| LEC # | TOPICS | READINGS |
|---|---|---|
| 1 | Maxwell's equations and linear algebra | Textbook: Chapter 2 For a more sophisticated treatment of Hilbert spaces, adjoints, and other topics in functional analysis, a good text is: Notes on the Algebraic Structure of Wave Equations (PDF) |
| 2 | Modes of a metal box and mirror symmetry | Textbook: Chapter 2, chapter 3 (first section) |
| 3 | Symmetry groups, representation theory, and eigenstates | Textbook: Chapter 3 (for a basic overview of the consequences of symmetry) Refer to Innui or Tinkham for a more in-depth discussion. |
| 4 | Translational symmetry, waves, and conservation laws | Textbook: Chapter 3 (section on translational symmetry) |
| 5 | Total internal reflection and the variational theorem | Textbook: Chapter 3 (sections on index guiding and variational theorem) |
| 6 | Discrete translations and Bloch's theorem MPB demo | Textbook: Chapter 3 (section on discrete translation symmetry) For a similar theorem in 3d, see Bamberger, A., and A. S. Bonnet. "Mathematical Analysis of the Guided Modes of an Optical Fiber." SIAM J Math Anal 21 (1990): 1487-1510. |
| 7 | Bloch's theorem, time reversal, and diffraction | Textbook: Chapter 3 (sections on mirror symmetry/polarization and time-reversal symmetry) |
| 8 | Photonic band gaps in 1d, perturbation theory | Textbook: Chapter 2 (section on perturbations), chapter 4 (introduction, sections on origin of the gap, and final section on omnidirectional reflection), chapter 10 (last section, discusses reflection, refraction, and diffraction) For the same derivation of perturbation theory, see "time-independent perturbation theory" in any quantum-mechanics textbook. See any book on optics or advanced electromagnetism for Brewster's angle. |
| 9 | 1d band gaps, evanescent modes, and defects | |
| 10 | Waveguides and surface states, omni-directional reflection | |
| 11 | Group velocity and dispersion | Textbook: Chapter 3 (section on phase and group velocity, see footnotes in that section for a derivation of group velocity from this perspective) |
| 12 | 2d periodicity, Brillouin zones, and band diagrams | Textbook: Chapter 5 (2d photonic crystals), appendix B (reciprocal lattice and Brillouin zone) |
| 13 | Band diagrams of 2d lattices, symmetries, and gaps | Textbook: Chapter 5 Notes on Coordinate Transforms in Electromagnetism (PDF) |
| 14 | Triangular lattice, complete gaps, and point defects | |
| 15 | Line and surface defects in 2d, numerical methods introduction | |
| 16 | Conjugate-gradient, finite-difference time-domain (FDTD) method | |
| 17 | More FDTD: Yee lattices, accuracy, Von-Neumann stability |  Taflove, A., and S. C. Hagness. Computational Electrodynamics: The Finite-Difference Time-Domain Method. Norwood, MA: Artech House, Inc., 2005. ISBN: 9781580538329. |
| 18 | Perfectly matched layers (PML), filter diagonalization | Notes on Perfectly Matched Layers (PDF) |
| 19 | 3d photonic crystals and lattices | Textbook: Chapter 8 Watts, M. R., S. G. Johnson, H. A. Haus, and J. D. Joannopoulos. "Electromagnetic Cavity with Arbitrary Q and Small Modal Volume without a Complete Photonic Bandgap." Optics Letters 27 (2002): 1785-1787. |
| 20 | Haus coupled-mode theory, resonance, and Q | Textbook: Chapter 10 |
| 21 | Coupled-mode theory with losses, splitter / bend / crossing / filter devices | |
| 22 | Bistability in a nonlinear filter, periodic waveguides | |
| 23 | Photonic-crystal slabs: gaps, guided modes, waveguides | Textbook: Chapter 8 |
| 24 | Cavities in photonic-crystal slabs Photonic-crystal fibers | |
| 25 | Hollow-core and solid-core photonic-bandgap fibers | Textbook: Chapter 9 (sections on index-guiding holey fibers, hollow-core holey fibers, and Bragg fibers) |
Table of Contents
Study Materials
Readings
| When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more. |
Readings listed below from 'Textbook' are from the required course text: Joannopoulos, John D., Steven G. Johnson, Robert D. Meade, and Joshua N. Winn. Photonic Crystals: Molding the Flow of Light. Princeton, NJ: Princeton University Press, 2008. ISBN: 9780691124568.