Enhanced the Complete Photonic Band Gaps for Three-Dimensional Photonic Crystals Consisting of Epsilon-Negative Materials in Pyrochlore Arrangement

In this paper, the properties of photonic band gaps (PBGs) for three-dimensional (3D) photonic crystals (PCs) composed of isotropic positive-index materials and epsilon-negative materials with pyrochlore lattices are theoretically investigated by a modified plane wave expansion method. The eigenvalue equations of calculating the band structures for such 3D PCs in the first irreducible Brillouin zone (spheres with the isotropic positive-index materials inserted in the epsilon-negative materials background) are theoretically deduced. Numerical simulations show that the PBG and a flatbands region can be achieved. It is also found that larger PBG can be obtained in such PCs structure than the conventional lattices, such as diamond, face-centered-cubic, body-centered-cubic and simple-cubic lattices. The influences of the relative dielectric constant of spheres, filling factor, electronic plasma frequency, dielectric constant of epsilon-negative materials and damping factor on the properties of PBG for such 3D PCs are studied in detail, respectively, and some corresponding physical explanations are also given. The calculated results also show that the PBG can be manipulated by the parameters mentioned above except for the damping factor. Introducing the epsilon-negative materials into 3D dielectric PCs can obtain the complete and larger PBG as such 3D PCs with pyrochlore lattices, and also provides a way to design the potential devices.