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Electric field for eq 2 in the new coordinate system or .....................(4) where represents the component of the electric field along x' and that of along y' for the eq 4 (which is representing the same field of eq 2).

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Polarization of light by reflection: Polarization at Brewseter angle: when the angle of incidence is equal to the Breswter angle, then the reflectivity for the p component () is zero. Thus if a randomly polarized light is made to incident at Breswter angle on air-glass interface then the reflected light will be s polarized (Fig 1.).

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Elliptically polarized light: Considering the general expression for electric field of a plane wave propagating along z axis ..................... (1) under the situation , The x and y components of electric fields are given by

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Representation of polarized light in Jones calculus: Sometimes, for convenience, equation can also be written in terms of complex exponential form ................................ (1)

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Electromagnetic waves at the interface of two dielectric mediums: When an electromagnetic wave strikes at and air dielectric interface, from air to the dielectric medium, part of it is reflected back and part of it is transmitted into the dielectric medium. The amount of light reflected and transmitted depends on the angle of incidence, refractive indices of the medium forming the interface and the angle of incidence. Let us consider an interface formed by two dielectric medium I and II of refractive index n₁ and n₂ respectively as shown in fig 1.In the previous lecture we summed up the properties of electromagnetic waves and its representation. In this lecture we will be looking into the modification which an EM wave under goes when it strikes the interface of two dielectric medium. fig 1: The different portions of light at a material interface

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Propagation of light through birefringent crystal: Let us consider a uniaxial crystal placed in air. As discussed in the previous module, the radiation falling at an interface may be resolved in two kinds of polarization, viz: in plane polarization and perpendicular polarization. To make the discussion simple, we will consider the normal incidence only. If n_o> n_e, the crystal is called as positive crystal and if n_o< n_e, the crystal is called as negative crystal. Case I:Let us consider the first case when the optics axis is perpendicular to the interface formed by the uniaxial crystal and the air as shown in Fig.1. In this case, the refractive indicies for both polarization is same and is given by n_o. Both the s and p waves will travel with the same speed. One can show the wave front by drawing a circile of radius c/n_o with the center at the interface at point O, where the radiation is hitting the interface as shown in fig. The wave front will be spherical corresponding to both the components, . The situation will be similar to that of isotropic medium.

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Equation (6) represents the equation of circle. There fore we can describe the wave given by equation (2) as a wave whose direction of electric field is rotating in x-y plane with the angular frequency , the frequency of the wave and the tip of the electric field vector is moving in a circle in clock wise direction as shown in the fig 1 below. fig..(1) This kind of wave is termed as right circularly polarized light.

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Description: Co-ordination number is the number of equidistant neighbours surrounding an atom in the given crystal structure. When the coordination number is larger, the structure is more closely packed. 1. Simple cubic lattice

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Introduction: Bravais demonstrated mathematically that in 3-dimensions, there are only 14 different types of arrangements possible. These 14 Bravais lattices are classified into the seven crystal systems on the basis of relative lengths of basis vectors and interfacial angles.

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Primitive and Non primitive cells: A primitive cell is a minimum volume unit cell. Consider a bravais lattice (in two dimensions) as shown below:

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The electric field E of the light coming out of the polarizer (polarized light) can be resolved in two mutually perpendicular components. E₁ component, having electric field in the plane of the incidence of analyzer and other E₂ perpendicular to it as shown in Fig. 3. fig..(3) Components of electric filed in two mutually perpendicular direction

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Description: Many physical properties of crystalline solids are dependent on the direction of measurement or the planes across which the properties are studied. In order to specify directions in a lattice, we make use of lattice basis vectors a, b and c.

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Electromagnetic Spectrum; The areas of Optical sciences normally refer to a small spectral region of electromagnetic radiation. Normally it covers the region from UV to IR region. Every part of electromagnetic spectrum has one or more than one application. Some of the common applications of the various regions of electromagnetic spectrum are listed below : Gamma Rays: Medical diagonistics

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Retardation Plate: The retardation plate or the phase shifter is an optical component which can rotate or modify the plane of polarization of the incident beam falling on to it. In its simplest form, the retardation plate consists of a uniaxial crystal cut in such a way that the the optics axis or symmetry axis lies in the plane of the plate. If a retardation plates introduces a phase change of or (p being an integer) in the two mutually orthogonal components of electric field associated with the light wave then it is called as half wave plate . As in such case the relative path difference introduced in the two components is or half the wavelength. If the corresponding phase difference introduced is or , then it is called as quarter wave plate as in this situation the relative path difference introduced is . With in the retardation plate, the optics axis and the axis normal to it are called as slow axis and the fast axis. The slow axis will be the axis for which refractive index is large and the fast axis is the axis for which the refractive index is small and hence the speed of propagation will be small in former and large in later case. Let us consider a half wave plate such that optics axis is making an angle of with the y axis and is placed in y-z plane. A linearly polarized plane wave is allowed to fall at normal incidence on this wave plate as shown in Fig 1. The direction of propagation of this wave is along x axis.The wave is polarized along y direction and its electric field can be represented as (1)

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quarter-wave-plate: Let us consider a quarter wave plate such that optics axis is making an angle of with the y axis and is placed in y-z plane. A linearly polarized plane wave is allowed to fall at normal incidence on this wave plate as shown in Fig 1. fig..(1) The direction of propagation of this wave is along x axis. The wave is polarized along y direction and its electric field is given by equation 1. The two orthogonal components; E_|| , along the optics axis and , perpendicular to the optics axis are given by

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Electromagnetic wave as the transverse wave: phase factor: The factor is termed as the phase factor and plays an important role in determining the status of the wave at any instant of time and or at any location in space. If the phase factor is constant in the transverse plane x-y, than the wave will be called as the plane wave and all the rays in it will be parallel to each other. The planes containing the constant phase are termed as the wavefront. The wave front is perpendicular to the direction of propagation. Fig 2. shows the plane wave front for a plane wave propagating along z axis. fig..(1) plant wavefront Intensity :The power (energy) associated with the radiation field is measured in terms of intensity I. It is defined in terms of watt/cm². It is related to the electric field associated with em wave given by

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Phenomena of double refraction: A randomly polarized light or two mutually orthogonal polarized lights will see the same refractive index in all the direction while propagating through the medium. Recalling the Huygen's principle, one can say that if there is a point source of light inside the medium, it will emit a spherical wave front, as shown in Fig.1, irrespective of the state of polarization. Such materials are called as isotropic medium. Ordinary glass is a good example of isotropic material. There are certain material for which the refractive index is different in different direction or we can say simply that the speed of propagation will not be same in all direction and also it may depend on the state of polarization. In such materials a point source may result into the elliptical wave warfront or for different polarization the wave front will be different, as shown in fig 1. Such materials are called as anisotropic material. Crystals like Quartz (SiO 2 ), calcite (CaCo 3 ) and KDP (potassium dihydrogen phosphate, KH 2 PO 4 ) are good example of anisotropic material. Such anisotropy is due to difference in the arrangement of the atoms and molecules in different direction in the crystal which leads to direction dependent polarization property of the system.

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............................................(5) will be negative and its magnitude will increase with the angle of incidence taking the value of 1 at as shown in fig 2. the negative sign in the region of inequality (3) indicate that the electric field for the reflected wave is out of phase with the corresponding incident wave. For the angle of incidence satisfying equation (4), the reflected light is purely s polarized. This particular angle of incidence denoted by is termed as the Brewster angle and from equation (8) it can be easily shown .

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Fresnel's equations: Fresnel's equation relates the ratio of the amplitude of the electric field of reflected and transmitted light to that of the incident field, angle of incidence and the refractive indices of two media forming the interface. Let us denote the amplitude of incident electric field in the plane of incidence as and that of nomal to the plane of incidence as . Accordingly the reflected and transmitted amplitude of electric fields are: Amplitude of the parallel component of electric field transmitted. Amplitude of the normal component of electric field reflected.

