycrystalline material. DOMAIN GROWTH Now when the magnetic field is applied, then the magnetization occurs in the specimen by two ways 1.By motion of domain walls 2. By rotation of domain walls By motion of domain walls The motion of domain walls takes place in weak magnetic fields. Due to this weak field applied to the specimen the magnetic moment increases and hence the boundary of domains displaced, so that the volume of the domains changes as shown in fig (4). By rotation of domain walls The rotation of domain walls takes place in strong magnetic fields. When the external field is high then the magnetization changes by means of rotation of the direction of magnetization towards the direction of the applied field as shown fig(4). Fig 4. Domain theory of ferromagnetism 57 Energies involved in the domain growth (or) Origin of Domain theory of Ferromagnetism We can understand the origin of domains from the thermodynamic principle i.e., in equilibrium, the total energy of the system is minimum. To study the domain structure clearly, we must know four types of energy involved in the process of domain growth. Exchange energy (or) Magnetic field energy. Crystalline energy (or) Anisotropy energy. Domain wall energy (or) Bloch wall energy. Magnetostriction energy 1. Exchange energy (or) Magnetic Field energy The interaction energy which makes the adjacent dipoles align themselves is the called exchange energy (or) magnetic field energy. The interaction energy makes the adjacent dipoles align themselves. It arises from interaction of electron spins. It depends upon the interatomic distance. This exchange energy also called magnetic field energy is the energy required in assembling the atomic magnets into a single domain and this work done is stored as potential energy. The size of the domains for a particular domain structure may be obtained from the principle of minimum energy. The volume of the domain may vary between say, say, 10–2 to 10–6 cm3. Fig.5 Exchange energy in ferromagnetism 2.Anisotropy energy 58 The excess energy required to magnetize a specimen in particular direction over that required to magnetize it along the easy direction is called the crystalline anisotropy energy. It is found that the ferromagnetic crystals have easy and hard directions of magnetisation i.e., higher fields are required to magnetize a crystal in a particular direction than others. In easy direction of magnetization, weak field can be applied and in hard direction of magnetization, strong field should be applied. For producing the same saturation magnetization along both hard and easy direction, strong fields are required in the hard direction than the easy direction. For example in iron easy direction is , medium direction is and the hard direction is and it is shown in fig. From the fig we can see that very strong field is required to produce magnetic saturation in hard direction compared to the easy direction. Therefore the excess of energy required to magnetize the specimen along hard direction over that required to magnetize the specimen along easy direction is called crystalline anisotropy energy. In easy direction of magnetization, weak field can be applied and in hard direction of magnetization, strong field should be applied. As shown in figure magnetization curves for iron with the applied field along different crystallographic direction crystallographic directions have been drawn. For example, in BCC iron the easy direction is , the medium direction is , and the hard direction. The energy difference between hard and easy direction to magnetize the material is about. This energy is very important in determining the characteristic domain boundaries. Fig 5 Anisotropy energy in ferromagnetism 3. Domain wall energy or Bloch wall energy 59 Domain wall or Bloch wall is a transition layer which separates the adjacent domains, magnetized in different directions. A thin boundary or region that separates adjacent domains magnetized in different directions is called domain wall or Bloch wall. Fig.6 The change of electron spin in the transition region of Bloch wall The size of the Bloch walls is about 200 to 300 lattice constant thickness. In going from one domain to another domain, the electron spin changes gradually as shown in figure. The energy of domain wall is due to both exchange energy and anisotropic energy. Based on the spin alignments, two types of Bloch walls may arise, namely Thick wall: When the spins at the boundary are misaligned and if the direction of the spin changes gradually as shown figure, it leads to a thick Bloch wall. Here the misalignments of spins are associated with exchange energy. Fig.7 The change of electron spin in the transition region of thick wall 60 Thin wall: When the spins at the boundaries changes abruptly, then the anisotropic energy becomes very less. Since the anisotropic energy is directly proportional to the thickness of the wall, this leads to a thin Bloch wall. Fig.8 The change of electron spin in the transition region of thin wall 4. Magnetostriction energy When a material is magnetized, it is found that it suffers a change in dimensions. This phenomenon is known as Magnetostriction. This deformation is different along different crystal directions. So if the domains are magnetized in different directions, they will either expand or shrink. For a nickel rod the length decreases while for permalloy the length increases in the presence of magnetic field. When placed inside the alternating field, the rod vibrates with a frequency twice that of the frequency of the alternating field. This magnetostriction effect is used in generation of ultrasonic waves. This means that work must be done against the elastic restoring forces. The work done by the magnetic field against these elastic restoring forces is called magneto-elastic energy or Magnetostrictive energy. EXPLANATION OF HYSTERESIS When a ferromagnetic material is made to undergo through a cycle of magnetization, the variation of magnetic induction (B) with respect to applied field (H) can be represented by a closed hysteresis loop (or) curve. (i.e) it refers to the lagging of magnetization behind the magnetizing field. Hysteresis comes from the Greek word (hysteresis means later) and refers to the retardation in the response of a material to a change in the applied field. If magnetizing field (H) is applied to a ferromagnetic material and if H is increased to Hmax the material acquires magnetism. So the magnetic induction also increases, represented by oa in the fig.9. 