Lie groups, Lie algebras, cartan sub-algebra, roots, Dynkin diagrams, classification of simple Lie algebras. Toda equations and their integrability.  Higgs fields, self-dual monopoles. Classification of unitary representations of simple Lie groups.  Weyl’s character formula.

Standard cosmology, Robertson-Walker metric, thermal history of the universe, relativistic thermodynamics, phase transitions. Nucleosynthesis, dark matter, density fluctuations, galaxy formation.  Inflation. Cosmic strings.  Recent work on cosmological models; super-strings.  Recent work on cosmological models; super-strings, super-gravity, Kaluza-Klein. 

 Crystal optics (tensors, symmetry, anisotropy, resonance, momentum-space). Optical modulation (electrooptics, acoustoptics, magnetooptics). Second order nonlinearity (frequency doubling, parametric interactions, cascaded nonlinearity), Third order nonlinearity (optical Kerr effect, stimulated Brill scattering, stimulated Raman scat., bistability, phase conjugation, self focusing, solitons).. Nonlinearities in semiconductors. Ultrafast nonlinear optics. Nonlinear interaction of radiation with matter.

Nano, pico, femto second pulse generation. Q-switching, mode-locking, DFB, relaxation oscillation. Measurement: auto and cross correlation function, two photon, SH generation for detection, optical time delay, femto second, chirping, cooling pulses-generating compression. Applications in molecular relaxation, biology, semiconductor dynamics…etc.

Laser beam characteristics- Beam focusing effects - Semi classical theory of absorption and emission – Reflectivity & transmission of matter – Photon transport theory - Laser beam heating, melting, vaporization – Plasma formation- Rate of heating and cooling – Operational regimes in material processing -Depth of penetration – Key hole effect – Surface treatment (modification, cladding, alloying and hardening) – High power laser int. with solids (welding , cutting) – Optical properties of tissue - Laser tissue interaction (thermal, photochemical, photo mechanical, photo ablation, plasma induced ablation and photo description).

Propagation of EM waves in Dielectric wave guide – Fiber optics (boundary conditions, phase and group velocity, attenuation and dispersion, cut off frequency, single and multimode fibers) – Emitters (LED &laser diodes DH, QW, BDR, DFB, VCSEL’s) -  Fabrication techniques – Materials for photonics – Laser modulation (AM, FM and PM) and Demodulation – Receivers ( Detectors PIN, PMT, APD), homodyne and heterodyne detection – Sensors – Switching devices and wave guide switching.    

Laser safety, Lasers in Optical Communication and Data Storage,  Medical Applications: Optical properties of tissue – Models of laser-tissue propagation – Montecarlo simulation of laser tissue interaction – Laser effects on tissue (thermal, photochemical, photmechanical, ionizing..) – Medical applications (Opthalmology,  dermatology, dentistry, surgery, NET, gynecology, urology, neursurgery…..) - Low level laser therapy(LLLT)  – Laser safety and precautions- Diagnostic by laser – Laser types in medicine.  Industrial Applications, Metrological Applications, Holography.  Detectors, Laser system for remote sensing (CO2, Excimer, dye, semiconductor lasers. Optics. Telescopes). Basic equation for sensors. LIDAR, Differential Absorption, LIF, Raman, Atmospheric & Hydrospheric Monitoring., Industrial Pollution, Atmospheric / Underwater transmission, Practical Considerations, Deep Sea Coral Reefs, Industrial Pollution, Oil Spills. 

Mixtures and the density operator (level damping, density matrix, vector model of density matrix)- CW field interactions(polarization of two-level medium, inhomogeneous broadened media, polarization of semiconductor gain media) – Laser theory(laser self-consistency equations, single-mode semiconductor laser theory, transverse variations and Gaussian beam....) -  Coherent transient – Field quantization (single and multimode field quantization, coherence of quantum fields..)- Interaction between atoms and quantized field- Squeezed states of light( squeezing the coherent state, two-side mode master equation, two-mode squeezing, squeezed vacuum).

Exp. Data Analysis, Detector Theory and Performance Parameters, Thermal Detectors (pneumatic, pyroelectric, thermpelectric,  bolometers, ) , Photon Detectors (photemissive, vacuum photodiode, photomultiplier, photncounting, image intensifier), Junction detectors (PIN, APD, Schottky PD, phototransistor), Vidicon , Plumbicon , Diode arrays, CCD Camera. Noise in photon devices.

Gas Laser Design: Gas discharge phenomena – Vacuum techniques- Cooling systems – Power supplies for low and high power cw lasers – High power pulsed lasers(CO2, TEA…) - Blumbin  circuits (TEA, Excimer, N2 dynamic and chemical lasers design). Liquid Lasers Design: Preparation of dye solvents – pump geometry –jet flow transverse pumping – high energy dye laser (flash and laser pumped) – fs lasers. Insulator Solid Lasers: Flash and arc lamp – Diode pumped YAG lasers – Ti:sapphire laser design – Ring and Traveling wave laser design. Injection Lasers: Fabrication and characterization- Diode array lasers for pumping. Laser Mirrors: Dielectric coating – thin films – dichroic mirrors. Detection circuits problems.

Vacuum principles and vacuum system design basics, Overview of thin film technology, crystal structures of thin films, Defects sin Thin films, Nano crystalline, polycrystalline, and epitaxial thin films, thin film nucleation and growth models, (2D, 3D, and 2D- Epitaxial growth of thin films, super lattice structures and quantum wells, diffusions: inter-diffusion, grain boundary diffusions, reaction and phase transformation, Thin film growth techniques (CBD, Spray, Reactive evaporation,  PVD, Sputtering, MBE, Laser MBE PLD, CVD, PECVD, MOCVD, Sol-Gel, PAD.), Thin film processing, Thin film characterization techniques.