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Introduction: Heisenberg’s uncertainty Principle Quantum mechanics is a fundamental branch of physics which generalizes classical mechanics to provide accurate descriptions for many previously unexplained phenomena such as black body radiation, photoelectric effect and Compton effect. The term quantum mechanics was first coined by Max Born in 1924.Within the field of engineering, quantum mechanics plays an important role. The study of quantum mechanics has lead to many new inventions that include the laser, the diode, the transistor, the electron microscope, and magnetic resonance imaging. Flash memory chips found in USB drives also use quantum ideas to erase their memory cells. The entire science of Nanotechnology is based on the quantum mechanics. Researchers are currently seeking robust methods of directly manipulating quantum states. Efforts are being made to develop quantum cryptography, which will allow guaranteed secure transmission of information. A more distant goal is the development of quantum computers, which are expected to perform certain computational tasks exponentially faster than the regular computers. This chapter attempts to give you an elementary introduction to the topic.

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Twin Paradox: There is a twin brother A & B. A takes space voyage and B remain in the earth. According to time dilation, the clock with B runs faster than clock with A. we know that, For example, if B is measuring a span of 50 years, A would be measuring only 30 years.

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Introduction: The uncertainty principle has far reaching implications. In fact, it has been very useful in explaining many observations which cannot be explained otherwise.

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Introduction: In quantum mechanics, because of the wave-particle duality, the properties of the particle can be described as a wave. Therefore, its quantum state can be represented as a wave of arbitrary shape and extending over all of space. This is called a wave function. The wave function is usually complex and is represented by Ψ. Since the wave function is complex, its direct measurement in any physical experiment is not possible. It is just mathematical function of x, t etc. Once the wave function corresponding to a system is known, the state of the system can be determined. The physical state of system is completely characterized by a wave function.

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Introduction of Theory of Relativity: We are familiar with the word ‘motion'. In every day life we see the motion of several objects around us. If we have been asked to define motion we would say “change of position with time”. In an attempt to define motion we have used two concepts space (position) and time. By our intuition, we know what is space and time and these are defined as follows according to Newton's view. Space is absolute, in the sense that it exists permanently and independently whether any matter in the space or moving through it. Thus space is a sort of three dimensions matrix into which one can place objects or through which objects can move without producing any interaction between space and object. Each object in the universe exists at a particular point in space at a particular time. An object in motion undergoes continuous change of position with time. Time in Newton's view is also absolute and flows on without regard to any physical object or event. One can neither speed up the time nor slow down its rate. The flow of time exists uniformly through the universe. If we imagine the instant “now”, it occurs simultaneously on every planet and star in the universe. The time interval between two events is same everywhere in the universe, it can be verified by observing of physical, chemical and biological events. We have defined space and time, with our everyday knowledge about nature and surroundings. However there are some contradictions with our intuition, when the motion of an object is at very high speed, approaching or equaling the speed of light. It was Einstein who exposed some of the most important limitations of classical ideas including that of Newton. Einstein contribution led to the development of special theory of relativity (STR).

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Introduction and Explanation: We know that the probability density of the particle is given by the square of the wavefunction; we also know that the particle must be somewhere in the box. Therefore, if we add up the total probability density in the box we must get the answer 1, i.e. there is 100% probability of finding the particle somewhere in the box.

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Introduction to Eigenvalues and eigenfunctions: Generally, quantum mechanics does not assign definite values to observables. Instead, it makes predictions about probability distributions; that is, the probability of obtaining each of the possible outcomes from measuring an observable. Naturally, these probabilities will depend on the quantum state at the instant of the measurement. There are, however, certain states that are associated with a definite value of a particular observable. These are known as eigenvalues of the observable and the corresponding wave functions are called eigenfunctions. The eigenfunctions are those eigenfunctions which are definite and single valued. When something is in the condition of being definitely ‘pinned-down’, it is said to possess an eigenvalue. For example, if the position of an electron has been made definite, it is said to have an eigenvalue of position. The term eigen can be roughly translated from German as inherent or as a characteristic). The German word ”eigen” was first used in this context by the mathematician David Hilbert in 1904.

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Frames of References: When someone say 'the bus is moving', we would be certain that what is being described is a change of position of bus with respect to earth's surface or any building, tree etc which are fixed to the earth. We accept the local surroundings - a collection of objects attached to earth and therefore at rest relative to each other as our frame of reference. It is clear that the choice of particular frame of reference is just a matter of convenience. It is often helpful to use a frame of reference in which the description of motion is simplest. Within a frame of reference, we set up a coordinate system, which is used to manage the position of an object. To specify the position of any object, we use three numbers. The choice of number is determined by the type of coordinate system we use. The generally used coordinate systems are rectangular coordinates (x, y, z), spherical polar coordinates () and cylindrical coordinates (). Inertial Frame and Galilean Transformation: The reference frames, which we described earlier such as earth, buildings, trees, etc., are called inertial frames. Here an object remains at rest if it is not influenced by any other forces i.e. forces arising from its interaction with other objects. Imagine a football kept on a playground, the ball remains at rest unless you kick or pick the ball (in the absence of wind). Here, the playground can be taken as an inertial frame. If one inertial frame is identified, then any other frame moving with constant velocity with respect to inertial frame is also inertial. This argument implies that all un-accelerated frames constitute the class of inertial frames. All inertial frames are equivalent in the sense that any dynamical experiment gives same result in all these frames. Both the values of force and acceleration for an object remain same when we go from one frame to another.

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Simultaneity: We have an intuitive idea of what is meant when we say that two events are simultaneous. With respect to a given coordinate system two events are simultaneous if their time coordinates have the same value. However events which are simultaneous in one coordinate system are not necessarily simultaneous in another coordinate system. For an example, consider a railway man standing at the middle of a freight car (stationary)length 2L. He flicks his lantern and light pulse travels in all directions with velocity c. Light arrives at the two ends of the car after a time interval L/c. In this system, the freight cars rest system light arrives simultaneously at A and B. Freight car system : Let us take the origin at the position of railway man (middle of car).

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when so, the Kinetic Energy . Thus the kinetic energy approaches the classical limit for ------------(9) Total energy = Kinetic energy Rest mass energy. Where is the total energy. The first term in the right hand side arises due to external work done on the particle and the second term is due to rest mass energy.

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Introduction: Time-independent form of the Schrödinger wave equation in one-dimension. Explanation of Eigen value particles in a potential well of infinite depth:

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Length Contraction: Two dramatic results of the special theory of relativity are that a meter stick is shorter when moving than at rest and the moving clock runs slow. These results are quite real. Consider a stick at rest in the system lying along the axis with its ends at and . The length of the stick is, is called the rest or proper length of the system.

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So the Lorentz transformation equations would be, The above equations are called Lorentz transformation equations.

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Non-inertial frame and Fictitious forces: A football is kept in a stationary bus and we can find that it would at rest. If the bus starts moving, we will find the ball moving from its initial position without applying any external force by the way of interaction with other objects. The above movement is as a result of accelerating frame (bus). Any frame that is found to accelerate is called non inertial frame. Here, Newton's second law 'f = ma ' cannot be used without accounting for additional force acting on the object due to accelerated frame. We turn our attention to appearance of physical laws to an observer in a system accelerating at rate with respect to, inertial system. By rewriting the acceleration relation, where is the acceleration of primed coordinate system. By multiplying the mass of the body, 'm' we get or Here is the true force due to the physical interaction, is the force due to physical interactions observed in the primed coordinate system (apparent force) and is the fictitious force. Fictitious force in some text is called inertial force. The fictitious force experienced in a uniformly accelerating system is uniform and proportional to the mass of the system, like a gravitational force. The fictitious forces originate from the acceleration of coordinate system and not due to interaction between bodies.

