Effects of filling rates on the photonic band gaps in the photonic crystal

The plane wave expansion method was implemented in modeling and simulating the band structures of 2D photonic crystals (PhCs) with square, triangular and honeycomb lattices. Two types of PhCs are presented, the first is circular air holes in dielectric and the second is circular GaAs rods in air, respectively. The eigenvalue equations of TE and TM modes will solved using Matlab environment. The results shown that the first type of PhCs is more flexible than the second type in controlling the band widths and the achieved frequency positions, and the triangular lattice showed the greatest flexibility. On the other hand, the work showed the significant effect of the filling ratio and the lattice constant on the achieved bandwidth.