为了研究3维函数光子晶体的光子禁带特性, 采用平面波展开法计算得到色散曲线, 推导了平面波展开法的相关计算公式以及介质球介电常数的函数关系式, 探讨了可调参量函数系数I和介质球半径R1对光子禁带特性的影响。结果表明, 3维函数光子晶体呈立方体晶格分布, 由介质球填充空气背景; 与常规3维介质光子晶体相比, 3维函数光子晶体不仅能得到可调谐的光子禁带, 而且可以拓展禁带带宽, 并增加光子禁带的数量;改变函数系数I的大小可以实现对光子禁带数量、位置和带宽的调谐;改变介质球半径R1可以对光子禁带带宽实现展宽, 并改变光子禁带的位置。该研究对设计新型可调谐器件是有帮助的。

In order to study photonic band gap of 3-D functional photonic crystal, dispersion curve was calculated by using plane wave expansion method. Correlation calculation formula of plane wave expansion method and function relation of dielectric constant of dielectric sphere were derived. The effects of the adjustable parameter I and dielectric sphere radius R1 on photonic band gap were discussed. The result shows that, 3-D function photonic crystal is cube lattice distribution and air background is filled with medium ball. Compared with conventional 3-D dielectric photonic crystals, 3-D function photonic crystal can obtain the tunable photonic band gap, expand the bandwidth of forbidden band, and increase the number of photonic band gaps. The number, position and bandwidth of photonic band gaps can be tuned by changing the size of tunable parameter I. At the same time, the bandwidth and position of photonic band gaps can be tuned by changing the sphere radius R1 of the medium. The study is helpful for the design of new tunable devices.