Quantitative isolation of band-gap formation mechanisms by randomizing the lattice arrangement in photonic crystals

Abstract

The band-gap formation mechanisms for photonic crystals (PCs) have been theoretically investigated on the basis of the analogy of the band gap to that for the semiconductors. On the reasonable assumption that the photonic band-gaps are created through both or either of the Bragg and the Mie processes, we attempted to quantitatively determine which process is more responsible for the band-gap formation. To achieve this purpose, we introduced the randomness of the lattice arrangement into the PCs. Through the analysis of the band-gap shrinkage as a function of the randomness, we have succeeded for the first time in quantitatively isolating the gap formation mechanisms in the dielectric PCs. From these results, we further conclude that the dielectric PCs have a greater tolerance than the metallic PCs for the fluctuation of the lattice arrangements, which would undoubtedly facilitate the fabrication of the crystals.