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: Goldberg, Israel, Seymour Goldberg, and Marinus Kaashoek. Basic Classes of Linear Operators. Boston, MA: Birkhauser Verlag, 2004. ISBN: 9783764369309. 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 indepth 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): 14871510. 
7  Bloch's theorem, time reversal, and diffraction  Textbook: Chapter 3 (sections on mirror symmetry/polarization and timereversal 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 "timeindependent perturbation theory" in any quantummechanics 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, omnidirectional 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  Conjugategradient, finitedifference timedomain (FDTD) method  
17  More FDTD: Yee lattices, accuracy, VonNeumann stability  Taflove, A., and S. C. Hagness. Computational Electrodynamics: The FiniteDifference TimeDomain 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): 17851787. 
20  Haus coupledmode theory, resonance, and Q  Textbook: Chapter 10 
21  Coupledmode theory with losses, splitter / bend / crossing / filter devices  
22  Bistability in a nonlinear filter, periodic waveguides  
23  Photoniccrystal slabs: gaps, guided modes, waveguides  Textbook: Chapter 8 
24 
Cavities in photoniccrystal slabs Photoniccrystal fibers 

25  Hollowcore and solidcore photonicbandgap fibers  Textbook: Chapter 9 (sections on indexguiding holey fibers, hollowcore holey fibers, and Bragg fibers) 