Band Structure Of Three-dimensional Photonic Crystal Consisting Of Dielectric Spheres A Plane-wave Approach

In recent years there has been a fast development in the research of photonic crystals, and many works have been done both in theories and experiments. Photonic crystals have the properties of photonic band gap and localization, and many potential applications in communication can be expected. To find a photonic crystal structure with a large absolute gap is still one of research direction in this field.Using the plane-wave method, we calculate the band structure and transmission characteristics of the three-dimensional photonic crystals. For a SiO₂ opal and invers-opal photonic crystals, we calculate the energy spectrums and the transmissions feature of electromagnetic waves. We found SiO₂ opal has a stop gap along the (111) direction using both the plane-wave method and transfer-matrix method,the obtained results are consistent with each other. If the dielectric ratio is large enough, a full band gap between eighth and ninth band can be achieved for anti-opal crystals, which is in agreement with the results from Yablonovitch et.al .For an fcc lattice of core-shell sphere, it is shown that the relative L-gap width of a suitable coating of dielectric spheres with lower dielectric materials can be increased. When a dielectric sphere consists of two layers of dielectric, the relative L-gap width can be increased by 46% as compared with that of homogeneous high-dielectric spheres. And we also find that the optimum radius ratio between interior and entire spheres is 0.69. When a dielectric sphere consists of three layers of dielectric, the relative band-gap width depends mainly on the radius R₂ of intermediate layer, and little effect by radius R₁. As the radius ratio R₂/R₁ , R₃/R₁ is 0.65, 0.45 respectively, the relative band-gap width approaches the maximum, and it enhances about 60 per than which is obtained from only two layers of dielectric sphere.Finally, we discuss the band structure of photonic crystals made of multiple lattices. And we achieve a full photonic band gap for diamond crystals between second and third bands, which is in good agreement with the results from Ho.K.M et.al.for NaCl-like crystals, we do not find a photonic band gap.