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As per equation (9), the momentum is not conserved in frame. We get different results with change in internal frame and it violates Einstein theory of relativity that laws of physics are invariant in different inertial frames. We have used Lorentz transformation for the transfer of velocity from S to frame. Lorentz theory is correct because it explains the cosntancy of velocity of light. So, the problem could be, the definition of linear momentum in relativistic dynamics. One has to take the appropriate definition of linear momentum such that it follows the fundamental laws physics like conservation of momentum in the absence of applied force. It should also reduce to the definition of classical physics, when the velocity of the body U< The relativistic momentum can be defined as , . . . . . . . . . . . . . . . . . . . . . ( 10 ) where is the distance traveled by a particle of mass m and the time interval . Here is the proper time, that is the time measured with respect to the moving frame of velocity attached to the body. As per the time dilaton relation, we know that,

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The postulates of special theory of Relativity: Einstein in 1905, formulated this special theory of relativity on the basis of following postulates: The first postulate implies that not only the laws of mechanics but also that of electrodynamics and optics should be same for all inertial reference systems. There is no privileged frame like ether or absolute space. The second postulate is really a consequence of the first, because if Maxwell’s equations hold in all inertial frames, then the only possible value for the speed of light is c. These postulates embody Einstein’s Special Theory of Relativity, first published in 1905 in a paper titled On the Electrodynamics of Moving Bodies. Later he would incorporate gravity and acceleration in his General Theory of Relativity. As in Newtonian Relativity, there is no way to detect absolute motion. Only the relative velocities between two inertial reference frames matters. These seemingly simple postulates have extraordinary consequences. For example, when you turn on the headlights of a car, the light beam leaves the car at a relative velocity of c = (3.0* 10⁸)m/s. However, someone standing on the sidewalk also measures the speed of the light beam as c independent of the velocity of the car! How can this be? As we shall see, our concepts of space and time must be modified.

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This is the time-independent form of the Schrödinger wave equation in one-dimension. This is also known as Schrödinger’s steady-state equation.

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...................................... ( 3 ) So the time taken by the second beam to reach and back to the plate P is, .......................... ( 4 ) If the apparatus is rotated through 90⁰, thus making the as cross-stream length (vertical) and as down-stream length (parallel to movement of earth) and the corresponding times are now designated as and respectively,

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The Relativistic Addition of Velocity: In classical physics, if we consider a case of a train moving with velocity with respect to ground and a passenger on the train moving with a velocity with respect to train, Then the velocity of passanger with respect to the ground is, ....................... ( 1 ) This is simply Galilean or classical velocity addition theorem. Let us discuss how the velocities are added according to special theory of relativity.

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System for observing interference phenomenon: Various systems based on these principles have been designed and are used to observe these phenomenon. These systems find several applications in science and engineering such as measurement of wavelength of a light source, the wavelength difference between two closely separated waves, the optical flatness of surfaces, thickness of the film, refractive index of material etc. We shall be discussing some of these systems and their applications in the following sections. The major systems for observing interference phenomenon are as follows. Fresnel Biprism : A freshnel biprism is a thin double prism placed base to base and have very small refracting angle ( ). This is equivalent to a single prism with one of its angle nearly 179° and other two of each. Here the interference is observed by the division of wave front. Monochromatic light through a narrow slit S falls on biprism ABC , which divides it into two components. One of these component is refracted from portion AC of biprism and appears to come from S₁ where the other one refracted through portion BC appears to come from S₂. Thus S₁ and S₂ act as two virtual coherent sources formed from the original source. Light waves arising from S₁ and S₂ interfere in the shaded region and interference fringes are formed which can be observed by placing a screen MN . If d is the separation between the virtual sources S₁and S₂, Z₁ is separation between source S and biprism and Z₂ is the separation between biprism and the screen then

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Classification of Interference Phenomenon: In order to observe interference phenomenon, the two super imposing waves must be originating from the same source, so that the phase difference between them remains constant with time. These waves can be derived by single source using number of methods. Depending on the process by which the waves are derived, these can be classified as follows : i) division of wavefront ii) division of amplitude. Division of wave front: when the two super imposing waves are derived from the two regions of parent waves, the process is known as division of wave front. Since the phase on the wave front is constant, the waves from two regions of waves will bear a constant phase difference at any point of observations. An earliest method to obtain two coherent waves (source) by division of wave front of parent wave is young's double slit method and is described below.

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Measurement of thickness of thin film: The thickness of thin film is measured using multiple beam interferometry. The film is deposited on a substrate such that it has a step. The film and remaining surface of the substrate is then coated with aluminum film (by evaporation). Since the reflection coefficient of both the surfaces are high, multiple beam fringes in the wedge are obtained. The fringe pattern from the two area of the surfaces (where there is a film and where there is no film) , are shifted. This fringe step is used to measure the thickness of the film . Fig. A: Experimental arrangement to measure the thickness of thin film

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Intensity distribution: We have seen in the earlier sections, that whenever two waves superimpose the resultant wave's amplitude gets modified. If the two superimposing waves are of same frequency and wave vector, then the amplitude (thus intensity) at any time and position depends upon the phase difference between the two propagating waves. As these waves are traveling waves, at a given time t, the phase of the waves vary with the position in space. Now if we consider the superposition of these waves at different points in space (at time t), the intensity will depend upon the relative phase difference between the two waves, at these points, where the phase difference between the waves in even multiple of , the intensity will be maximum and more than the sum of intensity of individual waves ; where as at points where the phase difference is odd multiple of , the intensity will be minimum and is less than the sum of intensity of indivisual waves . At all other points, intensity will be between this maximum and minimum intensity depending upon the phase difference. Fig 1 shows the variation of intensity with phase difference between the two waves. This spatial variation of intensity gives the interference pattern on screen. fig..(1)

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Twymann-Green Interferometer : A set up for the Twyman-Green interferometer is shown in (Fig.A(a)). The interferometer is used to test the flat surfaces, beam splitters, prism and lens. Light from a source S is collimated using lens L₁ which falls on a beam splitter and is divided into two beams which move towards mirrors M₁ & M₂ respectively. These beams are then reflected back and combine again at beam splitter. Another lens L₂ is used to project the fringe pattern on screen. The mirrors and beam splitters used in the set up are of high optical quality. Interference phenomenon takes place between two plane waves. A monochromatic source (such as laser light) or quasi monochromatic source (such as mercury vapour lamp along with different color filters to select desired ) is used to observe interference fringes. The straight line fringes are obtained when the plane waves enclose a small angle. The orientation of these fringes can be varied by changing the orientation of one mirror with respect to the other (finite fringe setting). The test surfaces/optical elements are introduced in the path of one beam. The various arrangements for different elements are shown in the (Fig.A(b)) Fig.A (a) The Twyman-Green Inferometer

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Conditions for Interference: It is not always necessary that two superimposing light waves always interfere and result in redistribution of energy (fringes). Only when these superimposing waves satisfy certain conditions the fringe pattern is observed on screen. These conditions are as follows. Coherent and Non coherent Sources: A light source emits photons, when the atoms undergo transition from one state to another. This process is highly chaotic, as the photons emission process from a collection of atoms is independent of each other. The light wave coming from the source, is therefore, superposition of many waves with random phases, and resembles a sinusoidal wave for about 10ns or so (the typical time interval in an emission process). Since the phase of the resultant wave from the source is not constant with time, such a source is called a non coherent source. Now if the two super imposing waves are coming from different sources, their phases will change randomly and their phase difference will not be constant with time and the waves will not interfere.

