**Optics: (86-246)**

Propagation of light, Plane and spherical mirrors, Refraction, Snell's law, prisms, Thin lenses, Lens-mirror systems, Optical instruments, Aberrations, The eye, Coherence, Interference and interferometers, Diffraction, The diffraction limit of light focusing, Gratings, Propagation of light – interference, Polarized light and resnel's equations, Double refraction and optical activity

**Modern Optics and Lasers: (86-365)**

Properties of light, Theory of the laser: basic concepts; amplification; losses; oscillations; rate equations; stable and dynamic state, Longitudinal and transverse resonant modes in an optical cavity, Cavity design, Survey of structure and properties of lasers: solid-state ruby laser; helium-neon and carbon-dioxide gas lasers; semiconductor lasers; pulsed laser, Introduction to Fourier optics, Nonlinear optics: two-photon absorption; harmonic multiplication; Raman scattering

**Quantum Optics: (86-840)**

Planck’s radiation law and Einstein coefficients. Interaction of light and matter in simple quantum systems - two level atom, Rabi oscillations, Bloch equations and Bloch vectors, Rapid adiabatic passage, Ramsey fringes, line broadening mechanisms (power, pressure, Doppler), dressed atom picture. Three level systems – Matter coherence, bright and dark states, Electromagnetically induced transparency (EIT), stimulated Raman adiabatic passage (STIRAP). Classical optical coherence. Coherence time and length, first order coherence and Young experiment, second order coherence and the Hanbury Brown and Twiss experiment, relation between coherence function and power spectrum. The quantized radiation field – Review of second quantization. Photon number states, thermal state, coherent states, squeezed states, photon statistics. Quantum description of the beam splitter – Splitting noise, Phase – Amplitude relations, Mach-Zehnder interferometer, standard quantum limit of phase detection, Heisenberg limit of phase detection. Generation and amplification of light – The laser oscillator in classical and quantum view, phase noise in classical oscillators, quantum noise limit on the laser linewidth, Schwallow – Townes formula. Entangled states of photons – Photon-pair emission and absorption. Spontaneous parametric down-conversion, the Hong-Ou-Mandel interferometer, time-energy entanglement, EPR states, Bell’s inequalities and experiments to check them.

**Optics Laboratory: (86-248) **

Geometrical optics and Aberrations; interference and interferometers; Polarized light, Double refraction and optical activity; Gratings and wavelength Analysis.

**Mathematical methods for Physicists III** **(86-207)**

Variational Calculus, Laplace Equation: Separation of Variables, Sturm-Liouville Theory, Spectral Theory of Laplace Operator, Green's Functions for Ordinary Differential Equations, Fourier series, Fourier transform and Laplace transform, Discrete Fourier transforms, Partial Differential Equations of the First Order.