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.
| 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 |
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| 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) |