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Interference: Light is an electromagnetic wave. The energy in such a wave is due to the electric and magnetic field vectors associated with them. In all electromagnetic waves, the electric and magnetic field vectors are mutually perpendicular to each other and also perpendicular to the direction in which the wave propagates(transverse wave). When two light waves cross each other, due to superposition, the distribution of energy in space may takes place. This is similar to the superposition of any two waves like mechanical, sound etc. It is possible that in some region of space the energy is more than the energy due to individual waves and in some other region of space, it is less than that due to individual waves. The phenomenon of redistribution of energy due to superposition of waves is called interference. This redistribution of energy depends upon the frequency, amplitude and the phases of individual waves. In the following, we shall be discussing these phenomenon and the conditions to observe interference. Superposition of Waves: Consider two light waves each of frequency , propagating along z axis in vacuum.

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Central spot ‘O', is dark although the film thickness is zero there, This is because of the phase difference of π(equivalent path difference = λ/2) introduced in the ray reflected by flat glass plate. The radius of the n^th dark or bright ring can be measured by measuring the diameter of the ring. In an experimental set up the cross wire of eye piece is focused on the n^th order ring on both side the center spot respectively by moving the micrometer screw and noting down the corresponding reading on micrometer scale. For an accurate determination of λ the diameter 'D' (=2x) of every 5^th ring is measured, while the space between the plano convex lens and flat surface has only air film . In this case, for bright rings .

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Superposition of waves of slightly different wavelengths and frequency: Let us now consider two light waves of frequency and wavelengths .The corresponding small wave vectors will be . Again for the case of simplicity, let both the waves be propagating in same direction and let both have same state of polarization (i.e. their electric field vectors point along the axis) and amplitude . The two waves can be written as

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Superposition of waves with different polarization: So far, we have discussed the case, when the electric field vectors two light waves point in the same direction. Let us now consider a more general case. Once again we assume that the two waves are propagating in the z direction. The electric field vectors of these waves must lie in the x-y plane . We have seen in the earlier section, that the amplitude of the resultant wave, depends on the phase difference between the two waves and not on the phases of individual waves. Let, at a given point z, one of these waves has phase zero and other is having a phase . The two waves are now given as ---------------------- (1) ---------------------- (2)

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The reflected flux density is given by ------------------------(4) Where I_inc is the incident flux density () and is co - efficient of finesse .

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Engineering applications of Interference phenomenon: While discussing various methods of producing interference fringes, we discussed how these can be used to determine the wavelength of monochromatic light, the separation between the two closely spaced wavelengths, thickness and refractive index of thin transparent sheet and refractive index of a liquid. Apart from these, interference phenomenon finds many interesting engineering applications. These include testing of flatness of optical surfaces, the angle of beam splitter, testing of prism and lens for chromatic aberrations,, measurement of thickness of a thin film, collimation testing, measurement of angle of a wedge etc. We shall discuss a few in the following. Testing of optical surfaces –The optical surfaces are tested either by contact method where the test surface is put in contact with the master surface (an experimental arrangement similar to Newton's ring method) or by inserting the test surface in the path of two beams (experimental arrangement is similar to Michelson interferometer) and is known as Twyman-Green interferometer)

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Michelson interferometer: In Michelson interferometer the two coherent sources are derived from the principle of division of amplitude. The parallel light rays from a monochromatic source are incident on beams splitter (glass plate) G₁ which is semi silvered on its back surface and mounted at 45° to the axis. Light ray incident ‘O' is refracted into the glass plate and reaches point A , where where it is partially reflected (ray 1) and partially transmitted ray 2. These rays then fall normally on mirrors M₁ (movable) and M₂ (fixed) and are reflected back. These reflected rays reunite at point A again and follow path AT. Since these two rays are derived from same source(at A) and are therefore coherent, can interfere and form interference pattern. In this geometry, the reflected ray 1, travels an extra optical path, a compensating plate G₂ of same thickness as plate G₁ ) is inserted in the path of ray 2 such that G₂ is parallel to G₁ . This introduces the same optical path in glass medium for ray 2 as ray 1 travels in plate G₁ (therefore is called a compensating plate). Any optical path difference between the ray 1 and ray 2 is now equal to actual path difference between them. To understand, how the fringes are formed, refer to fig. An observer at 'T' will see the images of mirror M₂ and source S ( M'₂ and S' respectively) through beam splitter along with the mirror M₁. S₁ and S₂ are the images of source in mirrors M₁ and M₂ respectively. The position of these elements in figure depend upon their relative distances from point A .

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Division of Amplitude: When a light wave (AO) falls on a thin film of material having a different refractive index, it is partially reflected back (OB) and partially transmitted (OC) to the medium. The transmitted wave OC suffers a partial reflection (CD) on the other interface of thin film and another medium. The wave CD after another partial transmission (DE) on the first interface comes out to first medium and is parallel to OE. The two light rays OB and DE are therefore derived from the same parent wave and thus bear a constant phase difference (arising due to different optical paths traveled by wave OB and wave OCDE) and are therefore coherent. However in this process, the energy of incident wave is distributed between different reflected and transmitted components. This process of obtaining two coherent waves is called “Method of division of amplitude”. Depending upon the phase difference between the two waves these may interfere constructively (bright fringe) or destructively (dark fringe) The path difference between the two waves is ----------------------------------------(1)

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Classification of fringes: we see that for superposition of two waves derived by division of amplitude, the intensity can be varied by varying the thickness of the film; varying angle of refraction (or angle of incidence ) or the wavelength of the light rays. In each of these cases, fringes of different types are obtained on screen, which can be classified into three types. In the following section, we shall be discussing these cases. Fringes of constant inclination:

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Diffraction by multiple slits: Diffraction Grating: In earlier lecture, we have seen the effect on intensity distribution when the light waves passe through two nearby narrow slits. As a result of this, the broad principal maximum produced by single slit actually consists of alternate dark and bright region. Now we will see the combined effect of interference and diffraction on intensity distribution, when the light waves are allowed to pass through large number of narrow slits, very close to each other. This arrangement of slits(Fig.12.3.1 ) is known as diffraction grating and finds lots of application in optics. Once again, each of these slits acts as source of secondary wavelengths and we will see again combined effect of interference and diffraction on screen. In this case, the broad principal maxima corresponding to single slit pattern, consists of several principal maxima and very low intensity secondary maxima separated by minima. We assume that width of each slit is ‘d' and the separation between the centers of any two adjacent slits is ‘b'. We will calculate the resultant intensity at the point P on the screen due to N such slits. In order to find intensity distribution, we have to calculate the resultant amplitude of all waves reaching the point P . These wavelets are now originating from N slits and the calculation of the amplitude, as we did in case of single slit and double slit, is complicated. However, we can use the complex amplitude method. Here we note that the phase difference between the waves originating from similar position of two consecutive slits is ( b is separation between the two slits). The amplitude part from each wave is Thus if we have two slits Fig.A

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Resolving power of image forming systems: Telescope and Microscope: So far we discussed the diffraction pattern due to apertures which were extending in one dimension only. To calculate the resultant amplitude at a point on screen, we had to perform the integration along one direction only. However, in any image forming system, be it our eye, camera lens, telescope or microscope, light enters through a circular aperture followed by a lens which forms the image on the screen. The image of a distant point source is therefore not a point, but a sort of diffraction pattern. In this case, to calculate the resultant intensity distribution we have to perform a double integral for calculating resultant amplitude, which is quite complex. However, in this case, we can intutively feel that the diffraction pattern will be in the form of central circular disk surrounded by dark and bright circles. The condition of minima is given by , where D is the diameter of the aperture and is angular separation of m^th order minima from the center. However, in this case m is not an integer as it was for single slit diffraction. Airy showed that the condition for first order minima (first dark circle) is . Telescope When we use a telescope to image two stars, we can determine their angular separation in space. However, whether this resolution is possible, will be determined by the resolving power of telescope. We have seen earlier that two sources can be well resolved if their angular separation is such that the central maxima of one falls on the first minima of other (in other words )

