分野別セミナー

Photonic crystals are usually modelled by a spectral problem
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.