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Isaac Newton Institute for Mathematical Sciences

A computer-assisted existence proof for photonic band gaps

13th March 2007

Author: M Plum (Karlsruhe)


Authors: V. Hoang, M. Plum, Ch. Wieners (Karlsruhe, Germany)

The investigation of monochromatic waves in a periodic dielectric medium ("photonic crystal") leads to a spectral problem for a Maxwell operator. It is well known that the spectrum is characterized as a countable union of compact real intervals (``bands'') which may or may not be separated by gaps, and the occurrence of such gaps is of great practical interest but difficult to prove analytically. In this talk, we will attack this problem, for the 2D case, by computer-assisted means. First we reduce the problem, using an analytical perturbation type argument, to the computation of enclosures for finitely many eigenvalues of finitely many periodic eigenvalue problems. This task is then carried out by computer-assisted variational methods.