Fibonacci序列一维光子晶体色散关系解析解和数值解的对比研究

A Comparative Study of Analytical and Numerical Dispersion Relations of Fibonacci Sequence One-dimensional Photonic Crystals

利用转移矩阵方法给出Fibonacci序列一维光子晶体能带,等频率表面的解析公式,同时给出物理量,如等效相折射率、群速度、波矢量的解析式.利用解析公式以及时域有限差分方法对一维光子晶体的色散关系进行对比研究.结果表明:在强调制一维光子晶体色散关系的计算中,数值方法与解析方法得到的结果总体趋势保持一致.但在弱调制一维光子晶体中,等频率表面的数值结果出现了颠覆性的错误.因而,对于弱调制光子晶体色散关系的数值结果,必须通过解析计算或数值模拟计算等方法进行验证.

A transfer matrix method is used to analytical calculation formulas of photonic band and equifrequency surface of onedimensional Fibonacci sequence photonic crystal.Analytical physical quantities such as equivalent phase refractive index,group velocity and wave vector are given.Dispersion relations of this kind one-dimensional photonic crystal are studied contrastively with formulas and finite difference time domain method.It shows that results obtained by numerical method and analytical method are consistent with each other in overall trend.However,in weakly modulated one-dimensional photonic crystal,fatal error was made in numerical calculation result of equifrequency surfaces.Therefore,numerical results of weakly modulated photonic crystals must be verified with other methods such as analytical calculation or numerical simulation.