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Optics: Diffraction: If an opaque obstacle (or aperture) is placed between a source of light and screen, a sufficiently distinct shadow of opaque (or an illuminated aperture) is obtained on the screen .This shows that the light travels approximately in a straight lines. If, however, the size of obstacle (or aperture) is small (comparable with the wavelength of light), there is a departure from straight line propagation and the light bends round the corners of the obstacles(or aperture) and enters the geometrical shadow. The bending of light at sharp corners/edges is called diffraction. As a result of diffraction, the edges of the shadow (or illuminated region) are not sharp , but the intensity is distributed in a certain way depending upon the nature of obstacle (or aperture). Let us first explain, how the light bends around a sharp corner. According to Huygen's principle, when a wave propagates, each point on its wave front serves as the source of spherical secondary wavelets having same frequency as that of original wave [Fig. 1a]. The resultant at any point afterward is the envelope of these secondary wavelets. However, this picture does not explain the diffraction of light through small apertures. If we assume that, as shown in fig.1b, each unobstructed point of a wavefront, at a given instant, serves as a source of spherical secondary wavefront, the amplitude of the optical field at any point beyond is the superposition of all these wavefronts. The maximum path difference between these secondary wave fronts at any point P is equal to AB . (Path difference will be equal to AB if point P merges with either point A or point B) .

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Analysis of Diffraction pattern due to single slit: The intensity on the screen for diffraction due to single slit is where . The intensity will be minimum (or zero) when or m=1,2,...................................... or

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Upon rearranging, Where,

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Resolving Power of Grating and other Image forming system: Resolution of image forming system An optical system is used to form the image of objects. These objects may be situated at very large distances (like stars in galaxy) or very fine in size (microscopic size) The quality of image depends upon the quality of lenses used (Abberations). Even if we have perfect lens systems, the quality of image (sharpness) is limited by the diffraction at the aperture (entrance slit of the optical instruments). It means that if there are more than two light sources (illuminated objects) nearby, whether the images of these two sources (intensity distribution on screen) is separate or overlaps on each other will depend upon intensity distribution due to either sources on screen. Till now we discuss the cases where monochromatic light was coming from a distant source (so that when it reaches the slit the wave front is plane). We discussed the intensity distribution on screen after the light passes through a slit or a system of slits. Clearly, the intensity distribution will change, if light is coming from some other source also(at some angle of incidence not equal to 0⁰) or having more than one wavelength. Resolution or resolving power an optical instrument is the ability to separate the image pattern arising due to two nearby sources or due to two closely spaced wavelengths.

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The wave fronts reaching P from other elements ds will vary in phase due to extra path travelled by them. The displacements produced by another element ds at a distance s from the center(origin) will be given by Where is the path difference. The net amplitude at P will be sum of effect due to all the elements ds and can be obtained by integrating dE_s from s=-d/2 to d/2 where d is the width of the slit. In doing so, we can first sum the amplitude produced by the symmetrically placed elements ds and then integrate it from s=0 to d/2. The contribution due to a pair of symmetrically placed element ds is

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fig..(3) or,

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Width of principal maxima The angular separartion between the m'^th order principal maxima and the next first minima will follow the following conditions (maxima) and (minima)

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Introduction: Principle and production: Under normal circumstances when light interacts with matter, electrons in the matter may absorb the light energy and go to the higher energy level and come back to the ground state by emitting the light of the same frequency. But in any given situation the number of electrons in the ground state is more than that in the excited state. The Laser is based on the principle of light amplification by stimulated emission of radiation. This is achieved by having excess concentration of electrons in the higher energy states and stimulating the system by radiation to bring about the de-excitation process. Induced absorption, spontaneous emission and stimulated emission:

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Introduction: Many thousands of kinds of laser are known, but most of them are not used beyond specialized research. The chief types of lasers are solid state lasers, gas lasers and liquid lasers. A solid, liquid, gas or semiconductor can act as the laser medium. Here we discuss only Helium-Neon and semiconductor lasers. Helium-Neon Laser:

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Expression for Einstein’s coefficient: By rearranging the terms, we get From Boltzmann’s law, we know that the ratio of the population densities N₁ and N₂in the ground state E₁ and excited state E₁ respectively is given by,

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Introduction: There are many scientific, industrial, military, medical and commercial laser applications. The coherency, high monochromaticity, focussability, directionality and ability to reach extremely high powers are all properties which allow for these specialized applications.

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eq...(1) where l = SS′, d is the distance between pinholes S and S2 and D is the distance of the pinholes from the sources S and S′. Equation (1) gives

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Ruby Laser: Ruby laser is historically the first one to be discovered; It gives laser radiation on a pulsed length (1 nm = 10^-9 m). It consists of a ruby rod xenon flash tube, a suitable cavity to reflect the light from flash tube to the ruby rod, and a high voltage power supply to give electrical energy to the flash tube. Maiman's laser set-up is shown in Fig. 1. During his experiment, Maiman found that the ideal composition for the ruby crystal is five atoms of chromium for every ten thousand atoms of aluminum, i.e., a concentration of 0.05 percent. The ruby rod used was 4 cm long and 1/2 cm in diameter and the ends were ground to a high degree of flatness and parallelism. One end was silvered making it a mirror (almost 100 percent reflective) to reflect all the rays of light striking it. The other end of the rod was partially silvered; the laser beam was emitted through that end. The ruby rod was surrounded by a helical xenon flash lamp and both of them were held inside a cylindrical cavity, coated with a reflective material. The light from the xenon flash tube was focused by the cylindrical cavity onto the ruby rod, thereby exciting the chromium atoms which were responsible for the laser action The ruby laser is a three-Level system since only three energy levels

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HELIUM-NEON LASER: The helium-neon (He-Ne) laser is the first gas laser operated successfully in 1961, by Ali Javan and his co-workers at Bell Telephone Laboratories in U.S.A. It consists of the following main components. 1. Active Material: Mixture of helium and neon gases in the ratio 7 : 1 at total pressure of 1 torr (1 torr = 1 mm of Hg column) is used as an active material. However, this ratio 5 : 1 to 10 : 1 may be taken. In the mixture helium is used for population inversion only whereas levels of neon are involved in laser action. 2. Resonator Cavity: Resonator cavity is made of quartz tube of about 80 cm length and 1 cm diameter. The gas mixture is enclosed between a pair of mirrors. One mirror is completely reflecting (99.99% reflectivity) and the other mirror called the output mirror is partially transmitting (about 90% reflectivity). 3. Exciting Source: Exciting source for creating discharge in the tube is the high voltage radio frequency such as Tesla coil. As is shown below its operation involves four energy levels—three of neon and one of helium. Operation: The working of the He-Ne laser is based on the fact that neon has excitation energy levels very close to meta-stable energy levels of helium. Few energy levels of He and Ne excited states are shown in Fig. 2. fig..(1)He-Ne laser fig..(2)Few energy levels of He and Ne excited states

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Population Inversion: It is well-known that the process of spontaneous emission is independent of external radiations. Einstein proved theoretically that transition probability of absorption is equal to transition probability of induced emission between same two levels. If the number of atoms N₁ in lower state (energy E₁₎ is more than the number of atoms N₂ in the upper state (energy E₂) then in the presence of external radiations of frequency (E₂ – E₁)/h, the absorption dominates over emission. On the other hand, if N₁ is less than N₂ then the emission dominates. In general at room temperature N₁ is greater than N₂, so the absorption is more than emission. In some materials if the life time of any upper state (level) is of the order of 10–3 sec, called metastable state, then it is possible to have that material with N₂ > N₁. If this happens, then the population inversion takes place in the medium. These materials are called active materials and they can be used for lasing transition. Thus for laser action population inversion is necessary. Population of a particular energy level of atoms is given by Maxwell-Boltzmann distribution function as where N is the number of atoms in the state whose energy is E, T is the temperature of the material and k is the Boltzmann constant. Using this relation we get

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Introduction: There are many scientific, industrial, military, medical and commercial laser applications. The coherency, high monochromaticity, focussability, directionality and ability to reach extremely high powers are all properties which allow for these specialized applications.

