Courses

PH101 Physics - I

* Existing Credit: 2-1-0-6; Proposed Credit: 3-1-0-8

Orthogonal coordinate systems and frames of reference, conservative and non-conservative forces , work-energy theorem, potential energy and concept of equilibrium; Rotation about fixed axis, translational-rotational motion, vector nature of angular velocity, rigid body rotation and its applications, Euler's equations; Gyroscopic motion and its application; Accelerated frame of reference, centrifugal and Coriolis forces.

Harmonic oscillator, damped and forced oscillations, resonance, coupled oscillations, small oscillation, normal modes, longitudinal and transverse waves, wave equation, plane waves, phase velocity, superposition wave packets and group velocity, two and three dimensional waves.

Failure of classical concepts, Black body radiation, photo-electric effect, Compton effect, Davison and Germer's experiment, Frank-Hertz experiment, Bohr's theory, Sommerfeld's model, correspondence principle, Planck hypothesis, De Broglie's hypothesis, Hilbert space, observables, Dirac notation, principle of superposition, wave packets, phase and group velocities, probability & continuity equation, eigenvalues and eigenfunctions, orthonormality, expectation values, uncertainty principle, postulates of QM, Schrodinger equation & its applications to 1D potentials, field quantization, periodic potential wells: Kronig Penny model and origin of band gap.

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PH102 Physics - II

Vector Calculus: Gradient, Divergence and Curl. Line, Surface and Volume integrals. Gauss’s divergence theorem and Stokes’ theorem in Cartesian, Spherical polar and cylindrical polar coordinates. Dirac Delta function.

Electrodynamics: Coulomb’s law and Electrostatic field, Fields of continuous charge distributions. Gauss’s law and its applications. Electrostatic Potential. Work and Energy. Conductors, capacitors. Laplace’s equation. Method of images. Dielectrics. Polarization. Bound charges. Energy in dielectrics. Boundary conditions. Lorentz force. Biot-Savart and Ampere’s laws and their applications. Vector Potential. Force and torque on a magnetic dipole. Magnetic materials. Magnetization, Bound currents. Boundary conditions. Motional EMF, Ohm’s law. Faraday’s law. Lenz’s law. Self and Mutual inductance. Energy stored in magnetic field. Maxwell’s equations.

Optics: huygens’ principle. Young’s experiment. Superposition of waves. Concepts of coherence sources. Interference by division of wavefront. Fresnel’s biprism, Phase change on reflection. Lioyd’s mirror. Interference by division of amplitude. Parallel film. Film of varying thickness. Colours of thin films. Newton’s rings. The Michelson interferometer. Fraunhofer diffraction. Single slit, double slit and N-slit patterns. The diffraction grating.

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PH110 Physics Laboratory

Instructions to Students

Introduction to Error Analysis

Optics & Lasers

Review of basic optics: Polarization, Reflection and refraction of plane waves. Diffraction: diffraction by circular aperture, Gaussian beams.

Interference: two beam interference-Mach-Zehnder interferometer and multiple beam interference-Fabry-Perot interferometer. Monochromatic aberrations. Fourier optics, Holography. The Einstein coefficients, Spontaneous and stimulated emission, Optical amplification and population inversion. Laser rate equations, three level and four level systems; Optical Resonators: resonator stability; modes of a spherical mirror resonator, mode selection; Q-switching and mode locking in lasers. Properties of laser radiation and some laser systems: Ruby, He-Ne, CO2, Semiconductor lasers. Some important applications of lasers, Fiber optics communication, Lasers in Industry, Lasers in medicine, Lidar.

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Vacuum Science and Techniques

Fundamentals of vacuum, units of pressure measurements, Gas Laws (Boyles, Charles), load-lock chamber pressures, Partial and Vapor Pressures, Gas flow, Mean free path, Conductance, Gauges, Capacitance Manometer, Thermal Gauges, Thermocouple, Pirani Gauge, Penning Gauge, High Vacuum Gauges, Leak Detection, Helium Leak Detection, Cold Cathode Gauge, Roughing (Mechanical) Pumps, Pressure ranges, High Vacuum Pumps: Oil Diffusion Pump, Tolerable fore line pressure System configuration, Oils, Traps Crossover pressure calculations, Pump usage and procedures, Turbomolecular pump, Cryopumps, Pump usages, Out gassing and Leak Testing.

Introduction to Deposition, Anti Reflection (AR) Coatings, Mono-dimensionally modulated (MDM) Filters, Vacuum Coatings, High reflectors, e-Beam deposition systems, Film Stoichiometry, Sputtering, Itching and Lithography, Chemical Vapour deposition and Pulse Laser deposition, Mass Flow control, Reactive sputtering, Film growth control.

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Introduction to Nanomaterials

Introduction: Overview of Nanotechnology, Quantum effect, Naotechnology in nature. Properties: Physical, Chemical and biological properties of nanomaterials, Effects on structure, ionization potential, melting point, and heat capacity Electronic structure at nanoscale, Magnetism at Nanoscale. Metal and Semiconductor Nanoparticles: Surface Plasmon Resonance, Theory, Stability of metal particles, metamaterials, Nanowires and Nanotubes.

Metal and Semiconductor Nanoparticles: Surface Plasmon Resonance, Theory, Stability of metal particles, metamaterials, Nanowires and Nanotubes.

Synthesis of Nanomaterials: Chemical, Physical, Biological and hybrid Methods of synthesis, Assembly. Carbon Nanotubes, Lithographic methods, Scanning Probe Microscopic Methods, Physical and Chemical Vapor Deposition Methods. MEMS fabrication technique.

Nanotribology and Nanomechanics: Micro/Nanotribology and Materials Characterization Studies using Scanning Probe Microscopy, Surface Forces and Nanorheology of Molecularly Thin Films, Scanning Probe Studies of Nanoscale Adhesion Between Solids in the Presence of Liquids and Monolayer Films, Friction and Wear on the Atomic Scale, Nanoscale Mechanical Properties, Nanomechanical Properties of Solid Surfaces and Thin Films, Mechanics of Biological Nanotechnology, Mechanical Properties of Nanostructures, Micro/Nanotribology of MEMS/NEMS Materials and Devices. Applications of Nanomaterials: Materials, Sensors and Actuators, Catalysis Medical Applications, Advanced Electronic Materials and Novel Devices. MEMS/NEMS Devices and Applications, Current Challenges and Future Trends.

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Solid State Devices

Semiconductor Devices: Basic introduction, principles of device fabrication and operation–heterojunction bipolar transistors (HBTs), heterostructure field effect transistors (HFETs),modulation doped field effect transistors (MODFETs), high electron mobility transistors (HEMTs), resonant tunneling diodes (RTDs), single electron transistors (SETs), negative conductance in semiconductors, transit time devices, IMPATT, TRAPATT, THz devices, micro and mm wave devices.

Optical Devices: Optical absorption in a semiconductor, photoconductors, photovoltaic effect, semiconductor lasers, quantum well lasers, longwavelength detectors, Optical waveguides, waveguide fabrication techniques, losses in optical waveguides, Optical sensors, integrated optical devices.

Ferroic Phenomena & Devices: Electrical & optical properties of linear and non-linear dielectrics, Ferroelectrics, Pyroelectric, Piezoelectric and electro-optic devices, non-volatile memory; Magnetic memory and superconducting devices, shape memory effect, Spintronic devices.

