Studies Of Photonic Band Gap In The Face-centered Cubic Lattice Of Non-closed-packed Hollow Spheres

Photonic crystal is a new type of optical material with photonic bandgap. Because of their peculiar properties in controlling photonic propagation,they have tremendous applications or potential applications in optical fibercommunication, photonic computer and other fields.The width and the middle gap frequency of photonic band gap aredetermined by the photonic crystal structures, which influence the photonicproperties directly. Up to now, the enthusiasm for finding novel photonicband structures, which possess wide photonic band gaps and low criticaldielectric contrast, is still undiminished.In this work, we designed a new type of photonic crystal structures,which consist of hollow-spheres located at face-centered cubic lattice sitesand each sphere connected to all of its 12 nearest neighbors by cylindricalrods. We called the new topological network hollow-sphericalnon-closed-packed structure (HNS). Theoretical calculations show that thiskind of structure exhibits two large complete photonic band gaps: one isbetween the eighth and ninth bands with the maximum photonic band gap ofΔω/ω0 = 17.3% and the critical dielectric contrast of ε = 5.8;the other isbetween the thirteen and fourteen bands, which does not exist in otherstructures reported in previous paper, and it possess the maximum photonicband gap of Δω/ω0 = 15.1% and a critical dielectric contrast of ε = 7.3.There even exists a case where two complete band gaps coexist if theparameters take proper values. We also investigated the influence ofdielectric contrast and structure parameters in the structure on the gap sizeand the mid gap frequency. We find that the mid gap frequency decreases(increases) with the increasing (decreasing) of the total volume fraction ofthe dielectric material.We present a method based on a combination of colloidal self-assembly,thermal sintering, etching, infiltrating and template technique to achieve thesubmicroscopic crystal of HNS. However, theoretical calculations show thatit does not possess a complete photonic band gap in the structure obtainedfrom the experiment as described. Because the ratios of the structureparameters only take special values, they could not satisfy the requirement ofappearance of photonic band gap. We calculate and optimize the bandstructure of HNS only when the thickness of the sphere shells equals to thatof tube walls and the dielectric contrast, ε, equals to 7.84. The results showthat it only presents one band gap between the eighth and ninth bands. Themaximum width of the band gap could reach 9.1% and the critical dielectriccontrast for the existence of the band gap is only 5.3, which is lower than thatof other face-centered-cubic structures.