Wave phenomena in metamaterials and photonic crystals
Metamaterials are materials whose electromagnetic or acoustic
properties are controlled by their internal structure. Typically these
structures can be periodic and the period or characteristic length scale
of the internal structure is much smaller than the wavelength. A familiar
example is red stained glass made from sub wavelength gold nanoparticles.
On the other hand when the period of the internal structure is on the same
length scale as the wavelength then destructive interference can occur.
This gives rise to frequency intervals where no waves can propagate inside
the material. These are the well known photonic band gap crystals and
their effects can be seen in the coloration of butterfly wings. In this
lecture we provide a brief history of metamaterials and photonic band gap
crystals and provide an overview of the mathematical modeling. We
highlight auxiliary spectral problems directly related to the physical
structure of these materials. We illustrate how these spectra can be used
as tools in the design of both metamaterials and photonic band gap
crystals. This is joint work with Yue Chen and Robert Viator.