Energy Storage/Conversion Devices: Portable power sources, Solar cell, Fuel cells, Secondary batteries, Supercapacitors. Sensors & Actuators: Elementary concepts of sensors, actuators and transducers, an introduction to Microsensors and MEMS, Evolution of Microsensors & MEMS, Microsensors & MEMS applications, Biosensors.

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Photovoltaic’s & Fuel Cell Technology

Photovoltaics: Global energy scenario and impending energy crisis, Basic introduction of energy storage/conversion devices, State-of-the art status of portable power sources, Solar/photovoltaic (PV) cells, PV energy generation and consumption, fundamentals of solar cell materials, Elementary concept of solar cell and its design, solar cell technologies (Si-wafer based, Thin film and concentrator solar cells), Emerging solar cell technologies (GaAs solar cell, dye-sensitized solar cell, organic solar cell, Thermo-photovoltaics), Photovoltaic system design and applications, Analysis of the cost performance ratio for the photovoltaic energy and problems in wide-spread commercialization of the technology.

Fuel Cells: Fuel cells and its classification; Transport mechanism in fuel cells and concept of energy conversion; Fuels and fuel processing, Fuel cell design and its characterization; Technological issues in Solid oxide fuel cells (SOFC); PEM fuel cells; Direct methanol fuel cells (DMFC), Molten carbonate fuel cell (MCFC), Power conditioning and control of fuel cell systems.

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M.Tech Courses

Core Courses

PROPOSED CONTENTS

Nanomaterials in daily life with examples (GMR read heads, NEMS goniometers, health care, energy materials, etc); Foundations of Quantum and Statistical Mechanics for nanomaterials, idea of tunneling, bound state and scattering, notion of quasiparticles, Light matter interaction; DOS, Bose-Einstein and Fermi-Dirac Statistics; Properties of individual nanostructures; Bulk nanostructured materials; Selection rules and spectroscopic techniques; Size and dimensionality effects; Quantum confinement; Properties dependent on density of states; Single electron tunneling; current-induced forces, current-induced heating and electromigration in nanowires; nanotribology; carbon based nanomaterials; biological materials and biomimetic strategies for nanosynthesis; magnetic nanomaterials; nanodevices and nanomachines.

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PROPOSED CONTENTS

Ellipsometer; Surface profile analysis; Scanning Probe Microscope (AFM and STM); Auger Electron Spectroscopy; Scanning Electron Microscopy; Transmission Electron Microscopy; Energy Disperssive Spectrum; Confocal Microscope; Kerr Microscope; Ferromagnetic Resonance Microscope, X-ray Diffraction; Small Angle X-ray Scattering; High Power X-ray (Syncrotron) Diffraction; Neutron Diffraction, Microprobe station, Impendance measurement, Electrical transport measurement (ac and DC conductivity, TEP measurement), Magnetic transport properties characterization, Vibrating Sample Magnetometer, SQUID, Electron Spin Resonance, UV-VIS Spectrophotometer; FT-IR Spectrophotometer; Micro-raman Spectrometer; Thermal Gravimetric Analysis (TGA); Differential thermal analysis (DTA); Differential scanning calorimetry (DSC); BET surface area analyzer; Dynamic Light Scattering; Differential Mechanical Analysis (DMA); Universal testing machine (UTM).

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Pre Mid-Semester

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Post Mid-Semester

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Chemical Routes for Synthesis of Nanomaterials: Chemical precipitation and co-precipitation; Sol-gel synthesis; Microemulsions or reverse micelles; Solvothermal synthesis; Thermolysis routes, Microwave heating synthesis; Sonochemical synthesis; Photochemical synthesis; Synthesis in supercritical fluids.

Metal Nanoparticles: Size and shape control of metal Nanoparticles and their characterization; Study of their properties: Optical, electronic, magnetic; Surface plasmon band and its application; Role in catalysis, Alloy Nanoparticles,

Semiconductor Nanoparticles: Size and shape control of semiconductor Nanoparticles and their characterization; Study of their properties: optical and electronic and its application; Synthesis and application of Core-Shell structured semicoductor nanoparticles (Type I and Type II).

Organic nanoparticles: Size and shape control of nanoparticles and their characterization; inorganic-organic hybrid nanoparticles; Nanopolymers: Preparation and characterization of diblock Copolymer based nanocomposites; Applications of Nanopolymers in Catalysis.

Top-down techniques: photolithography, other optical lithography (EUV, X-Ray, LIL), particle-beam lithographies (e-beam, FIB, shadow mask evaporation), scanning probe lithographies.

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Challenges in Nanoscience & Nanotechnology, Quantum mechanical, Physical and Biological aspects of Nanoscience & Technology, Nanodefects, Nanolayers and Nanostructuring, Growth and Fabrication of Nanostructures, Electron transport in nanostructures, Nanostructured electronic devices, Nano tunneling devices, Self organization phenomena at nanocrystal surfaces, Engineering of complex nanostructures, Quantum dot nanostructures for single electron devices, Carbon nanotubes and carbon electronics, Quantum electronic devices (QEDs), Organic electronics, Complex integrated systems and information processing at nanoscale, Limits of integrated systems and nanodevices, Concept of heterostructure devices (e.g.; oxide heterostructures, photovoltaics, sensors, actuators, quantum dot heterostructure lasers etc.), Nano-MEMS, Introduction to quantum computation and soft computing.

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Pre Mid-Semester

Post Mid-Semester

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Introduction to thin films, Technology as a drive and vice versa; Structure, defects, thermodynamics of materials, mechanical kinetics and nucleation; grain growth and thin film morphology; Basics of Vacuum Science and Technology, Kinetic theory of gases; gas transport and pumping; vacuum pumps and systems; vacuum gauges; oil free pumping; aspects of chamber design from thin film growth perspectives; various Thin film growth techniques with examples and limitations; Spin and dip coating; Langmuir Blodgett technique; Metal organic chemical vapor deposition; Electron Beam Deposition; Pulsed Laser deposition; DC, RF and Reactive Sputtering; Molecular beam epitaxy; Characterization of Thin films and surfaces; Thin Film processing from Devices and other applications perspective

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Solar radiations as a source of energy and mechanism for its entrapment; Measurements and limits of solar energy entrapment; Flat plate collectors and solar concentrators; Solar energy for industrial process heat (IHP) and design of solar green house; Solar refrigeration and conditioning; Solar thermo-mechanical power.

Introduction of energy storage/conversion devices, State-of-the art status of portable power sources, Solar/photovoltaic (PV) cells as a source of green energy; Fundamentals, Materials, Design and Implementation aspects of PV energy generation and consumption; Solar cell technologies (Si-wafer based, Thin film, GaAs based, dye-sensitized, PESC and organic solar cells), Efficiency of solar cells and PV array analysis, Photovoltaic system design (stand alone and grid connected) and applications; Balance of system (BOS) with emphasis on role of storage batteries; Cost analysis, Case study for performance evaluation and problem identification in wide-spread commercialization of the technology.

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Programming fundamentals, Flow Chart, plotting, fitting data, building new functions, and making iterations and loops.

Application on elementary numerical methods (e.g., Taylor-series summations, roots of equations, roots of polynomials, systems of linear and nonlinear algebraic equations, integration). Applications in nanotechnology engineering.

Ordinary differential equations with constant coefficients. Boundary value problems and applications to quantum mechanics. Numerical solution of ordinary differential equations. Numerical solution of partial differential equations.

Finite Difference Time-Domain Method: Optical Responses, advantage & disadvantage, Practical implementation, Numerical examples.

