Dirichlet-to-Neumann Map Method for Analyzing Hole Arrays in a Slab

A rigorous and efficient computational method is developed to calculate transmission and reflection spectra for finite number of air-hole arrays in a slab, where the incident waves are propagating modes of the slab. The method is a three-dimensional extension of the Dirichlet-to-Neumann (DtN) map method previously developed for ideal two-dimensional photonic crystals which are infinite and invariant in one spatial direction. The method relies on the DtN maps of the unit cells to avoid repeated calculations in identical unit cells. The DtN map of a unit cell is constructed using eigenmode expansions in the vertical direction (perpendicular to the slab) and cylindrical wave expansions in the horizontal directions.