The anisotropic photonic band gaps in three-dimensional photonic crystals with high-symmetry lattices composed of metamaterials and uniaxial materials

In this paper, the properties of anisotropic photonic band gaps (PBGs) for three-dimensional (3D) photonic crystals (PCs) composed of tellurium (Te) spheres (the uniaxial materials) in homogeneous single-negative metamaterials (epsilon-negative materials) background with high-symmetry (simple-cubic) lattices are theoretically investigated based on the plane wave expansion method. The equations for calculating the anisotropic PBGs in the first irreducible Brillouin zone are theoretically deduced. The influences of the ordinary-refractive index, extraordinary-refractive index, filling factor of dielectric, the electronic plasma frequency, the dielectric constant of epsilon-negative materials on the anisotropic PBGs are also studied in detail, respectively, and some corresponding physical explanations are also given. The numerical results show that the anisotropy can open partial band gaps in simple-cubic lattices and the complete PBGs also can be achieved compared to such 3D PCs doped by the conventional isotropic materials. It also is shown that the anisotropic PBGs can be manipulated by the parameters as mentioned above. Introducing the uniaxial materials into 3D dielectric-epsilon-negative materials PCs can enlarge the PBGs, and also provide a way to obtain the complete PBGs as such kind of 3D PCs with high-symmetry lattices.