折射率连续周期分布一维光子晶体的带隙分析

微分传输矩阵法(DTMM)可以解析求解一维非均匀介质中的波动方程。用该方法,对几种折射率连续且周期分布的一维光子晶体进行了带隙分析。结果表明,折射率连续变化的一维周期结构也具有明显的带隙特征,折射率变化越平缓,光带隙的宽度越小。对于折射率正弦变化的一维光子晶体,其折射率变化得越剧烈,光子晶体的中心频率越小,带隙越宽;同时,折射率的平均值越大,中心频率越小,带隙越窄。由于材料的物理特性都是连续变化的,同样可以把结构推广到一维周期性功能梯度材料。

Band Structure Analysis of One-Dimensional Photonic Crystals with Continuous Index of Refraction

Differential transfer matrix method(DTMM) is an efficient tool to solve the wave propagation equation in inhomogeneous media analytically.Using it,the band structure of one-dimensional photonic crystals with continuous indexes of refraction is analyzed.The results show they also have clear band gaps.The more smoothly their refraction indexes change,the narrower their band gaps are.As to the photonic crystals with sine shape index of refraction,the more sharply their indexes of refraction change,the broader their band gaps and low their central frequencies are.The analysis method used is also applicable to one-dimensional periodical functional gradient materials.