61 Fig. 9 Hysteresis curve Now if the magnetic field is decreased from Hmax to zero, the magnetic induction will not fall rabidly to zero, but falls to ‘b’ rather than removed, the material still acquire some magnetic induction (ob) which is so called residual magnetismor retentivity. Now, to remove the residual magnetism, the magnetic field strength is reversed and increased to –Hmax represented as ‘oc’ so called coercivity(-H)isreduced to zero and the corresponding curve ‘defa’ is obtained. Retentivity (or) Remanence When the external magnetic field is applied to a magnetic material is removed, the magnetic material will not loss its magnetic property immediately. There exits some residual intensity of magnetization in the specimen even when the magnetic field is cut off. This is called residual magnetism (or) retentivity. Coercivity The residual magnetism can be completely removed from the material by applying a reverse magnetic field. Hence coercivity of the magnetic material is the strength of reverse magnetic field (-Hc) which is used to completely demagnetize the material. HYSTERESIS ON THE BASIS OF DOMAIN THEORY We know when the ferromagnetic material is subjected to external field, there is an increase in the value of the magnetic moment due to two process. 62 1.The movement of domain walls 2. Rotation of domain walls When small external field is applied, the domains walls displaced slightly in the easy direction of magnetization. This gives rise to small magnetization corresponding to the initial portion of the hysteresis curve (OA) as shown in figure. Now if the field is removed, then the domains returns to the original state, and is known as reversible domains. When the field is increased, large numbers of domains contribute to the magnetization and thus the magnetization increases rabidly with H.Now, even when the field is removed, because of the displacement of domain wall to a very large distance, the domain boundaries do not come back to their original position. This process is indicating as AB in figure and these domains are called irreversible domains. Now, when the field is further increased, the domains starts rotating along the field direction and the anisotropic energy stored in the hard direction, represented as BC in the figure. Thus the specimen is said to attain the maximum magnetization. At this position, even when the field is removed the material possess maximum magnetization, called residual magnetism or retentivity, represented by OD in fig.10 Actually after the removal of external field, the specimen will try to attain the original configuration by the moment of domain wall. But this moment is stopped due to presence of impurities, lattice imperfections etc. therefore to overcome this; a large amount of reverse magnetic field is applied to the specimen. The amount of energy spend to reduce the magnetization to zero is called coercivity represented by OE in the fig.10 Fig. 10 Hysteresis loss Hysteresis loss is the loss of energy in taking a ferromagnetic material through a complete cycle of magnetization and this loss is represented by the area enclosed by the hysteresis loop. 63 Based on the area of the hysteresis, magnetic materials can be classified into hard and soft materials. TYPES OF MAGNETIC MATERIALS Magnetic materials are classified onto two types. 1. Soft magnetic materials 2. Hard magnetic materials Soft magnetic materials: Materials which are easy to magnetize and demagnetize are called soft magnetic materials. Example –pure iron, cast iron, carbon steel, silicon steel, mumetal. 1. The magnetic materials can be easily magnetize and demagnetize. 2. The have high permeability. 3. Magnetic energy stored is not high. 4. Low hysteresis loss due to small hysteresis loop area. 5. Coercivity and retentivity are small. 6. The eddy current loss is small due to its high resistivity. 7. The domain walls are easy to move. 8. They are used in electric motor, generators, transformers, relays, telephone receivers, radar. Hard magnetic materials: 64 Materials which retain their magnetism and are difficult to demagnetize are called hard magnetic materials.Example –tungsten steel, cobalt steel, alini, alnico, hypernic 1. The magnetic materials cannot be easily magnetize and demagnetize. 2. The have low permeability. 3. Magnetic energy stored is high. 4. Large hysteresis loss due to large hysteresis loop area. 5. Coercivity and retentivity are large. 6. The eddy current loss is high due to its low resistivity. 7. The movement of domain wall must be prevented. 8. They are used in loud speakers and electrical measuring instruments. Difference between Soft and Hard magnetic materials S.No Soft Magnetic Materials Hard Magnetic materials 1 The magnetic materials can be easily The magnetic materials cannnot be magnetized and demagnetized. easily magnetized and demagnetized. 2 Domain wall movement is easy and Domain wall movement is difficult due hence even for a small applied field to presence of impurities and hence large magnetization occurs large field is required for magnetization. 3 Hysteresis loop is very narrow Hysteresis loop is broad 4 susceptibility and permeability are susceptibility and permeability are low high 5 Retentivity and coercivity are small Retentivity and coercivity are large 6 Low hysteresis loss due to small Large hysteresis loss due to large hysteresis loop area. hysteresis loop area. 7 The eddy current loss is small due to The eddy current loss is high due to its its high resistivity. low resistivity. 8 Examples Iron, silicon alloys, Examples Carbon steel, Tungsten steel, Ferrites, Garnets, etc Chromium steel, Cu-Ni-Fe, Al-Ni-Co Energy product 65 For permanent magnets a hard material is needed with a high saturation magnetization, high remanence and high coercivity. Such a material is characterized by a fat hysteresis loop and the shape of the loop in the second quadrant is used as a measure of the effectiveness of the material as a permanent magnet. The energy product is the product of residual magnetism B r and coercivity which HC gives the maximum amount of energy stored in the specimen. Energy product = Br × HC MAGNETIC PRINCIPLE IN COMPUTER DATA STORAGE The most common type of storage device is magnetic storage device. In magnetic storage devices, data is stored on a magnetized medium. Magnetic storage use different patterns of magnetization to in a magnetisable medium to store data. A large number of information are stored in or retrieved from the storage devices, by using the magnetic phenomena. The main part of these magnetic storage devices is magnetic recording heads and they function according to the principles of magnetic induction. Generally ferromagnetic or ferromagnetic materials are used in the storage devices because in this type of materials only the magnetic interaction between any two dipoles align themselves parallel to each other. Du to this parallel alignment, even if we apply small amount of magnetic field a large value of magnetisation is produced. By using this property information are stored in the storage devices. In the storage devices, the recording of digital data (0’s and 1’s) depends upon the direction of magnetisation in the medium. Magnetic parameters for recording 1. When

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