Photonic band gap in Ge-based two-dimensional triangular lattice photonic crystals

The relationship between the filling factor and the circumcircle radius of the regular polygon scatter is deduced in a two-dimensional triangular lattice photonic crystal. The photonic band gaps (PBGs) are calculated with the plane wave expansion method in Ge-based two-dimensional triangular lattice photonic crystals. When Ge cylinder is placed in air background, the TM band gaps and TE band gaps appear with the TM band gaps dominating. As Ge filling factor increases, the width of the photonic band gaps increase initially but then decrease and the center frequency decrease. The width of the first band gap of the TM band gaps reaches the maximum at the radius of 0.14a. On the contrary, when air cylinder is placed in Ge background, the TM band gaps and TE band gaps as well as the complete band gaps appear with the TE band gaps dominating. With the air filling factor increasing, the width of the photonic band gaps also increase initially then decrease, whereas the center frequency increase. The width of the first band gap of TE band gaps and the largest complete band gap reaches the maximum at the radius of 0.46a and 0.49a, respectively.