Abstract
We have introduced a high accuracy version of the Yee algorithm based on nonstandard finite differences for which the error is ε∼(h/λ)2 compared with ε∼(h/λ)6 for the ordinary one. This high accuracy allows the use of coarse numerical grids, which greatly reduces the computational cost. Realistic two-dimensional calculations can run on a personal computer, while three-dimensional ones can run on a fast workstation. Using this high accuracy algorithm, we developed computational models and methods to simulate optical propagation in photonic crystals, and to compute their transmission spectra, and bandgap structures. In addition, methodologies were developed to accurately represent arbitrary lattice structures on coarse grids.
