Abstract:
We outline a theory for electromagnetic scattering
by cylinder gratings in conical incidence, based on
a multipole method. The theory, and its numerical
implementation; can be applied to photonic crystaLs
consisting of stacks of one-dimensional gratings.
One such configuration is the woodpile
structure, consisting of layers of crossed rods with
a stacking sequence, which repeats itself every four
layers.
We show how to use the plane wave scattering
matrices of the layers in combination with Bloch's
theorem to determine the band structure of the
photonic crystal from the solution of an eigenvalue
problem. We deduce the spectral properties of the
woodpile layering, and show transmission spectra
and band diagrams for woodpile photonic crystals.