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Principal components of a laser system: The principal components of a laser system are 1. Gain medium or optical medium which supports population inversion

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Major condition of laser action: The two conditions to achieve lasing actions are 1. Population inversion

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INTRODUCTION: LASER: No other scientific discovery of the 20th century has been demonstrated with so manyexciting applications as laser acronym for (Light Amplification by Stimulated Emission of Radiation). The basic concepts of laser were first given by an American scientist, Charles Hard Townes and two Soviet scientists, Alexander Mikhailovich Prokhorov and Nikolai Gennediyevich Basov who shared the coveted Nobel Prize (1964). However, TH Maiman of the Hughes Research Laboratory, California, was the first scientist who experimentally demonstrated laser by flashing light through a ruby crystal, in 1960. Laser is a powerful source of light having extraordinary properties which are not found in the normal light sources like tungsten lamps, mercury lamps, etc. The unique property of laser is that its light waves travel very long distances with e very little divergence. In case of a conventional e source of light, the light is emitted in a jumble of e separate waves that cancel each other at random (Fig. 1.1a) and hence can travel very short distances only. An analogy can be made with a situation where a large number of pebbles are thrown It into a pool at the same time. Each pebble generates a wave of its own. Since the pebbles are thrown at random, the waves generated by all the pebbles cancel each other and as a result they travel a very short distance only. On the other hand, if the pebbles are thrown into a pool one by one at the same place and also at constant intervals of time, the waves thus generated strengthen each other and travel long distances. In this case, the waves are said to travel coherently. In laser, the light waves are exactly in step with each other and thus have a fixed phase relationship . It is this coherency that makes all the difference to make the laser light so narrow, so powerful and so easy to focus on a given object. The light with such qualities is not found in nature.

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Substituting the value of N1/N2in Eqn. (1), we get eq..2 &eq.. 3 comparing eq..2 and 3 we get.

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SPONTANEOUS EMISSION: It is well known that there are various energy levels in an atom. Ground state of the atom is the minimum energy state and it is the most stable state. When the atom gets suitable thermal energy, its valence electron (say of energy E1) jumps to higher energy level (say to energy E2) called excited level. Electrons in this level are also called atoms in its excited state. Life time of electron in the excited state is very small, of the order of 10–8 sec, hence the electron within this time falls back to lower energy level E1 by emitting a radiation. This process is called spontaneous emission. The frequency, ν of the emitted radiation is given by where h is the Planck constant. We also say that in this transition a photon of energy hν is emitted. If there are large number of atoms in the upper energy level then the emitted radiations will have randomly different initial phases and directions and the emitted radiations will be incoherent.

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Numerical aperture: The numerical aperture (NA) is the sine of the vertex half-angle of the largest cone of rays that can enter or leave the core of an optical fibre, multiplied by the refractive index of the medium in which the vertex of the cone is located. All values are measured at 850 nm. The value of the numerical aperture is about 5% lower than the value of the maximum theoretical numerical aperture NA_tmax which is derived from a refractive index measurements trace of the core and cladding: in which n₁ is the maximum refractive index of the core and n₂ is the refractive index of the innermost homogeneous cladding. Macrobending loss: For single-mode fibres macrobending loss varies with wavelength, bend radius and number of turns about a mandrel with a specified radius. Therefore, the limit for the macrobending loss is specified in ITU-T Recommendations for defined wavelength(s), bend radius, and number of turns. The recommended number of turns corresponds to the approximate number of turns deployed in all splice cases of a typical repeater span. The recommended radius is equivalent to the minimum bend-radius widely accepted for long-term deployment of fibres in practical systems installations to avoid static-fatigue failure. For multimode fibres the launch condition is of paramount importance for macrobending loss, in particular the presence of higher order modes which are the most sensitive being stripped off due to bending. The mode distribution encountered at a specific macrobend may depend on how many macrobends precede it. For example, the first bend might influence the launch condition at the second bend, and the second bend might influence the launch condition at the third bend, etc. Consequently, the macrobending added loss at a given bend might be different than the macrobending added loss at another bend. In particular, the first bend may have the largest influence on following bends. Consequently, the macrobending added loss produced by multiple bends should not be expressed in the units of “dB/bend” by dividing the total added loss by the number of bends, but in dB for the specified number of bends. Fibre and protective materials: The substances of which the fibres are made should be known because care may be needed in fusion splicing fibres of different substances. However adequate splice loss and strength can be achieved when splicing different high-silica fibres. The physical and chemical properties of the material used for the fibre primary coating and the best way of removing it (if necessary for the splicing of the fibres) should be indicated. The primary coating is made by the layer(s) of protective coating material applied to the fibre cladding during or after the drawing process to preserve the integrity of the cladding surface and to give a minimum amount of required protection (e.g. a 250 μm protective coating). A secondary coating made by layer(s) of coating material can be applied over one or more primary coated fibres in order to give additional required protection or to arrange fibres together in a particular structure, e.g. a 900 μm “buffer” coating, “tight jacket”, or a ribbon coating (see Chapter 2).

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Fibre attributes: Fibre attributes are those characteristics that are retained throughout cabling and installation processes. The values specified for each type of fibre can be found in the appropriate ITU-T Recommendation for multimode fibre (Recommendation ITU-T G.651.1) or single-mode fibre Recommendations ITU-T G.652, …, G.657. Core characteristics: A value for the core diameter and for core non-circularity is specified for multimode fibres. The core centre is the centre of a circle which best fits the points at a constant level in the near-field intensity pattern emitted from the central region of the fibre, using wavelengths above and/or below the fibre’s cut-off wavelength. Usually the core centre represents a good approximation of the mode field centre. The cladding centre is the centre of a circle which best fits the cladding boundary. The core concentricity error is the distance between the core centre and the cladding centre. The tolerances on the physical dimensions of an optical fibre (core, mode field, cladding) are the primary contributors to splice loss and splice yield in the field. The maximum value for these tolerances (concentricity errors, non-circularities, etc.) specified in ITU-T Recommendations help to reduce systems costs and support a low maximum splice-loss requirement typically around 0.1 dB. Fibres with tightly controlled geometry tolerances will not only be easier and faster to splice, but will also reduce the need for testing in order to ensure high-quality splice performance. This is particularly true when fibres are spliced by passive, mechanical or fusion techniques for both single fibres and fibre ribbons

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Cables attributes:Attenuation: Cable attributes are those recommended for cables as they are delivered. Attenuation: The attenuation A(λ) at wavelength λ of a fibre between two cross-sections, 1 and 2, separated by distance L is defined, as:

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Introduction of Holography: Holography is a technique that allows the light scattered from an object to be recorded and later reconstructed so that it appears as if the object is in the same position relative to the recording medium as it was when recorded. The image changes as the position and orientation of the viewing system changes in exactly the same way as if the object was still present, thus making the recorded image (hologram) appear three dimensional. The technique of holography can also be used to optically store, retrieve, and process information. Holography is commonly used to display static 3-D pictures. Holography was invented in 1947 by Hungarian physicist Dennis Gabor for which he received the Nobel Prize in Physics in 1971.

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Applications: Some of the applications of holography are discussed in brief below. 1. Holographic interferometry: The most successful application of holography, however, is in interferometry. If two holograms of the same object are recorded on the same plate, then upon reconstruction the two holographic images will interfere. If the object has undergone a deformation between the two recordings, phase differences in certain parts of the two images will result, creating an interference pattern that clearly shows the deformation.

