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Photonic Crystals:
Periodic Surprises in Electromagnetism

Steven G. Johnson

a one-week seminar (five 1.5-hour lectures)
MIT MRS Chapter, 2003 IAP tutorial series, organized by Ion Bita

(with subsequent supplements)

See also: Photonic Crystals: Molding the Flow of Light (second edition)
— our new (2008) textbook, available online at no cost

See also: MIT Fall Semester 2005: 18.325 — Mathematical Methods in Nanophotonics

See also: MIT Spring Semester 2008: 18.369 — Mathematical Methods in Nanophotonics

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.):

  • Photonic Crystals: A Crash Course: PDF (39MB) and PowerPoint (46MB) slides.

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These are older lecture materials from the IAP short course mentioned above; they are mainly superseded by the SPIE course notes above.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 structures.

  • 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 alignment.

Additional Lectures

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.

Computational Tools

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 /mit/mpb/README.

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.)

Additional Reading

  • 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: QC793.5.P427.J64

Acknowledgements

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.