The supercell method is used to study the variation of the photonic bandgaps
in one-dimensional photonic crystals under random perturbations to thicknesses
of the layers. The results of both plane wave and analytical band structure and
density of states calculations are presented along with the transmission
cofficient as the level of randomness and the supercell size is increased. It
is found that higher bandgaps disappear first as the randomness is gradually
increased. The lowest bandgap is found to persist up to a randomness level of
55 percent.Comment: Submitted to Physical Review B on April 8 200