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Basic Concepts: holography: TYPES OF HOLOGRAMS: A hologram is a recording in a two- or three-dimensional medium of the interference pattern formed when a point source of light (the reference beam) of fixed wavelength encounters light of the same fixed wavelength arriving from an object (the object beam). When the hologram is illuminated by the reference beam alone, the diffraction pattern recreates the wave fronts of light from the original object. Thus, the viewer sees an image indistinguishable from the original object. There are many types of holograms, and there are varying ways of classifying them. For our purpose, we can divide them into two types: reflection holograms and transmission holograms. A. The reflection hologram The reflection hologram, in which a truly three-dimensional image is seen near its surface, is the most common type shown in galleries. The hologram is illuminated by a “spot” of white incandescent light, held at a specific angle and distance and located on the viewer’s side of the hologram. Thus, the image consists of light reflected by the hologram. Recently, these holograms have been made and displayed in color—their images optically indistinguishable from the original objects. If a mirror is the object, the holographic image of the mirror reflects white light; if a diamond is the object, the holographic image of the diamond is seen to “sparkle.” Although mass-produced holograms such as the eagle on the VISA card are viewed with reflected light, they are actually transmission holograms “mirrorized” with a layer of aluminum on the back. B. Transmission holograms The typical transmission hologram is viewed with laser light, usually of the same type used to make the recording. This light is directed from behind the hologram and the image is transmitted to the observer’s side. The virtual image can be very sharp and deep. For example, through a small hologram, a full-size room with people in it can be seen as if the hologram were a window. If this hologram is broken into small pieces (to be less wasteful, the hologram can be covered by a piece of paper with a hole in it), one can still see the entire scene through each piece. Depending on the location of the piece (hole), a different perspective is observed. Furthermore, if an undiverged laser beam is directed backward (relative to the direction of the reference beam) through the hologram, a real image can be projected onto a screen located at the original position of the object. C. Hybrid holograms Between the reflection and transmission types of holograms, many variations can be made. · Embossed holograms: To mass produce cheap holograms for security application such as the eagle on VISA cards, a two-dimensional interference pattern is pressed onto thin plastic foils. The original hologram is usually recorded on a photosensitive material called photoresist. When developed, the hologram consists of grooves on the surface. A layer of nickel is deposited on this hologram and then peeled off, resulting in a metallic “shim.” More secondary shims can be produced from the first one. The shim is placed on a roller. Under high temperature and pressure, the shim presses (embosses) the hologram onto a roll of composite material similar to Mylar. Integral holograms: A transmission or reflection hologram can be made from a series of photographs (usually transparencies) of an object—which can be a live person, an outdoor scene, a computer graphic, or an X-ray picture. Usually, the object is “scanned” by a camera, thus recording many discrete views. Each view is shown on an LCD screen illuminated with laser light and is used as the object beam to record a hologram on a narrow vertical strip of holographic plate (holoplate). The next view is similarly recorded on an adjacent strip, until all the views are recorded. When viewing the finished composite hologram, the left and right eyes see images from different narrow holograms; thus, a stereoscopic image is observed. Recently, video cameras have been used for the original recording, which allows images to be manipulated through the use of computer software. Holographic interferometry: Microscopic changes on an object can be quantitatively measured by making two exposures on a changing object. The two images interfere with each other and fringes can be seen on the object that reveal the vector displacement. In real-time holographic interferometry, the virtual image of the object is compared directly with the real object. Even invisible objects, such as heat or shock waves, can be rendered visible. There are countless engineering applications in this field of holometry. Multichannel holograms: With changes in the angle of the viewing light on the same hologram, completely different scenes can be observed. This concept has enormous\ potential for massive computer memories. Computer-generated holograms: The mathematics of holography is now well understood. Essentially, there are three basic elements in holography: the light source, the hologram, and the image. If any two of the elements are predetermined, the third can be computed. For example, if we know that we have a parallel beam of light of certain wavelength and we have a “double-slit” system (a simple “hologram”), we can calculate the diffraction pattern. Also, knowing the diffraction pattern and the details of the double-slit system, we can calculate the wavelength of the light. Therefore, we can dream up any pattern we want to see. After we decide what wavelength we will use for observation, the hologram can be designed by a computer. This computer-generated holography (CGH) has become a sub-branch that is growing rapidly. For example, CGH is used to make holographic optical elements (HOE) for scanning, splitting, focusing, and, in general, controlling laser light in many optical devices such as a common CD player.

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Signal Loss in Multimode and Single-Mode Fiber-Optic Cable: Multimode fiber is large enough in diameter to allow rays of light to reflect internally (bounce off the walls of the fiber). Interfaces with multimode optics typically use LEDs as light sources. However, LEDs are not coherent light sources. They spray varying wavelengths of light into the multimode fiber, which reflects the light at different angles. Light rays travel in jagged lines through a multimode fiber, causing signal dispersion. When light traveling in the fiber core radiates into the fiber cladding (layers of lower refractive index material in close contact with a core material of higher refractive index), higher-order mode loss (HOL) occurs. Together, these factors reduce the transmission distance of multimode fiber compared to that of single-mode fiber. Single-mode fiber is so small in diameter that rays of light reflect internally through one layer only. Interfaces with single-mode optics use lasers as light sources. Lasers generate a single wavelength of light, which travels in a straight line through the single-mode fiber. Compared to multimode fiber, single-mode fiber has a higher bandwidth and can carry signals for longer distances. It is consequently more expensive. For information about the maximum transmission distance and supported wavelength range for the types of single-mode and multimode fiber-optic cables that are connected to line cards on the EX 8200 series switches, see Optical Interface Support in EX 8200 series Switches. Exceeding the maximum transmission distances can result in significant signal loss, which causes unreliable transmission. Attenuation and Dispersion in Fiber-Optic Cable: An optical data link functions correctly provided that modulated light reaching the receiver has enough power to be demodulated correctly. Attenuation is the reduction in strength of the light signal during transmission. Passive media components such as cables, cable splices, and connectors cause attenuation. Although attenuation is significantly lower for optical fiber than for other media, it still occurs in both multimode and single-mode transmission. An efficient optical data link must transmit enough light to overcome attenuation. Dispersion is the spreading of the signal over time. The following two types of dispersion can affect signal transmission through an optical data link: ■ Chromatic dispersion, which is the spreading of the signal over time caused by the different speeds of light rays. ■ Modal dispersion, which is the spreading of the signal over time caused by the different propagation modes in the fiber. For multimode transmission, modal dispersion, rather than chromatic dispersion or attenuation, usually limits the maximum bit rate and link length. For single-mode transmission, modal dispersion is not a factor. However, at higher bit rates and over longer distances, chromatic dispersion limits the maximum link length. An efficient optical data link must have enough light to exceed the minimum power that the receiver requires to operate within its specifications. In addition, the total dispersion must be within the limits specified for the type of link in Telcordia Technologies document GR-253-CORE (Section 4.3) and International Telecommunications Union (ITU) document G.957. When chromatic dispersion is at the maximum allowed, its effect can be considered as a power penalty in the power budget. The optical power budget must allow for the sum of component attenuation, power penalties (including those from dispersion), and a safety margin for unexpected losses.

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Fibre design issues: its simplest form a step-index fibre consists of a cylindrical core surrounded by a cladding layer whose index is slightly lower than that of the core. Both core and cladding use silica as the basic material, the difference in the refractive indexes is realized by doping the core or the cladding or both. Dopants such as GeO2 and P2O5 increase the refractive index of silica and are suitable for the core. On the other hand, dopants such as B2O3 and fluorine decrease the refractive index of silica and are suitable for the cladding. The major design issues for the optical fibres are related to the refractive-index profile, to the amount of dopants, and the core and cladding dimensions. Figure 1 shows typical index profiles that have been used for different types of fibres. Figure 1 – Examples of index profiles of single-mode fibres

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Optical Fibres characterstics: Single-mode and multimode optical fibres: Multimode optical fibres are dielectric waveguides which can have many propagation modes. Light in these modes follows paths that can be represented by rays as shown in Figure 1-1a and 1-1b, where regions 1, 2 and 3 are the core, cladding and coating, respectively. The cladding glass has a refractive index, a parameter related to the dielectric constant, which is slightly lower than the refractive index of the core glass.

