FDTD analysis of 12-fold photonic quasi-crystal central pattern localized states

Abstract

The TM bandgap features of the 2D 12-fold quasi-crystal are examined based on the width of the dielectric strip and pattern central symmetry location within the quasi-crystal. Results indicate that the bandgap properties observed for a particular fill factor is independent of the rotational symmetry center when the dielectric strip is wide, and still observable when the strip width is considerably reduced, confirming the general belief that the bandgap generating properties of the quasi-crystal are a local dielectric effect for the lower frequency band. Thin strips are shown to posses defect states in the bandgap region of the thicker equivalent strips, defect states analogous to intentionally introduced defect states of translational symmetric photonic crystals. We explore the mode profiles of the defect state when the defect is coincidental with the rotational symmetry central pivot point of the quasi-crystal pattern. In addition we show that the rotational center “defect” may be used to enhance the optical guidance of light around a 90° bend in a waveguide implanted in the quasi-crystal.