Introduction: Numerical Weather Prediction as an Initial Value Problem, Filtering Problem, Finite Difference techniques for various partial differential equations (parabolic, hyperbolic and elliptic), Time integration schemes, Explicit, Implicit, and semi-implicit Schemes.

Introduction to Planets and Planetary Systems- Orbital motion – Gravitational field that shape the Earth – Internal structure of planet and its satellite, Equation of state, Density profiles, MassRadius relationship, The origin and evolution solar system, planetary atmospheres, Elemental abundance, outgassing processes, capture processes, Erosion and escape processes, surface processes – condensation, Adsorption, dissolution, chemical weathering, Atmospheric feedbacks – Observed atmospheric changes in Earth and other planets.

Quantum bits and quantum gates: quantum bits, basic computations with 1-qubit quantum gates, Pauli matrices or I, X, Y, Z-gates, Hadamard matrix gate or H-gate, quantum gates with multiple qubit inputs and outputs, quantum circuits, non cloning theorem.

Quantum measurements: quantum measurements and types, quantum measurements in the orthonormal basis,  Projective  or  von-Neumann  measurements,   POVM   measurements,   quantum   measurements on joint states.

Theoretical Foundations: Macroscopic electrodynamics, wave equations, time harmonic fields, Dyadic Green’s function, Evanescent fields. Propagation and focusing of optical fields – field operators, paraxial approximation of optical fields, polarized electric and magnetic fields, focusing of fields, point spread function, principles of confocal microscopy, near field optical microscopy, scanning near –field optical microscopy.

Quantum theory of light: quantization of the electromagnetic field, evolution of the field operators, quantum states of the electromagnetic field. Quantum information processing: quantum information, quantum communication, quantum computation with qubits, quantum computation with continuous variables. Density operators and super operators, fidelity, entropy, information and entanglement measures, correlation functions and interference of light, photon correlation measurements.

Laser for detection and ranging- LIDAR applications-Doppler wind LIDAR, Differential Absorption LIDAR for water vapor monitoring. Laser application in material processing – esp. CO2, YAG , Excimer,Ruby lasers-[material processing, Cutting, Welding, drilling, micro machining] – Interation of laser radiation with matter, Heat Flow Theory, Process characteristics etc. Laser anemometry, Schlieren Techniques for wind tunnels, Holography etc Lasers for metrology – Interferometery for surface characterization, precision length measurement, time standards etc, Medical applications of laser.

 I. Introduction to MEMS and MOEMS

Introduction to MEMS Technology and Applications Introduction to sensing and actuation principles, applications, various types of sensors and actuators Open loop and closed loop systems Materials used for MEMS fabrication and reasons to select them

Design of Microstructures with specific case studies like accelerometers, gyroscopes, RF switches Silicon micromachining and its opportunities

II. MEMS Devices: Fabrication and Technologies

Nonlinear optical susceptibility, wave equation description of nonlinear optical interactions - Sum frequency generation, Difference frequency generation, Second Harmonic generation, Phase matching condition,Optical parametric Oscillators, Quantum mechanical theory of nonlinear optical susceptibility- Schrodinger equation calculation, density matrix calculation.

Introduction to probability theory, properties of probabilities, random variabes and probability distribution, generating functions, examples of probability distributions, Gaussian probability distribution, central limit theorem, multivariate Gaussian distribution. Random processes, statistical ensembles, stationarity and ergodicity, properties of autocorrelation function, spectral properties of stationary random processes, orthogonal representation of a random process, Wiener Khinchine theorem, Karhunen–Loeve expansion.

Review of Semiconductor device Physics, Semiconductor Opto electronics- Solid State Materials, Emitters, Detectors and Amplifiers, Semiconductor Emitters- LEDs, Diodes, SLDs, CCDs, Semiconductor lasers- basic Structure, theory and device characteristics, DFB, DBR, Quantum well lasers ,Laser diode arrays, VCSEL etc. Semiconductor photo detectors:Materials - Si, Hg Cd Te, InGa As, Al Ga As, GaN etc for different wavelengths.

Detectors :Photoconductors, photo diodes, PIN , APD ,Photo transistors, solar cells, CCDs, IR and UV detectors.

Quantum Mechanics: Fundamentals

Compensating TE modes of a symmetric step index planar, understanding modes, TE modes of parabolic index planar waveguide, TM modes of a symmetric step index planar waveguide, waveguide theory, Single mode fibers, pulse dispersion in single mode fibers, strip and channel wave guides, anisotropic waveguides, segmented waveguide, electro-optic and acousto optic waveguide devices, directional couplers, optical switch phase and amplitude modulators, filters etc, Y junction, power splitters, arrayed waveguide devices, fiber pigtailing, fabrication and integrated optical waveguides and devices, w