Renewable energy assessment, Solar radiation models, Solar-Thermal, Photovoltaic systems, Wind energy systems, Fuel cells applications, Biomass: Gas and liquid conversion, Hydrogen energy applications, Other renewable energies, Renewable energy economics and feasibility studies, Environmental factors and renewable energy, Typical examples at national and international levels. Waste and recycled energy, Ecological effects and thermal pollution and Energy policy for future. 

Structure in Materials, Techniques and advanced systems in materials, Destructive and non-destructive testing, Mechanical properties, Metals, Polymers,, Ceramics and carbon materials, Composites, Electronics and Optical properties, Nano Materials, Biomaterials and Biological Materials, Gas Sensing Materials, Photo & IR Detectors.

Energy States in Semiconductors, Perturbation of Semiconductors by external parameters, Absorption, Relationships between Optical constants, Absorption spectroscopy, Radiative and nonradiative transitions, processes in p-n junctions, stimulated emission, Excitation of luminescence and lasing in semiconductors, Photoelectric emission, Photovoltaic and photochemical  effects, Effect of traps on luminescence, Optical characteristics related to mobile electrons, Absorption of light by electronic transitions, Interaction of radiation with oriented quantum wells, Photoconductivity.

Electrical conductivity, mobility, and Hall effect in semiconductors, Temperature dependence of mobility , Geometric magneto resistance, Four point probe and sheet resistivity, Spreading resistance techniques, Capacitance - voltage techniques, Depth profiling and electrical assessment, Deep Level transient Spectroscopy, Determining the structures of semiconductors using X-rays, Rocking curves and crystal perfections, EXAFS and SEXAFS, Raman spectroscopy, The experimental measurement of optical constants, Photoluminescence, photoconductivity and photo thermal effects, Secondary ion beam spectroscopy, Auger electron spectroscopy, Electron microscopy, Atomic Force Microscopy (AFM), FTIR (Fourier Transform Infra Red Spectroscopy), TED, LEED, RHEED.

Symmetry in quantum mechanics: Symmetries, conservation laws, and degeneracies.  Discreet symmetries, parity.  Lattice translation, Time –Reversal.

Identical particles:  Permutation symmetry, Symmetrization postulate, two-electron system. The Helium atom. Permutation symmetry and Young Tableaux.

Scattering theory:  The Lippmann-Schwinger equation, The Born approximation, Optical theorem. Methods of partial waves, Low energy scattering and bound states, Resonance scattering.  Identical particles and scattering, Coulomb scattering.  

Quantization of a free scalar field.  Classical e.m. field, gauge transformations. Quantization of the e.m. field, Lorentz gauge, extended Fock space, Green’s functions.   Dirac equation. Interaction picture, Perturbation theory, Feynman rules, phase space.  The processes eg , em  and e+e-.  Divergences, regularization and renormalization., General gauges.

Gauge theories, symmetry breaking.  Standard electroweak model, particle representations, generations, neutral currents, relation to four-fermion theory, particle masses, GIM mechanism, universality.  The electroweak interactions.  Kobayashi-Maskawa matrix, experimental determination of the parameters.  The running coupling constants, implications of the renormalization group equations, grand unification.

Quark model of hadrons, solutions, bag models. Gluon exchange, mass formulae, quark masses, heavy quarks.  Quark-parton model, deep inelastic electron-nucleon scattering, scaling, corrections to scaling behaviour, jets.  Chiral symmetry, chiral symmetry breaking, quark masses. 

The colour group, asymptotic freedom, scaling violatius in deep in elastic scattering.  Renormalization group – functions.  Operator-produce expansions, anomalous dimensions.  Non-perturbative QCD, dispersion sum rules. The QCD vacuum, U(1)-problem, confinement; strong CP violation.

Review of Lie groups and their representations.  The groups SU(5), SO(10) and E6.  Unification I the standard model.  Georgi-Glashow SU(5) model.  Proton decay.  Other unification models: SO(10), E6, SU(4) x SU(4).  Problems of grand unified models.  Future outlook.

Two-dimensional superspace, superfield, scalar and vector multiplets; N=1/2, N=1, N=2. Four-dimensional superspace, supersymmetry groups, super-integration, expansion, projection operators. Classical N=1, superfield propagators, super . Explicit and spontaneous supersymmetry breaking, super-Higgs.

Path integrals, Faddeev-Popov quantization.  Free bosonic strings.  Quantization; light-cone, BRST. Trees, vertex operators, closed strings. Superstrings, NSR-model, ghosts, extended supersymmetry.  String group, tangent space, connections, covariant derivative.  Anomalies, Atiyah-Singer theorem.

Classical N=1 supergravity, covariant approach to supergravity, constraints, actions, Quantum  superields,  regularization, anomalies, Quantum N=1 supergravity, background splitting, ghosts, Feynman’s rules, dimensional regularization.  Supergravity and symmetry breaking.

Histostructure concepts and low dimensional systems, Quantum Wells, nanowires, quantum dots, tunneling transport, Quantum physics applied to such systems, Optical properties of low dimensional systems (transition rules, polarization etc). Transport properties of 2D and 1D systems. Quantized conductance with Landauer-formalism. Scattering phenomena in 1D. Devices based on quantum phenomena and Coulomb blockade