一维光子晶体的有效折射率

Effective Refractive Index of a Finite One-Dimensional Photonic Crystal

本文针对有限周期的一维光子晶体引入了有效折射率的概念.利用传输矩阵的方法计算了光子晶体的复透射系数,在此基础上进一步得到了有效折射率的解析表达式.考虑到光子晶体的特殊空间结构及其存在光子禁带的特性,进而探讨了光子晶体带隙结构的特征及其有效折射率与光子晶体单层材料的折射率、光学厚度、物理厚度和中心波长的关系.研究发现组成单层材料的两种介质的折射率的比值和单层材料的物理厚度影响有效折射率的振荡幅度,单层材料的光学厚度影响有效折射率的振荡周期.中心波长对有效折射率无影响.

The effective refractive index of finite one-dimensional photonic crystal(PC) was investigated.Firstly,the concept of a complex effective refractive index for the structure of finite periodic PC was introduced.Then the complex transmission coefficient was calculated by using the transfer matrix method.On this basis,analytical expression of the effective refractive index could be derived.Considered by the spatial structure of photonic crystal and the existence of photonic band-gap,the characteristics of photonic band-gap structure,the effective refractive index,optical thickness,physical thickness and the center wavelength were investigated.It is found that amplitude of oscillation for the effective refractive index can be effected by the ratio of refractive index of the basic periodic structure and the physical thickness of the basic periodic structure of PC;Center wavelength has no effect on the effective refractive index.