Course Meeting Times
Lectures: 3 sessions / week, 1 hour / session
Course Description
Tired of doing electromagnetism like it's 1865?
Find out what solidstate physics has brought to Electromagnetism II (8.02 or 8.022) in the last 20 years, in this new course surveying the physics and mathematics of nanophotonics  electromagnetic waves in media structured on the scale of the wavelength.
In this regime, which is the basis for everything from iridescent butterfly wings to distributedfeedback lasers and integrated optical devices to the next generation of optical fibers, the 140yearold analytical techniques you learned in Electromagnetism II aren't very useful. Instead, we will cover computational methods combined with highlevel algebraic techniques borrowed from solidstate quantum mechanics: linear algebra and eigensystems, group theory, Bloch's theorem and conservation laws, perturbation methods, and coupledmode theories, to understand surprising optical phenomena from band gaps to slow light to nonlinear filters.
Prerequisites
Advanced Analytic Methods in Science and Engineering (18.305) or permission of instructor. (Basically, some experience with partial differential equations and linear algebra.) This is a graduatelevel course aimed at beginning graduate students and suitably advanced undergraduates.
Texts
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.
This book is at an undergraduate level, and 18.369 is somewhat more advanced, but the book should provide a useful foundation. You can read the book online.
Useful (but not required) books for this course:
Inui, Tetsuro, Yukito Tanabe, and Y. Onodera. Group Theory and Its Applications in Physics (Springer Series in SolidState Sciences). 2nd corrected ed. New York, NY: SpringerVerlag, February 1996. ISBN: 9783540604457.
Tinkham, Michael. Group Theory and Quantum Mechanics. Mineola, NY: Dover Publications, 2003. ISBN: 9780486432472.
Homework
Problem sets are assigned on a roughly weekly basis and are worth one third of the total grade. The collaboration policy on homework is as follows:
First, talk to anyone you wish, and read anything you wish (with the exception of homework solutions from previous terms, which are strictly verboten). In fact, you are encouraged to discuss the course material and the homework problems with your classmates  often the best way to learn something is to force yourself to explain it to someone else. However, before you discuss a homework problem with a classmate or look for related information in some reference, you are expected to first make a solid effort at it on your own.
Second, after you discuss a homework problem with a classmate or read related information in some other reference, you must write up the solution on your own, in your own words, starting from something close to a blank sheet of paper.
Exams
There is one midterm exam that covers the first half of the course. There is no final exam, but there is a final project due at the end of the course.
Project
Students must choose a published paper on an interesting photoniccrystal phenomenon, replicate the results of that paper using the MIT numerical software, and then extend the results in some interesting way. Students must write one 510 page paper based on their project.
Grading
ACTIVITIES  PERCENTAGES 

Problem sets  33% 
Midterm exam  33% 
Final project  34% 
Calendar
LEC #  TOPICS  KEY DATES 

1  Maxwell's equations and linear algebra  
2  Modes of a metal box and mirror symmetry  Problem set 1 out 
3  Symmetry groups, representation theory, and eigenstates  
4  Translational symmetry, waves, and conservation laws  
5  Total internal reflection and the variational theorem  Problem set 1 due 
6 
Discrete translations and Bloch's theorem MPB demo 
Problem set 2 out 
7  Bloch's theorem, time reversal, and diffraction  
8  Photonic band gaps in 1d, perturbation theory  
9  1d band gaps, evanescent modes, and defects 
Problem set 2 due Problem set 3 out 
10  Waveguides and surface states, omnidirectional reflection  
11  Group velocity and dispersion 
Problem set 3 due Problem set 4 out 
12  2d periodicity, Brillouin zones, and band diagrams  
13  Band diagrams of 2d lattices, symmetries, and gaps  
14  Triangular lattice, complete gaps, and point defects 
Problem set 4 due Problem set 5 out 
15  Line and surface defects in 2d, numerical methods introduction  
16  Conjugategradient, finitedifference timedomain (FDTD) method 
Problem set 5 due Problem set 6 out 
17  More FDTD: Yee lattices, accuracy, VonNeumann stability  
18  Perfectly matched layers (PML), filter diagonalization  
19  3d photonic crystals and lattices  Problem set 6 due 
20  Haus coupledmode theory, resonance, and Q  
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  
24 
Cavities in photoniccrystal slabs Photoniccrystal fibers 

25  Hollowcore and solidcore photonicbandgap fibers  Project due 