Abstract:
Three-dimensional photonic band gap structures are the ultimate goal for photonic crystals
as, unlike one and two-dimensional crystals, they provide for total confinement.
One such configuration is the woodpile structure, consisting of crossed layers of dielectric
rods with a stacking sequence, repeating itself every four layers. Our study of
propagation in a woodpile involves the formulation of plane wave scattering matrices
for the structure, derived recursively from the scattering matrices of its component layers,
using a Rayleigh method, in which the field quantities are written as multipole expansions.
For each layer, there is dispersion in only one direction and thus the 20-
diffraction problem is characterised by a family of 10 problems, each associated with
incidence parameters corresponding to the diffracted orders of the orthogonal grating,
leading to scattering matrices that are block diagonal or some permutation thereof. The
theory is applied to deduce transmission spectra and band diagrams for woodpile
photonic crystals.
