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ECE 545, Monsoon 2021
Photonics:Fundamentals&Applications
Instructor
Sayak Bhattacharya
Office hour: By appointment (online)
E-mail: sayak|at|iiitd.ac.in
Lectures: Mon, Thu 2:30pm-4:00pm (online)
Tutorials: By announcement (online at a mutually convenient time)
Office hours: By appointment (online)
Announcements
In lieu of Thu (Aug 19), Photonics lecture will be held on Sat (Aug 21), as per the IIITD academic calendar.
Course overview and evaluation policy
Aug 16: Course webpage online, first lecture today!
Lectures
| S. No. | Date | Topic | Advised Reading | Lectures |
| 1 | Aug 16 | Course outline & grading policy, Introduction & historical background
Double slit experiment, light as a proability wave, Matter waves | Feynman
| Slides
| | 2 | Aug 21 | Eigenfunctions and Eigenvalues, Review of Maxwell's eqns: Maxwell's equations as eigenvalue problem | Joannopoulos
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| | 3 | Aug 23 | Review of Maxwell's eqns contd.: Potentials in Electromagnetics, Gauge freedom, Coulomb and Lorentz gauge Review EM waves: Polarization of waves, 1D scalar wave equation, uniform plane waves, special form of Maxwell's eqns for uniform plane waves | Griff. & ECE230 lecture notes
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| | 4 | Aug 26 | Comparison of forward, backward and central differences
Discretization of Maxwell's equations: staggered grid approach, Space-time marching of EM fields: the leap-frog model
| Taflove
| Lecture note
| | 5 | Sept 2 | Numerical dispersion, CFL stability criteria
PML
| Taflove
| Lecture note: refer to lecture note of previous lecture
| | 6 | Sept 6 | Scalability of Maxwell's equations
MEEP: dielectric slab waveguide and waveguide bend
| MEEP manual
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| | 7 | Sept 9 | Dispersive materials | Feynman, Griff.
| Lecture note
| | 8 | Sept 13 | Quiz 1 | |
| | 9 | Sept 16 | Intro to QM: Stern-Gerlach experiment, Superposition and measurement in QM | Sakurai
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| | 10 | Sept 20 | Linear vector space and Hilbert space, Dirac's Bra-ket notations, Operators in QM, Hermitian operators and their eigenvalues, Superposition and completeness | Sakurai
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| | 11 | Sept 23 | Projection operator, matrix representation of operators snd states, Compatible and incompatible observables, Measurement in quantum mechanics | Sakurai
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| | 12 | Oct 7 | Measurement in quantum mechanics, position space representation of states, Unitary operator, Infinitesimeal translation and its generator, Finite translation | Sakurai
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| | 13 | Oct 11 | Lattice, basis, crystal, primitive vectors and lattice vectors, Continuous and discrete translational symmetry, Bloch's theorem and its proof | Ashcroft-Mermin, Joannopoulos
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| | 14 | Oct 14 | Reciprocal space and reciprocal lattice vectors, Brillouin zone, Weigner-Seitz method, Introduction to photonic crystal: Master equation, Example: photonic bandgap of a triangular lattice | Joannopoulos
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| | 15 | Recorded | MIT Photonic Bands (MPB), Design illustrations: light localization in a point defect of a photonic crystal, wave guidance in a line defect of a photonic crystal | Joannopoulos, MPB manual
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| | 16 | Oct 21 | Infinitesimal time translation and Hamiltonian as its generator, Time-dependent and time-independent Schrodinger's equation, Simple harmonic potential, creation and annihilation operators, Number states, zero-point energy | Sakurai
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| | 17 | Oct 25 | Dirac's canonical quantization, Gauge freedom, Transverse nature of magnetic vector potential under Coulomb gauge, Electric field, magnetic field and EM energy in a cavity in terms of magnetic vector potential, correspondence between vector potential and creation/annihilation operators | Barnett
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| | 18 | Oct 28 | Generalized momentum and Hamiltonian of a charge in EM field, weak field approximation, Interaction Hamiltonian and electric dipole approximation | MIT lecture notes
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| | 19 | Nov 1 | Heisenberg's equation of motion; Schrodinger, Heisenberg and interaction picture | Sakurai
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| | 21 | Nov 15 | Introduction to cavity QED: A two state emitter (atom/Quantum dot) in a photonic crystal cavity; field, atomic and ineteraction Hamiltonian, Atomic transition operators, dipole matrix elements and symmetry considerations, Rabi frequency, Jaynes-Cummings Hamiltonian, Strong coupling regime: detuning | Arxiv
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| | 22 | Nov 18 | Time evolution of a perturbed system in interaction picture, Rotating wave approximation, Rabi oscillation, splitting of energy eigenstates under perturbation, Bare and dressed states | Barnett, Arxiv
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| | 23 | Nov 22 | Anharmonic dressed state ladder of a strongly coupled cavity-emitter system, Photon blockade, A simple all-optical switch | Arxiv
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| | 24 | Doubt clearance session | Analogy between photon polarization and spin: revisiting Stern-Gerlach experiment | Sakurai
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Reading
David J. Griffiths, Introduction to Electrodynamics, Pearson 4th Ed. (2015).
R. Feynman, R. Leighton, M. Sands, The Feynman Lectures on Physics
B. Saleh and M. Teich, "Fundamentals of Photonics", Wiley, 3 ed. (2019)
Stephen Barnett & Paul Radmore, "Methods in Theoretical Quantum optics", Oxford Series in Optical and Imaging Science (1997)
J. J. Sakurai, "Modern Quantum Mechanics", Addison Wesley (1994)
Jelena Vuckovic, "Quantum Optics and Cavity QED with Quantum Dots in Photonic Crystals", Oxford Univ. press (2017)
John D. Joannopoulos et al., "Photonic crystals: Molding the flow of light" , Princeton Univ. Press, 2 ed. (2008) [Read the free preprint]
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