Finite element method: Introduction, Matrix form of the problem, Various types of finite element methods, Approximation of elliptic problems, Piecewise polynomial approach, One dimensional model problem.

Numerical schemes for nonlinear systems. Basic modelling and simulation. Relevant applications: optical, thermal, mechanical, and fluidic, and nanoscale devices.

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PROPOSED CONTENTS

Module 1: Generic Methodologies for Nanobiotechnology Introduction to Nanobiotechnology; challenges and opportunities associated with biology on the Nanoscale; nanobiotechnology systems; introduction to bioelectronics; Biologically relevant molecular nanostructures-Carbon nanotubes, quantum dots, metal based nanostructures, naowires, polymer based nanostructures, protein and DNA based nanostructures; Characterisation techniques for biological molecular nanostructures.

Module 2: Biosensors Introduction to biosensors; the biological component; the sensor surface; Immobilisation of the sensor molecule; Transduction of the sensor signal -Optical sensors; Electrochemical sensors; Suppression or substraction of non-specific background interaction at sensor surfaces; Sensor stabilisation; Data analysis.

Module 3: Imaging of Bionanostructures Practical and theoretical aspects of imaging biological systems, from the cellular level through to whole-body medical imaging, basic physical concepts in imaging. Major techniques using ionising and non-ionising radiation including fluorescence and multi-photon microscopy, spectroscopy, OCT, MRI, X-ray CT, PET, Confocal and SPECT imaging.

Module 4: Bionanomaterials Biomolecules for designing nano-structures; nanoprinting of DNA, RNA and Proteins, use of these nano-structures in biological and medical applications. Principles of self-assembly, self-organisation and its application to biology. DNA nanostructures, DNA robot, DNA microarrays, Bio-MEMS: biological and biomedical analysis and measurements and micro total analysis systems.

Module 5: Toxicological and Medical Applications of Nanobiotechnology Environmental behaviour and speciation of nanoparticles; Introduction to Nanomaterials for toxicology; bioaccumulation of Nanomaterials, Nanoparticles cytotoxiciy, Applications of Nanostructures in Drug discovery, Delivery, and Controlled Release.

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Introduction to core concepts of supramolecular chemistry: definitions, Cooperativity and Preorganization, Supramolecular interactions (including those in Chemomechanical Polymers)

Self-Assembly of nanoscalar supramolecular entities: definition, thermodynamics, types; self-assembly in biological systems; self-assembly in synthetic systems involving coordination and hydrogen bonding interactions; self-assembly of nanoscalar capsules and their applications.

Supramolecular chemistry in solid state: Zeolites, clathrates, crystal engineering and solid state reactivity, coordination polymers: applications as microreactors and energy storage materials.

Supramolecular semiochemistry, colorimetric sensors and the indicator displacement assay, photophysical sensing and imaging, electrochemical sensors.

Molecular nanomachines: based on cyclodextrin, based on metal ion translocation molecular gyroscopes, shuttles and muscles based on transition metals, Nanocar.

Nanochemistry: Definition and description of transition metal nanoparticles and their application in catalysis.

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PROPOSED CONTENTS Nanotechnology for Disease Diagnostics: Quantum dot conjugation strategies with DNA-aptamer, Protein and Antibody and FRET/BRET based assays for Cancer, AIDS, tuberculosis and other disease diagnostics; Nanoparticle assisted multiplexed diagnostic assays (Bio-barcode amplification assay, Sandwich DNA assay, Eliza) and point-of care diagnostics (Lateral flow assay).

Nanotechnology for Drug delivery:Lipid, polymeric, Hyaluronic acid and heparin functionalized core shell nanoparticle as drug delivery vehicles; Carbon nanotube-based vectors for delivering immunotherapeutics and drugs, Hydrogels for drug delivery, nanoparticle induced Gene delivery for gene therapy.

Nanotechnology for therapy: Nanodrugs for treatment of cancer (abraxane and other drugs); concept of nanodrug-encapsulation, self assembly, controlled release (targeted and triggered release), nanoparticle recovery; modified Ag-nanoparticle for Photodynamic Therapy of cancer; nanoparticle assisted vaccine development; nanoshells for surgical procedures.

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Nanoelectronics: Why? Device scaling, Moore’s law, limitations, role of quantum mechanics, Feynmans nanobot; Nanostructures: Impact, technology and physical consideration; Mesoscopic observables: Ballistic transport, phase interference, universal conductance fluctuations, weak localization; Carrier heating; Novel molecules (Pentacene, carbon nanotube, Fullerenes and its derivatives etc.) and conjugated polymers (Polyacetylene, P3HT, PEDOT:PSS etc.); Preliminaries : Basic Quantum mechanics and Fermi statistics, Metals, Insulators and Semiconductor, Density of states (DOS) in 0D-3D, DOS in disordered materials, Physics of organic semiconductors: concept of HOMO and LUMO, band gap etc. ;Two terminal quantum dot and quantum wire devices: Equilibrium in two terminal devices, Current flow in the presence of a bias, numerical technique for self-consistent estimation of V-I ,Current flow, quantum of conductance, Landauer theory; Field Effect Transistors (FETs): Ballistic quantum wire FETs, conventional MOSFETs, CMOS, short channel and narrow width, hot electron effect, punch-through and thin gate oxide breakdown, OFET.

Spintronics: Spin, propagation, detection, spinFETs; Fluxtronics: Fluxon, ratchet effect, rectification, flux-QUBIT; Nano-fabrication techniques: Top-down and bottom-up strategies, advantages/disadvantages/ limitations, e-beam lithography, Focussed Ion beam milling, self-organized structures, laser nano-patterning, nano-imprint, electrochemical synthesis, Fabrication of OEDs etc.; Special topics: Graphene, return to Feynmann’s nanobot, future prospects .

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Introduction, solid state ionics vis-à-vis solid state electronics, Principles of ionic conduction in ordered and disordered nanostructures; Superionic materials classification – Crystalline anionic and cationic conductors, mixed ionic and electronic conductors, structural factors responsible for high ionic conductivity; Brief review on physical techniques for analysis of ion conducting solids; Transport properties and Ion dynamics; Ion transport in homogeneous and heterogeneous medium – Ion conducting glasses, ceramics, polymers and composites; Ion Transport Models - Phenomenological models, Free volume theory, Configurational entropy model, Jump relaxation and Ion hopping model, Bond percolation model and Effective medium theory; Concepts and feasibility of ion conducting polymer nanocomposites and nanocrystalline ceramics.

Material problems and processing techniques; Technological applications of ion conducting solids; Design, Fabrication and Evaluation of Solid State Lithium Batteries, Supercapacitors (EDLC and Redox), Fuel Cells (PEM Fuel cell, SOFC), Gas sensors and display devices. Thermodynamics and mass transport in solid sate batteries. Battery performance and electrode kinetics. Double layer and other polarization effects at solid /solid interface; Fuel Cells as micro-power houses, Power conditioning and control of fuel cell systems.

