Our numerical simulation results demonstrate that 2D lattices compounding can create either a broad single complete photonic band gap or both first and second order complete band gaps. The results also show that photonic band gap properties are dependent on both the parameters of the single lattices and the relative position of the two compound lattices. Furthermore, if a compound structure is composed of two sets of lattices, the one with a larger periodic constant (a2) will serve as defects. While the defect modes are direction independent as a2 > 5 a, they are direction dependent as a2 < 5 a. Moreover, by optimizing of the rod size of the lattice with a2, many kinds of defect modes can be obtained to satisfy the different applications. The transmitted spectra and reflected spectra of this kind of structures demonstrate that the transmittances of the defect modes are dependent a2.
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