Course Meeting Times
Lectures: 3 sessions / week, 1 hour / session
Course Description
Tired of doing electromagnetism like it's 1865?
Find out what solid-state 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 distributed-feedback lasers and integrated optical devices to the next generation of optical fibers, the 140-year-old analytical techniques you learned in Electromagnetism II aren't very useful. Instead, we will cover computational methods combined with high-level algebraic techniques borrowed from solid-state quantum mechanics: linear algebra and eigensystems, group theory, Bloch's theorem and conservation laws, perturbation methods, and coupled-mode 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 graduate-level 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 Solid-State Sciences). 2nd corrected ed. New York, NY: Springer-Verlag, 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 photonic-crystal 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 5-10 page paper based on their project.
Grading
| ACTIVITIES | PERCENTAGES |
|---|---|
| Problem sets | 33% |
| Mid-term 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, omni-directional 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 | Conjugate-gradient, finite-difference time-domain (FDTD) method |
Problem set 5 due Problem set 6 out |
| 17 | More FDTD: Yee lattices, accuracy, Von-Neumann stability | |
| 18 | Perfectly matched layers (PML), filter diagonalization | |
| 19 | 3d photonic crystals and lattices | Problem set 6 due |
| 20 | Haus coupled-mode theory, resonance, and Q | |
| 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 | |
| 24 |
Cavities in photonic-crystal slabs Photonic-crystal fibers |
|
| 25 | Hollow-core and solid-core photonic-bandgap fibers | Project due |