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Why magnetism at nanoscale ? experimental methods; Magnetic anisotropy at nanoscale; Magnetostriction and the effect of stress; Domains and magnetization process; Fine particle and thin films; soft magnetic materials and hard magnetic materials, One-dimensional Heisenberg model; Two-dimensional XY model; Three-dimensional Heisenberg ferromagnet; Three-dimensional antiferromagnet; Magnetism of the electron gas; Stoner model; Spin excitations in Stoner model; RKKY interaction; Field models of magnetization; Exchange model in two dimensions; Magnetic domains and domain walls; Random anisotropy model of amorphous magnet; Landau-Lifshitz equation; Spin waves; Magnetic resonance; Angular momentum and spin; Magnetism of atoms; Exchange interaction and magnetic anisotropy; Superparamagnetism; Quantum mechanics of a large spin; Quantum magnetization curve; Josephson effect; Spin-lattice relaxation of rigid atomic clusters; Spin transport at nanoscale; Magnetic materials in applications; Magnetoresistive Sensors Based on Magnetic Tunneling Junctions; Magnetoresistive Random Access Memory (MRAM); Emerging Spintronic Memories; GMR Spin-Valve Biosensors; Semiconductor Spin-Lasers; Spin Logic Devices and magnetic drug delivery; Magnetic materials in memory device.

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Introductory remarks on classical concepts of electrostatics and Maxwell e.m. field equations; Concept of dielectric constant for nanostructures; Quantum approach for carriers in dielectrics; Electric polarization and relaxation – frequency and temperature dependence; Optical properties and radiative process in dielectric heterostructures & nanostructures; Photoemission, Luminescence, Photoconduction, Quantum yield and quantum efficiency; Transport in nanostructure networks (e.g.; tunneling, hopping, coulomb blockade etc.), Transitions between electrical conductivity, Transient phenomena, Charge carrier injection from electrical contacts; Role of defects and impurities in transport properties; Dielectric properties of metals, semiconductors and insulators (with examples of polymer, ceramics and composites).

Spontaneous polarization and origin of Ferroelectricity; Phenomenology of Ferro, Antiferro, Pyro and Piezoelectric effects; Ferroelectric memory and its application for high density data storage; Charging of a dielectric nanostructure and mechanism of charge storage in it; Electrets and their applications; Ferroelectric-insulator-semiconductor junctions.

Non-radiative and relaxation processes – multi-phonon capture at point defects, hot carrier relaxation; Electro-optic processes – Electro-optic, Photo-refractive and Magneto-optic effects; Elementary idea of Magneto-dielectric effect and Multiferroicity, Magnetoelectricity and Magnetoelectric coupling; Applications of multiferroicity and magnetoelectricity; Dielectric breakdown phenomena.

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Mathematical Physics

Theory of Complex analysis, Complex integrals & applications: Geometrical representations of w = f(z): Conformal Transformations; Schwarz– Christoffel Transformation; Solutions to Dirichlet and Newmann problems; Applications to fluid flow, electrostatics and heat flow; Integral Transforms of derivatives, Convolution; Partial Differential Equations; Special Functions: Neumann and Hankel functions, Spherical Bessel functions, Hermite, Laguerre, Hypergeometric and Confluent hypergeometric functions, Chebyshev polynomials; Integral Equations: Generating functions, Newmann series, Separable degenerate Kernels, Hilbert-Schmidt Theory; Sturm – Liouville Theorem – Orthogonal functions: Self adjoint DE, Hermitian operators, Gram – Schmidt Orthogonalization, Completeness of Eigenfunctions, Green’s function – Eigen function Expansion; Group Theory: Definition, Subgroups and Classes, Group representations, Characters, Physical applications, Infinite groups, Irreducible representations of SU(2), SU(3) and O(3)

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Classical Mechanics

Review of Lagrangian and Hamiltonian formalisms in various systems, Legendre transforms, Principle of least action, Hamilton’s canonical equations and their applications; Isometries, Noether theorem and conservation laws; Lagrangian and Hamiltonian for relativistic particle; Canonical transformations, Infinitesimal Canonical transformation, Integral invariant of Poincare; Lagrange and Poisson brackets and their applications; Liouville’s theorem; Hamilton-Jacobi equation, Action and angle variable and their applications; Harmonic oscillator and Central Force problems including discussion of Normal modes and Scattering; Rigid body motion, Euler’s equations and applications; State space, limit cycles and their stability, linearization near fixed points, bifurcation and routes to chaos

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Quantum Mechanics-I

Review of Basic Concepts: Experimental Background; Wave packet & its spreading; Coordinate and Momentum representations; Simultaneous eigenfunctions; Complete set of eigenfunctions; One-dimensional problems: Square well problem; Delta-function potential; Double-well; Application to molecular inversion; Kronig-Penney model.

Hermitian & Unitary matrices, Linear vector spaces, Bra and ket vectors. Completeness, orthonormality, basis sets, change of basis; Generalized uncertainty relation; One dimensional harmonic oscillator by operator method, Time evolution operator, Schrödinger, Heisenberg and interaction pictures. Stern-Gerlach experiment, spin-1/2 system.

Three dimensional problems in Cartesian and spherical polar coordinates, spherical harmonics, 2-d & 3-d well, 3-d harmonic oscillator, degeneracy, Hydrogen atom.

Angular momentum algebra; Raising and lowering operators; Matrix representation of Angular momentum, spin-1/2 and finite rotations; Pauli matrices; Addition of angular momenta, Clebsch-Gordan coefficients.

Time independent perturbation theory, First and second order corrections to the energy eigenvalues; First order correction to the eigenvector; Degenerate perturbation theory; Application to one-electron system; Spin-orbit coupling (L-S and j-j), Zeeman effect and Stark effect; Helium atom.

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Numerical Techniques

Algorithm, flowchart, structure of C program, Keywords, Identifiers, Basic data types and sizes, Constants, Variables, Operators, Loops, Arrays- concepts, declaration, definition, accessing elements, and functions, two-dimensional and multi-dimensional arrays, applications of arrays, Functions, pointers

Solution of linear algebraic equation: Gauss-Jordan elimination, LU and Cholesky decomposition; Interpolation and extrapolation: Polynomial, Rational functions, Application in two or more dimension; Numerical integration: Romberg, Gaussian Quadration and Orthogonal polynomials; Numerical differentiation of functions; Root finding and nonlinear sets of equations: Bisection, Secant, Regula-falsi method, Newton Raphson method, Roots of polynomial, Globally convergent method for nonlinear systems of equations; Minimization or maximization: Golden section search, Parabolic and Brent's method, Downhill simplex, Conjugate gradient method; Eigensystems: Jacobi transformation, Eigenvalue and eigenvector, Hermitian, Reduction to Hessenberg form; FFT in two or more dimensions; Least square method and non-linear models; Integration of ODE: Runge-Kutta and Predictor-Corrector method; Two point boundary value problems; Integral equation: Linear Regularization and Backus-Gilbert method; PDE: Flux-conservative method for initial value problem, Relaxation-method for boundary value problem

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Electronics

Recap of Thevenin and Norton theorems; Ohmic and rectifying contacts, p-n junctions, Applications including Varactors, Zener diode, Schottky diode, switching diodes, Tunnel diode, Light emitting diodes, Semiconductor laser, Photodiodes, Solar cell, UJT, Gunn diode, IMPATT devices; Bipolar junction transistors, Operating point, Biasing, AC models, h-parameter analysis; Voltage amplifiers; Darlington pair; Field effect transistor action, JFET, Biasing in ohmic and active regions, MOSFETS; Thyristors and SCR crowbar;

Differential Amplifier, Instrumentation and operational amplifiers; Op-Amp Circuits: Characteristics of ideal and practical op-amp; inverting, noninverting and differential amplifier, Basic characteristics with detailed internal circuit of IC Op-Amp; Active filters; Nonlinear amplifiers using Op-Amps-log amplifier, anti-log amplifier, regenerative comparators; ADC and DAC circuits; Op-amp based self oscillator circuits- RC phase shift, Wien bridge, non-sinusoidal oscillators;

