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## 分野別セミナー

### A computer-assisted band-gap proof for 3D photonic crystals

2009-01-06 15:30～2009-01-06 17:00

Michael Plum (University of Karlsruhe)

for Maxwell's equations with periodic electric permittivity. By
Floquet-Bloch theory, the spectrum has band-gap structure, and
the bands are characterized by families of eigenvalue problems
on a periodicity cell, depending on a parameter $k$ varying in
the Brillouin zone $K$. We propose a computer-assisted method
for proving the presence of band-gaps: For $k$ in a finite grid
in $K$, we obtain eigenvalue enclosures by variational methods,
and then capture all $k \in K$ by a perturbation argument.