Band gap of silicon photonic crystal with square-lattice and windmill-shaped defects

Abstract

A new type of 2D square-lattice photonic crystal with different windmill-shaped defects is proposed. Based on the plane wave expansion method and super cell theory, the band gaps of defect models are numerically analyzed according to the symmetry. We aim at further reducing the defect symmetry of photonic crystals compared to previous studies and researching the effect of translation and rotation of different windmill-shaped defect structures on the transverse magnetic (TM) band gap. The results reveal that the translation distance of defects brings great impacts on the band gap of 2D square-lattice photonic crystals and the width of the TM band gap can be further expanded after rotating on the basis of translation. In addition, we discovery that the band gap of the model with even-numbered fan-shaped defects is wider than that of the model with odd-numbered fan-shaped defects. Among the five different defect models (three-wings, four-wings, five-wings, six-wings, rotating-cross), the four-wing windmill defect model produces the largest band gap, which reaches 5.307 × 10−2 (ɷa/2πc). This research is helpful to understand the band gap characteristics of photonic crystals, which will contribute to the design of photonic crystal devices.

Keywords

• Photonic crystal
• Fan-shaped defects
• Plane wave expansion method
• Band gap