Regulated power supplies, shunt and series regulators; Monolithic linear regulators;

Logic functions and Digital circuits; Karnaugh maps; SOP and POS design of logic circuits; MUX as universal building block; RCA, CLA and BCD adder circuits; ADD-SHIFT and array multiplier circuits; RS, JK and MS-JK flip-flops; registers and counters

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Electronics Laboratory

Introduction to passive and active electronic components and use of instruments including Oscilloscope, Digital storage oscilloscope, Multimeters, Wave-form generators; Use of printed circuit boards, soldering and breadboards;

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Quantum Mechanics-II

WKB Approximation, Bohr-Sommerfeld quantization condition; Time dependent perturbation theory, interaction picture; Constant and harmonic perturbations Fermi's Golden rule;

Scattering theory: Laboratory and centre of mass frames, differential and total scattering cross-sections, scattering amplitude; Born approximation, Greens functions, scattering for different kinds of potentials; Partial wave analysis;

Special topics in radiation theory: semi-classical treatment of interaction of radiation with matter, Einstein's coefficients, spontaneous and stimulated emission and absorption, application to lasers;

Symmetries in quantum mechanics: Conservation laws and degeneracy associated with symmetries; Continuous symmetries, space and time translations, rotations; Rotation group, Wigner-Eckart theorem; Discrete symmetries; parity and time reversal.

Relativistic quantum mechanics, Klein-Gordon equation, Interpretation of negative energy states and concept of antiparticles; Dirac equation, covariant form, adjoint equation; Plane wave solution and momentum space, spinors; Spin and magnetic moment of the electron.

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Applied Optics

Review on Canonical and Grand Canonical Ensemble: Ideal Gases, Equation of state for ideal quantum gas, Einstein’s derivation of Planck’s Law: Maser and Laser ; Partition function Z: Translational, Rotational and Vibrational; Application of Z: Vapour pressure, Real gas and van der Waal gas; Ideal Bose-Einstein (BE) gas: BE distribution and condensation, Thermodynamic properties, Phase space distribution function and Liouville theorem, Ergodicity and H-theorem; Liquid He, Two fluid model of liquid He II, Superfluid phases of 3He; Ideal Fermi-Dirac (FD) gas: FD distribution and degeneracy, Equation of state of FD gas, Landau Diamagnetism, De-Haas van Alfen Effect, Quantized Hall effect, Pauli Paramagnetism, Magnetic properties of imperfect gas, Thermionic emission; Transport theory: Transport processes and distribution functions, Boltzmann equation in absence of collision, Calculation of electrical conductivity (s) and coefficient of viscosity (h), Boltzmann Differential Transport (BTE) equation, Scattering cross-section and symmetry properties, Reformulation of BTE, Approximation methods for solving BTE, Evaluation of s and h.

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Electrodynamics

ectrodynamics:equations, pointing macroscopic electromagnetism, conservation laws, plane electromagnetic waves and propagation in non conducting medium and insulator, magneto hydrodynamic waves, wave guides, resonant cavities and optical fibers, Radiation systems, multiple fields and radiation scattering and diffraction dynamics of relativistic particles and electromagnetic fields, radiation by moving charge, Bremstrahlung , method of virtual quanta, radiation damping.

Basics in Quantum electrodynamics:agnetic field in quantum theory, wave equation for particles with spin zero, helicity states of a particle, wave equation for particles with spin ½, four dimensional spinors, Dirac equation in the spinor representation, Dirac equation for an electron in an external filed.

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Computational Physics

Recapitulation of numerical techniques and errors of computation (rounding, truncation);

Classical molecular dynamics simulations, Verlet algorithm, predictor corrector method, Continuous systems, hydrodynamic equations, particle in a cell and lattice Boltzmann methods; Schrodinger equation in a basis: numerical implementation of Numerov method, matrix methods and variational techniques; applications of basis functions for atomic, molecular, solid-state and nuclear calculations; Elements of Density functional theories; Monte Carlo simulations, Metropolis, critical slowing down and block algorithms with applications to classical and quantum lattice models; Tractable and intractable problems; P, NP and NP complete problems with examples; Shor and Grover algorithms; Quantum parallelism;

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General Physics Laboratory

Atomic and Molecular Physics

One electron atoms , Schrodinger equation for one-electron atoms, Interaction of one electron atoms with electromagnetic radiation, Transition rates, The dipole approximation, The Einstein coefficients, Selection rules, Spectrum of one electron atoms, Line intensities and the life time of the excited states, Line shapes and widths, Fine structure and Hyperfine structure, The Lamb Shift, Zeeman and Stark effect, Many electron systems: central field approximation, Thomas Fermi model, Hartree- Fock method and the SCF, L-S coupling and j-j coupling, Introduction to the Density functional theory, Interaction of many electron atoms with electromagnetic radiation, Molecular structure, Born -Oppenheimer approximation, The rotation and vibration of diatomic molecules, Electronic structure of diatomic molecule, Rotational and Vibrational Spectra of diatomic molecules, Electronic spectra of diatomic molecules, The Franck-Condon principle.

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Solid State Physics

physics: operations; Bravais lattices; Point and space groups; Miller indices and reciprocal lattice; Structure determination; diffraction; X-ray, electron and neutron; Crystal binding; Defects in crystals; Point and line defects.

Lattice vibration and thermal properties: Einstein and Debye models; continuous solid; linear lattice; acoustic and optical modes; dispersion relation; attenuation; density of states; phonons and quantization; Brillouin zones; thermal conductivity of metals and insulators

Eletronic&properties:ctron theory of metals; electrons in a periodic potential; Bloch equation; Kronig-Penny model; band theory; Semiconductor physics; Quantum Hall effect. Dielectric Response. Magnetic properties

Superconductivity:General properties of superconductors, Meissner effect; London equations; coherence length; type-I and type-II superconductors.

Noncrystalline Solids: Glasses, Amorphous ferromagnets, Amorphous Semiconductors.

Quasicrystals: Stable quasicrystal, metastable quasicrystal.

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Particle Physics

Review on relativistic quantum mechanics, Conservation laws, Parity charge conjugation and time reversal, CPT-theorem, Permutation Symmetry, Isospin, G-parity, Strange particles, Unitary symmetry in 2-dimensions, Lie algebra of SU(2), SU(2) Representations, Unitary symmetry in 3-dimensions, Lie Algebra for U(n), SU(n), Representations of SU(3), Quark model of Hadrons SU(6), Applications of Quark model, Structure of Hadrons, The Quark Parton Model, The weak interactions, Current from weak interactions, nonleptonic weak interaction, CP-Violation, CP-Violation in K-decays, Gauge invariance, The standard model, Charm and heavier flavours, Introduction to Grand Unified Theories, Beyond GUT model, Basics of supersymmetry.

