Periodic Surprises in Electromagnetism
a one-week seminar (five 1.5-hour lectures)
MIT MRS Chapter, 2003 IAP tutorial series,
organized by Ion Bita
(with subsequent supplements)
Has there been anything new in classical electromagnetism since
Maxwell laid down the law in 1864? If so, can one learn it without
wading through a vectorial mire of partial differential equations?
Come and find out what solid-state physics has brought to 8.02 in the last 15 years: photonic crystals and
the surprising new phenomena that arise when light propagates through
a periodic medium. This crash course will introduce Bloch's theorem
for electromagnetism, photonic band gaps, the confinement of light in
novel waveguides and cavities by synthetic optical "insulators,"
startling sub-micron fabrication advances, exotic optical fibers, and
will upend what you thought you knew about total internal
reflection. We will focus less on gory differential equations than on
high-level approaches such as linear algebra, variational theorems,
conservation laws, and coupled-mode theory; the course should be
accessible to anyone with a grasp of basic electromagnetism and who
does not quake in fear at the word "eigenvalue."
SPIE Short Course
My most recent lecture materials are from my short course (SC608)
offered periodically at the SPIE Photonics conferences
(Photonics West, Photonics North, Optics & Photonics, etc.):
Older Syllabus and Lecture Materials: IAP 2003
These are older lecture materials from the IAP short course
mentioned above; they are mainly superseded by the SPIE course notes above.
- Lecture 1: Wave propagation in periodic systems. Bloch's
theorem, the electromagnetic eigenvalue problem, band diagrams, the
variational theorem, and the origin of the photonic band gap.
1d/2d/3d crystal examples.
- Lecture 2: Point defects (cavities) and line defects
(waveguides). Their novel properties, and combination into interesting
devices such as filters. Coupled-mode theory and projected band
- Lecture 3: Fabrication technologies for 3d photonic crystals, a survey.
- Lecture 4: Hybrid structures lacking a complete band gap.
Photonic-crystal slabs: index-guiding in periodic systems, projected
band diagrams, waveguides, cavities, and losses. Omnidirectional
mirrors with 1d crystals.
- Lecture 5: Photonic-crystal and micro-structured fibers:
Bragg (& OmniGuide) fibers, 2d-crystal fibers, holey (index-guided)
fibers. Perturbation theory in electromagnetism.
The PDF slides are best viewed via the stand-alone Acrobat
reader program in full-screen mode, or at least using the
page-forward button instead of the scroll-bar, since many of the slide
transitions involve a crude animation that requires inter-slide
Here are provided the materials from subsequent lectures and
tutorials on photonic crystals by SGJ. Many of these slides
are taken or adapted from the tutorial seminar above.
The MIT Photonic-Bands (MPB)
Package is a free program that can be used to compute band
diagrams and eigenfields for the crystals and point/line defects
described in this seminar.
Meep is a free program
to perform time-domain (FDTD) simulations of arbitrary electromagnetic
structures, which can be used to calculate transmission spectra,
resonant modes, and many other things.
Both MPB and Meep are also installed on MIT's Project Athena (Sun and Linux
workstations only). To use it, type
add mpb at the Unix
prompt. A pointer to the documentation, and
examples, can be found in
Harminv is a
program for extracting frequencies and decay rates from time series,
and is a useful tool for modal analysis in time-domain simulations.
(It is integrated directly into Meep.)
- J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic
Crystals: Molding the Flow of Light, second edition (Princeton Univ. Press,
2008). MIT Libraries: QC793.5.P427.J63 (Physics Reading Room, Hayden
Reserves, Science Library).
- S. G. Johnson and J. D. Joannopoulos, Photonic Crystals: The
Road from Theory to Practice (Kluwer, 2002). MIT Science Library:
We are especially indebted to J. D. Joannopoulos, D. Norris,
Y. Fink, S. Hart, J. W. Perry, K. Aoki, and F. Garcia-Santamaria
for graciously providing additional materials for the lectures. Ion
Bita of the MIT Materials Science and Engineering Department provided
the impetus and initial inspiration for this seminar, as well as
invaluable organizational assistance.
These lectures would not have been possible without many
high-quality publications from research groups around
the globe, whom we have tried hard to cite properly for all excerpted
figures and quoted results. We are grateful to them in advance for
not suing us for copyright infringement, although hopefully this
educational presentation falls under the Fair Use exemption.
All mistakes and bad jokes are due to S. G. Johnson, however.