Investigating the dispersive properties of the three-dimensional photonic crystals with face-centered-cubic lattices containing epsilon-negative materials

In this paper, dispersive properties of three-dimensional (3D) photonic crystals (PCs) with face-centered-cubic (fcc) lattices composed of the isotropic positive-index materials and epsilon-negative materials are theoretically investigated based on a modified plane wave expansion (PWE) method. The eigenvalue equations of such structure (spheres with epsilon-negative materials inserted in the dielectric background) are deduced. The band structures can be obtained by solving such nonlinear eigenvalue equations. It can be obviously seen that a photonic band gap (PBG), a flat band region, and two stop band gaps (SBGs) in the Г-X and Г-L directions appear, respectively. The results show that the upper edges of flat band region cannot be tuned by any parameters except for the electronic plasma frequency. The first PBG and the first SBGs above the flat band region in the Г-X and Г-L directions for the 3D PCs can be modulated by the filling factor, relative dielectric constant and electronic plasma frequency, respectively. However, the damping factor has no effect on the locations of the first PBG and the first SBGs above the flat band region in the Г-X and Г-L directions. These results may provide theoretical instructions to design the future optoelectronic and communication devices containing epsilon-negative materials.