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Measurement Techniques

Basics of measurement: uncertainty in measurements, Comparison of measured & accepted values and Two measured values, Checking relationships with a graph, Fractional uncertainties, multiplying two measured numbers, Propagation of uncertainties;

Low level DC measurement of voltage, current and resistance, C-V and Impedance spectroscopy; Deep Level Transient Spectroscopy, Hall effect and Time of Flight methods for charge carriers; Magnetic Response using SQUID magnetometer and VSM;

UV-VIS-NIR spectro-photometer & Ellipsometry, FTIR, Raman spectroscopy; Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), Scanning Tunneling Microscopy (STM), Atomic Force Microscopy (AFM); X-ray diffraction (XRD) and grazing angle XRD;

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Elective I

Project I

Elective II

Elective III

Elective IV

Project II

Nanoscience

Background to Nanoscience, length scales and size effects in smaller systems-pre quantum, review of quantum and statistical mechanics, quantum wells, quantum wires and quantum dots, band structure and density of states, inter band transitions; Electrical transport in nanostructures – Quantum confinement, Coulomb blockade and Conductance quantization, conduction mechanisms – Thermionic effect, Schottky and Poole-Frenkel effect, Arrhenius type thermally activated conduction, variable range hopping conduction and Polaron conduction; Synthesis -Top –down and bottom-up approach, characterization of nanostructures; Semiconductor quantum dots, self assembled monolayers, Metal nanoparticles, core-shell nanoparticles, nano-shells, new nanostructures -carbon (fullerenes, CNTs, graphene, nanodiamond), BN nanotubes; Nanotribology and Nanorheology, stiction, van der Waal’s and Casimir forces; Applications in Nanobiology, Nano sensors, Nanoelectronics, Nanomedicines, Molecular nanomachines.

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Quantum Optics & Quantum Information

Basic Concepts in Quantum Optics; Quantization of free electromagnetic field; Fock or number states, Quadrature of the fields, Coherent & Squeezed states, Photon added & subtracted coherent state, Schrodinger cat state and the cat paradox; Q-representation and Wigner- Weyle distribution; First & second order Coherence, Correlation function; Hanbury Brown-Twiss experiments, Atom-field interaction; Laser without inversion, Quantum theory of laser-density operator approach; Atom optics;

Open quantum system, Master equation; Cavity quantum electrodynamics (cavity-QED), Jaynes-Cummings model, dispersive atom-field interaction in a cavity; Laser Cooling;

Quantum bits (Qubits), Bloch sphere, Quantum gates (single & two qubit); Quantum Entanglement, Bell’s Inequality; Quantum Algorithms; Principles of Teleportation;

Examples of Quantum information processing in physical systems: cavity-QED, Ultracold neutral atoms etc.; Current research and development in Quantum Optics & Quantum Information;

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Physics of Ultracold Atoms

Introduction to ultracold atoms and Bose-Einstein condensate (BEC), critical temperature Basic Scattering theory; Second quantization, Mean field theory, Gross-Pitaevskii equation; 1D nonlinear Schrödinger equation; weak, strong and higher order interactions; BEC in a trap, trap engineering and condensate density; Bright & dark Solitons, exact solution; Applications & future technologies: BEC optical lattices; Faraday waves, phase transition, BEC in a chip, atomic beam splitter, atom lasers, Negative temperature etc.

Alkali metal gases, Introduction to laser cooling, Velocity dependent force, Optical Molasses, Magneto optical trapping (MOT), Limitations of MOT, Different types of trapping, Magnetic and optical trapping, Evaporative cooling techniques in magnetic and optical trap, Applications in quasi-one dimension, Achieving Bose-Einstein Condensates in pure magnetic and optical traps, Hybrid trapping potentials; Various applications in experiments.

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Biophotonics

Fundamentals of light matter interaction [absorption, fluorescence, phosphorescence, Raman scattering, Mie-scattering, Second harmonic generation (SHG) and two photon absorption], Introduction to biological cells, viruses, protein molecules

Optical imaging of cells (using various optical microscopes): Optical microscopy, Bio-imaging with confocal fluorescence microscope, evanescent wave microscope, SHG and two photon microscopes, Different techniques to achieve super resolution with optical microscopes.

Biodetection in real time (using optical biosensors): Importance of biodetection in real time, detection of bioanalytes (viruses/protein molecules) using evanescent based fiber-optic biosensor, photonic crystal biosensor and whispering gallery mode biosensor.

Fӧrster resonance energy transfer (FRET) to study protein - protein interactions.

Super continuum sources for Biophotonic applications.

Optical trapping and manipulation for biomedical applications

Advanced photodynamic therapy (APT)

Nanoplasmonic biophotonics: Introduction to Nanoplasmonics, Applications of nanoplasmonics in optical trapping, biosensing, APT, and Raman scattering of nanometer sized bioanalytes

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Introduction to Medical Physics

Breathing and Metabolism: Breathing, Human Elevation limits, Oxygen transfer in the brain, Photo synthesis, Oxygen transfer in the body, Network theory of the human breathing apparatus, Transport phenomena at the cell membrane, Dielectric measurement of exocytosis processes, Diffusion and scale qualities.

Biomechanics and fluid dynamics of the circulatory system: Bone structures, Ski binding, Elasticity of the vertebrae, Lifting a patient, Bones of uniform strength, Lifting weights, The blood as a power fluid, Branching, Bypass, Flow coefficients, Narrowing of the aorta, Blood pressure in the aorta, pulsatile blood flow.

The Senses, Electric currents, Fields and Potential: Information processing, Glasses, Optical illusions, Retina implantation, threshold of vision of the human eye, Visual angle and resolution, Sound propagation, Threshold of hearing, Nerve stimulation, Electrical model of a cell membrane, Measurement of cell membrane potentials.

The physics of Diagnostics and Therapy: X-ray diagnostics and Computer tomography, Ultrasound, Nuclear magnetic resonance, Magnetic Resonance Imaging, Nuclear diagnostics and positron emission tomography, Temperature measurement system, Blood Pressure measurement, ECG, ECHO.

Radiation medicine and protection: Pair production in radiation therapy, Compton scattering, Radiation damage from potassium, Lethal energy dose, Fatal does equivalents, Laser therapy.

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Magnetic Materials and Applications

Atomic magnetism, diamagnetism and paramagnetism, Hund’s rule, Solid state magnetism, 3d transition metals and 4f rare earths, Magnetic interactions, direct exchange and indirect exchange, Magnetic order, Ferromagnetism, Ferrimagnetism, Antiferromagnetism, Spin glasses; Magneto-crystalline anisotropy, Shape anisotropy, Induced magnetic anisotropy, Stress anisotropy, Magnetic surface and interface anisotropy; Magnetic Domain structures and magnetization dynamics, Domain walls, Closure domains, closure domains, damping processes, ferromagnetic resonance; Magnetoresistivity, Anisotropic Magnetoresistance (AMR), Giant Magnetoresistance (GMR), Colossal Magnetoresistance (CMR), Tunneling Magnetoresistance (TMR), Spin polarization, Andreev reflection, Point contact Andreev reflection (PCAR) spectroscopy, BTK theory; Soft Magnetic Materials , Eddy currents, losses in electrical machines, applications in Transformers, Flux-gate magnetometers, recording heads, magnetic shielding, anti-theft systems; Hard Magnetic Materials, Permanent Magnets, operation and stability, applications in motors, loudspeakers, hard drives, wigglers, undulators; Magnetism in reduced dimensions, Atoms, Clusters, Nano-particles, Nanoscale wires, Thin films, Multilayers, Superparamagnetism, Exchange bias, Interlayer exchange coupling (non-magnetic spacer, AFM spacer), Spin engineering, Spin valves.

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Materials for Engineering Applications

Oientation: Why materials? Functionality driven material (re)search; Extraction, synthesis, processing, and characterization of materials.>

Structural Materials: Introduction to Alloys, Ceramics, Polymers and Composites; Preparation, Processing and Applications; Elastic and Plastic deformation, Residual stress, Hardness, Fracture, Fatigue, strengthening and forming, fracture resistance, fatigue life, creep resistance.

