Defect mode properties of self-similar symmetry order in triadic Cantor photonic crystals

Abstract

The discovery of quasi-crystal tells us that not only the translational symmetry order (TSO) but also other orders can produce Bragg diffraction. As far as we know, in one dimensional (1D) photonic crystals (PCs) there are two symmetry orders, TSO and self-similar symmetry order (SSO). There has been a lot of researches exploring the properties of defect of TSO in the 1D PCs, but until now we do not find any studies related to the defect of SSO. In this work we consider the triadic Cantor set (TCS) PCs to stage 6, and attempt to create the defect of SSO by changing the scale factor of stage 2 to 3 and stage 3 to 4, where for the high-refractive-index layer only the thickness of stage 3 changes. It's well known that the defect of TSO governs the frequency of a kind of transmission peaks, called defect mode. Our results show that the defect of SSO influences the background intensity of the transmittance spectrum rather than the transmission peaks. We note that the defect mode frequency and the transmittance background intensity interchange their roles for the two symmetry orders, and it follows that the long neglected transmittance background intensity should be a significant optical property.