Effects of Lattice Types on the Frequency Band Widths in Photonic Crystals

The plane wave expansion method was implemented in modeling and simulating the band structures of two dimensional photonic crystals (PhCs) with square, triangular and honeycomb lattices with circular air holes in dielectric or circular GaAs rods in air. The eigen value equation of TE and TM modes will presented. The Fourier transform of dielectric constant will analyzed and the effects of lattice type will discussed. The eigenvalue equations of TE and TM modes will solved using Matlab environment. Our results show 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, this work showed the significant effect of the dielectric constant and the lattice constant on the achieved bandwidth.