Optical Materials: Introduction to optical materials; Interaction of light with electrons in materials; Applications as dielectric coatings, electro-optical devices, optical recording, optical communications

Magnetic Materials: Properties and processing of magnetic materials; Field, Induction, Magnetization and Hysteresis; Applications as Permanent magnets, Magnetic recording and sensing.

Electronic Materials: Si as material for microelectronics and photovoltaic, preparation, processing and applications; III-V and II-VI semiconductors and optoelectronic applications; Thermoelectric materials, figure of merit, thermoelectric generators and refrigerators; Superconducting Materials and properties, applications including magnets, magneto-encephalography, Josephson junction, SQUID; Conducting Polymers, synthesis and applications; Ferroelectric materials, piezoelectricity and applications; Shape memory alloys and applications.

Energy storage materials: Batteries, principles of electrochemistry; Primary and secondary (rechargeable) batteries and materials; Fuels cells; Ultracapacitors.

Biomaterials: Requirements like absence of toxicity, corrosion resistance, biocompatibility; Metal, ceramic and polymer biomaterials; bio-resorbable and bio-erodible polymers; Applications as implants, and prosthesis.

Nanomaterials: A brief introduction to mechanical, optical, electronic and magnetic properties; Applications (including self healing structural materials, nano-photonic materials, nano-electronic materials, etc) and Safety concerns.

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Atomic collision physics

Signals and systems, Fourier transform (FT), FT theorems, sampling theorem, Space-bandwidth product; Review of diffraction theory: Fresnel-Kirchhoff formulation, FT properties of lenses; Coherent and incoherent imaging. Basics of holography, in-line and off-axis holography, plane and volume holograms, diffraction efficiency; Recording medium for holograms; Applications of holography: display, microscopy; memories, interferometry, Non-destructive testing of engineering objects, Digital Holography, Digital holographic microscope, 3D display, etc.; Analog optical information processing: Abbe-Porter experiment, phase contrast microscopy and other simple applications; Coherent image processing: Vander Lugt filter; joint-transform correlator; optical image encryption.

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Introductory Biophysics

Review of basic concepts in thermodynamics and statistical mechanics: Entropy, Free energy, Random walk in biology, Introduction to force, time and energy at mesoscopic scales. Hydrophobicity, Ficks law of diffusion, Rigidity and elasticity.

Bio-macromolecules: Nucleic acid structure and properties, Protein structure, Ramachandran’s plot, Protein folding problem, Levinthal Paradox, enzyme kinetics, Membrane structure and Ion channels, Central Dogma, Gene Expression, Genetic code.

Molecular Recognition: Thermodynamics of Binding, Allostery and Cooperatively, Specificity of macromolecular recognition, Protein-Nucleic acid Interaction, Protein-Protein Interaction.

Experimental methods for structure-function relation in biopolymers: Transient absorption and fluorescence, FRET, FCS, Forced spectroscopic technique (optical tweezers, AFM and Magnetic trap).

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Mathematical Physics

Linear Algebra: Vector spaces and its properties, inner product spaces, linear transformation, similarity transformations, orthonormal sets, eigenvalues and eigenvectors. Complex Analysis: Cauchy-Riemann conditions, contour integrals, Residue theorem and applications. Partial differential equations and special functions (Legendre, Hermite and Lauguerre polynomials, Bessel functions, Neumann functions, etc.), Separation of variables in cartesian, spherical and cylindrical coordinates, properties of special functions.

Numerical Methods

Error analysis. Roots of nonlinear equations: Newton-Raphson method, solution of linear equations: Gauss-Jordan elimination, matrix inversion and LU decomposition, Eigenvalues and Eigenvectors. Interpolation and curve fitting: Least square fitting, linear and nonlinear, application in physics problems. Numerical differentiation and integration: Numerical differentiation formulae, Simpson’s rule and Gauss-Legendre integration. Solution of ODE and PDE: Runge-Kutta and finite difference methods.

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Classical Mechanics

Review of Newtonian mechanics. Lagrange’s equation and its applications, variational principle, principle of least action. Central force: Equation of motion, classification of orbits, Virial theorem, Kepler problem. Rigid body motion: Euler angles, angular momentum and kinetic energy, inertia tensor, Euler equations and applications. Small oscillations: Eigenvalue problem, normal modes, forced vibrations, dissipation. Hamilton’s equations, Canonical transformations, Poisson brackets, Hamilton-Jacobi theory, action-angle variables.

Electrodynamics

Solution of Laplace’s and Poisson’s equations, multipole expansion and Green’s function approach to electrostatic and magnetostatic problems. Maxwell’s equations and electromagnetic waves, wave propagation in dielectric and conducting media. Lienard-Wiechert potential, accelerated charges, Bremsstrahlung, electric dipole fields and radiation. Relativistic Electrodynamics: Covariant formalism of Maxwell’s equations, transformation laws.

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Quantum Mechanics

Operator formalism, Schrodinger equation, applications such as particle in a box, harmonic oscillator, hydrogen atom. Angular momentum, L-S coupling, J-J coupling, Clebsch-Gordon coefficients, Pauli matrices, commutation relations. Perturbation theory: Stark effect, He atom, α- decay, anomalous Zeeman effect. Relativistic quantum mechanics: Klein-Gordon and Dirac equations.

Statistical Mechanics

Microcanonical, Canonical and Grand Canonical ensembles. Partition function and it’s applications. Ideal quantum gas. Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics, applications such as Doppler broadening, Einstein coefficients, specific heat of solid, black body radiation, electrons in metal, white dwarf stars, etc. Transport phenomena: Diffusion, random walk, Einstein’s relations, Boltzmann transport equation, electrical properties.

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Experimental Techniques

Low pressure: Rotary, sorption, oil diffusion, turbo molecular, getter and cryo pumps. McLeod, thermoelectric, Penning, hot cathode ionisation and Bayard Alpert gauges. Partial pressure measurement, leak detection, gas flow through pipes and apertures, effective pumping speed, vacuum components, thermal evaporation, e-beam, sputtering and laser ablation systems. Low temperature: Gas liquifiers, cryogenic fluid baths, cryostat design, closed cycle He refrigerator (CCR), low temperature thermometry. Sources, sensors and instruments: Principle and characteristics of LASERs. Classification and principle of various sensors. Signal averaging and lock-in detection. Principle and applications of powder X-ray diffractometer, spectrophotometer; Fourier transform-Infrared (FT-IR) spectrometer, fluorimeter, atomic force microscope, electron microscope, Energy dispersive X-ray analysis (EDAX) and optical spectrum analyzer.

Scientific Presentation

Art of scientific writing (steps to better writing, flow method, organization of material and style), development of communication skills, presentation of scientific seminars.

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Coherence and light sources. Theory of diffraction: Fresnel and Fraunhofer diffraction. Theory of interference: two beam interference, division of wavefront and division of amplitude, multiple-beam interference. Optical imaging (coherent and incoherent) and processing: Frequency analysis of optical imaging systems. Fourier transforms, Convolution and correlation. Wavefront modulation, Analog optical information processing. Holography: Types of holography and its applications.

