Department of Mathematics
Colloquium
by
Prof. Peter Kuchment

The talk contains an introduction into mathematical problems of the photonic crystals theory. A photonic crystal is an artificial material that is an optical analog of a semiconductor. The idea of creating photonic crystals was suggested in 1987. The main property of photonic crystals is existence of a frequency interval such that electromagnetic waves whose frequencies belong to this interval cannot propagate in the medium (in other words, some colors of light do not exist in this medium). It is believed that availability of such materials would lead to a revolution in optics and electronics (high efficiency lasers, laser diodes, antennas, mirrors, memories, switches, etc.). The problem of creating such a material has a very significant mathematical component and leads to beautiful mathematics. The arising mathematical problems (non-standard aspects of spectral theory of differential and pseudodifferential operators, operators on graphs, etc.) had been unexplored until very recently.

Additional References:

1. One can find a nice introduction into the problems of photonic crystals theory in the book "Photonic Crystals. Molding the Flow of Light" by J.D. Joannopoulos, R.D. Meade, and J. N. Winn , Princeton Univ. Press, 1995.
2. The results presented in the talk were obtained in a series of recent papers by the speaker and his collaborators (first two of these papers are published in SIAM J. Appl. Math. 56(1996), no.1, 68-88 and 56(1996), 1560-1621, several others are forthcoming).