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Link attributes: A concatenated link usually includes a number of spliced factory lengths of optical fibre cable. The characteristics of factory lengths are given in § 6. The transmission parameters for concatenated links must take into account not only the performance of the individual cable lengths but also the statistics of concatenation. The transmission characteristics of the factory length optical fibre cables will have a certain probability distribution which often needs to be taken into account if the most economic designs for the link are to be obtained. Link attributes are affected by factors other than optical fibre cables, by such things as splices, connectors, and installation. Attenuation: Attenuation of a link: The attenuation A of a link is given by: A = α L α _{S x} α _{C y} where: α : typical attenuation coefficient of the fibre cables in a link α _S : mean splice loss x : number of splices in a link α _C : mean loss of line connectors y : number of line connectors in a link (if provided) L : link length. A suitable margin should be allocated for future modifications of cable configurations (additional splices, extra cable lengths, ageing effects, temperature variations, etc.). The above equation does not include the signal loss of equipment connectors. The attenuation budget used in designing an actual system should account also for the statistical variations in these parameters. The attenuation coefficient of an installed optical fibre cable is wavelength-dependent.

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The holographic recording and reconstruction process may be described in general mathematical terms as follows . The object and reference fields satisfy the Helmholtz equation The first term in this equation for Ê T is simply the transmitted wave altered by an attenuation factor . The second term is the original object wave multiplied by an amplitude factor ; this term represents the virtual holographic image of the object . The third term is the conjugate object wave . In of f-axis holography , the real image formed by this wave is weak , lies out of the field of view , and does not make a significant contribution to the imaging process . However , for Gabor’s original in-line holography , this term represented an objectionable twin image which overlapped and obstructed viewing of the desired image . An important contribution of the Leith and Upatnieks of f-axis reference scheme was the elimination of this twin image .

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Optical Fiber Communications: The optical fiber found its first large-scale application in telecommunications systems . Beginning with the first LED-based systems , the technology progressed rapidly to longer wavelengths and laser-based systems of repeater lengths over 30 km . 3 6 The first applications were primarily digital , since source nonlinearities precluded multichannel analog applications . Early links were designed for the 800- to 900-nm window of the optical fiber transmission spectrum , consistent with the emission wavelengths of the GaAs-AlGaAs materials system for semiconductor lasers and LEDs . The development of sources and detectors in the 1 . 3- to 1 . 55- m m wavelength range and the further improvement in optical fiber loss over those ranges has directed most applications to either the 1 . 3- m m window (for low dispersion) or the 1 . 55- m m window (for minimum loss) . The design of dispersion-shifted single-mode fiber along the availability of erbium-doped fiber amplifiers has solidified 1 . 55 m m as the wavelength of choice for high-speed communications . The largest currently emerging application for optical fibers is in the local area network (LAN) environment for computer data communications , and the local subscriber loop for telephone , video , and data services for homes and small businesses . Both of these applications place a premium on reliability , connectivity , and economy . While existing systems still use point-to-point optical links as building blocks , there is a considerable range of networking components on the market which allow splitting , tapping , and multiplexing of optical components without the need for optical detection and retransmission .

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Types of fibers:Multimode optical fibres: A 50/125 μm multimode graded index optical fibre cable: The characteristics of a multimode graded index optical fibre cable were specified in Recommendation ITU-T G.651, originally published in 1984 and deleted in 2008. Recommendation ITU-T G.651 covered the geometrical and transmissive properties of multimode fibres having a 50 μm nominal core diameter and a125 μm nominal cladding diameter. That Recommendation was developed during the infancy of optical fibre solutions for publicly switched networks. At that time (pre-1984), these multimode fibres were considered as the only practical solution for transmission distances in the tens of kilometres and bit rates of up to 40 Mbit/s. Single-mode fibres, which became available shortly after the publication of ITU-T G.651, have almost completely replaced multimode fibres in the publicly switched networks. Today, multimode fibres continue to be widely used in premises cabling applications such as Ethernet in lengths from 300 to 2 000 m, depending on bit rate. With a change in the applications, the multimode fibre definitions, requirements, and measurements evolved away from the original ITU-T G.651 and were moved to the modern ITU equivalent, Recommendation ITU-T G.651.1. Recommendation ITU-T G.651.1, Characteristics of a 50/125 μm multimode graded index optical fibre cable for the optical access network, provides specifications for a 50/125 μm multimode graded index optical fibre cable suitable to be used in the 850 nm region or in the 1 300 nm region or alternatively may be used in both wavelength regions simultaneously. This Recommendation contains the recommended values for both the fibre and cable attributes. The applications of this fibre are in specific environments of the optical access network. These environments are multi-tenant building sub-networks in which broadband services have to be delivered to individual apartments. This multimode fibre supports the cost-effective use of 1 Gbit/s Ethernet systems over link lengths up to 550 m, usually based upon the use of 850 nm transceivers. Quite a large percentage of all customers in the world are living in these buildings. Due to the high connection density and the short distribution cable lengths, cost-effective high capacity optical networks can be designed and installed by making use of 50/125 μm graded-index multimode fibres. The effective use of this network type has been shown by its extended and experienced use for datacom systems in enterprise buildings with system bit-rates ranging from 10 Mbit/s up to 10 Gbit/s. This use is supported by a large series of IEEE system standards and IEC fibre and cable standards, which are used as the main references in Recommendation ITU-T G.651.1.

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Holography Applications: Holography is a very useful tool in many areas, such as in commerce, scientific research, medicine, and industry. Some current applications that use holographic technology are: Future applications of holography include:

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Types of fibers:Single-mode optical fibres: The ITU-T first single-mode optical fibre and cable: The first single-mode optical fibre was specified in Recommendation ITU-T G.652, Characteristics of a single-mode optical fibre and cable, and for this reason, the ITU-T G.652 fibres are often called, “standard single-mode fibres”. These fibres were the first to be widely deployed in the public network and they represent a large majority of fibres that have been installed. The agreements that led to the first publication of Recommendation ITU-T G.652 formed a key foundation to the modern optical networks that are the basis of all modern telecommunications. Recommendation ITU-T G.652 describes the geometrical, mechanical, and transmission attributes of a single-mode optical fibre and cable which has zero-dispersion wavelength around 1 310 nm. This fibre was originally optimized for use in the 1 310 nm wavelength region, but can also be used in the 1 550 nm region. Recommendation ITU-T G.652 was first created in 1984; several revisions have been intended to maintain the continuing commercial success of this fibre in the evolving world of high-performance optical transmission systems. Over the years, parameters have been added to Recommendation ITU-T G.652 and the requirements have been made more stringent to meet the changes in market and technological demands, and in manufacturing capability. An example is the addition of a requirement for attenuation at 1 550 nm in 1988. In that year, the chromatic dispersion parameters and requirements were also defined. Some other examples include the addition of low water peak fibres (LWP) with negligible sensitivity to hydrogen exposure and the addition of requirements for PMD. However at the advent of these new capabilities and perceived needs, there was a consensus that some applications would need these attributes for advanced technologies, bit rates, and transmission distances; however, there were also applications that would not need these capabilities. Therefore, some options had to be maintained. For this reason, it was agreed to create different categories of ITU-T G.652 fibres. At the present time there are four categories, A, B, C, and D, which are distinguished on the PMDQ link design value specification and whether the fibre is LWP or not, i.e. water peak is specified (LWP) or it is not specified (WPNS), as shown in Table 1. Table 1 – ITU-T G.652 fibre categories