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Energy Bands and Charge Carriers in Semiconductors: Bonding Forces and Energy Bands in solids; Charge carriers in semiconductors; Carrier concentrations; Drift of carriers in electric and magnetic fields; Invariance of Fermi level at equilibrium. Excess carriers in Semiconductors: Optical absorption; Photoluminescence; Electroluminescence; Direct and Indirect recombination of Electrons and Holes; Trapping; Steady State Carrier generation; Quasi Fermi Levels; Continuity Equation of Diffusion and Recombination; Diffusion length; Haynes-Shockley Experiment; Gradients in Quasi Fermi level. Junctions: Fabrication of p-n junction; Contact Potential; Space charge at junction; Forward and Reverse biased junctions; Carrier Injection; Zener and Avalanche breakdown; Time variation of stored charge; Reverse recovery transient; Switching diodes; Capacitance of p-n junction; Varactor diode; Effect of contact potential on carrier injection; Recombination and generation in the transition region; Ohmic losses; Graded junctions; Schottky barriers; Rectifying contacts; Ohmic contacts. Field Effect Transistors: Transistor operation; Junction FET characteristics; High Electron Mobility Transistor; short channel Effects; MISFET operation and characteristics; Ideal MOS capacitor; Effect Real surfaces; Threshold voltage; I-V characteristics of MOS Gate oxide MOS field effect transistor. MOS Field Effect Transistors: Output and Transfer Characteristics; Mobility models; Short channel effect and narrow width effects; Substrate bias Effect; Equivalent circuit of MOSFET; MOSFET scaling and hot electron effects; Drain induced barrier lowering; Gate induced Drain leakage.

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Magetism: Review of diamagnetism, paramagnetism, superparamagnetism, ferromagnetism, antiferromagnetism, ferri magnetism. Circular and helical order. Direct, exchange, double exchange, indirect and RKKY interactions, environment effects: crystal field, tetrahedral and octahedral sites; Jahn-Teller effect; Hund’s rule and rare earth ions in solids. Consequences of broken symmetry, phase transition, Landau’s theory, rigidity, excitation, magnons, domains and domain walls, magnetic hysteresis, pinning effects. Magneto resistance, giant magneto resistance, nuclear magnetic resonance. Technological aspects of magnetic materials: Magnetic sensor, spin valve, magnetic refrigeration, actuator etc.

Superconductivity: Properties of conventional (low temperature) superconductors, London and Pippard equation, Type II superconductors, intermediate state, vortex lines, flux pinning, Non ideal behavior of Type II superconductors, Thermodynamics of Type I and II superconductors, Ginzburg Landau (G-L) theory, G-L equations, current density, Josephson equations, superconducting quantum interference device. Cooper pairs and BCS theory, Energy gap, magic number, experimental determination of energy gap from I-V characteristics, McMillan’s upper limit of Tc. Properties of high Tc superconductors, flux pinning, current density, granular nature.Technological aspects of superconductors: High magnetic field, Transmission line, Maglev train, MRI, etc.

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Materials classification on the basis of physical constitution, crystal structure (e.g.; amorphous & crystalline-poly/nano) and electrical properties; Brief review of crystal structure of materials (e.g.; metals, alloys, ceramics, polymers, composites etc.); Electrical properties of conductors, insulators and semiconductors, Concept of band structure in solid materials; Mechanism of electronic and ionic charge transport in solids; Theories of electrical transport in ionic conductors and semiconductors (e.g.; crystalline and amorphous – polymeric, ceramic and composites); Dielectric and ferroelectric phenomena – polar and non-polar systems (e.g.; oxides); Physics of polarization, resonance, dispersion and relaxation behavior in materials; Frequency response characteristics of charge transport and scaling laws; Microstructure-property correlation in solid materials: Basic concepts of energy-matter interaction in solids; Optical properties of materials: Optical constants, absorption and emission properties; Elastic and thermal properties of materials, Phase transition phenomena – solid-liquid-gas, superfluidity, superconductivity etc.; Magnetic properties of materials, elementary idea of plastic magnets. Suggested Readings:

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Linearity and nonlinearity: Origin and Importance, Dispersion, Dissipation. Nonlinear excitations: group velocity dispersion, solitary waves. Examples of Nonlinear equations: Dynamics of a pendulum under the influence of gravity, Inverted pendulum, van der Pol equation, Korteweg-de Vries equation, Navier-Stokes equations,The Richards equation, Sine-Gordon equation, Nonlinear Schrodinger equation, Ginzburg-Landau equation. Nonlinear Optics: Second harmonic generation, Two photon absorption, Four wave-mixing, Spontaneous parametric down conversion, Kerr effect, Pockels effect, Optical Soliton: spatial and temporal solitons, self-phase modulation, modulational instability, optical fiber, selffocusing, dark and bright solitons and solitary waves, dynamics in presence of phase locked source. Atomic systems: Non resonant atomic media, doffing oscillator model, solitons. Bose-Einstein condensate (BEC): Physics behind BEC, Experiments with alkali metal gas, Laser cooling, magnetic trapping, evaporative cooling. Second quantization, scattering length, Gross-Pitaevskii equation. Lower dimensional nonlinear systems, experimental validity. Dynamics of a cigar-shaped BEC: Dark and bright solitons, weak and strong inter-atomic interactions.

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Basics of holography, holographic imaging; Wavefront reconstruction: in-line and off-axis holography. Types of holography: Fourier holograms, Fraunhofer holograms, Thin and volume holograms, Reflection, white light, rainbow and wave guided holograms; Theory of plane holograms, magnification, aberrations, coupled wave theory, wavelength and angular selectivity, diffraction efficiency. Recording medium for holograms: silver halides, dichromatic gelatin, photoresist, photoconductor, photorefractive crystals etc. Applications: Displays, microscopy; interferometry, non-destructing testing of engineering objects, particles sizing; imaging through aberrated media, phase amplification by holography; information storage and processing. Holographic Optical Elements: scanners, filters; Optical data processing, holographic solar concentrators; Colour holography: recording with multiple wavelength; Electron holography, acoustic and microwave holography, computer generated holography, digital holography.

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PROPOSED CONTENTS

Introduction to thin films, Technology as a drive and vice versa; Structure, defects, thermodynamics of materials, mechanical kinetics and nucleation; grain growth and thin film morphology; Basics of Vacuum Science and Technology, Kinetic theory of gases; gas transport and pumping; vacuum pumps and systems; vacuum gauges; oil free pumping; aspects of chamber design from thin film growth perspectives; various Thin film growth techniques with examples and limitations; Spin and dip coating; Langmuir Blodgett technique; Metal organic chemical vapor deposition; Electron Beam Deposition; Pulsed Laser deposition; DC, RF and Reactive Sputtering; Molecular beam epitaxy; Characterization of Thin films and surfaces; Thin Film processing from Devices and other applications perspective.

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Programming fundamentals, Flow Chart, plotting, fitting data, building new functions, and making iterations and loops.

Application on elementary numerical methods (e.g., Taylor-series summations, roots of equations, roots of polynomials, systems of linear and nonlinear algebraic equations, integration). Applications in nanotechnology engineering.

Finite Difference Time-Domain Method: Optical Responses, advantage & disadvantage, Practical implementation, Numerical examples.

Finite element method: Introduction, Matrix form of the problem, Various types of finite element methods, Approximation of elliptic problems, Piecewise polynomial approach, One dimensional model problem.

Numerical schemes for nonlinear systems. Basic modelling and simulation. Relevant applications: optical, thermal, mechanical, and fluidic, and nanoscale devices.

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Elective Courses (Elective IV –VI)