Photonic band gaps in quasicrystal-related approximant structures

Abstract

We propose a method for a systematic investigation of quasicrystal-related approximant structures in view of photonic bandgap applications. A detailed study is presented in the case of approximants formed by dielectric cylinders and constructed from a two-dimensional quasiperiodic lattice with octagonal symmetry. We show that isotropic photonic bandgaps are obtained even for the lowest order approximants generated by successive hyperspace shear. The main Fourier components of the dielectric function, responsible for the first photonic bandgap opening, are derived from the main component set of the quasiperiodic lattice. The magnitudes of the corresponding Brillouin zone vectors are shown to be directly related to the average distance between the planes passing by the dielectric cylinders. In other words, the approximant gap position is rather determined by the fundamental lattice parameters common to the quasiperiodic and approximant structures than by the approximant period. We also show that structure point symmetry is not indispensable for the band gap opening.