左手渐变折射率材料光子晶体的色散研究

Investigation of dispersion characteristics in photonic crystals consisted of left-handed materials with graded-index profiles

利用半解析法和矩量法相结合的数值方法,对含有一维左手渐变折射率材料光子晶体矩形波导的色散特性进行分析。定量地分析了周期结构的重复次数、渐变折射率分布函数类型(常数型、线性型及抛物线型)、及分布函数系数等因素的改变对于色散特性的影响。结果表明,含有一维左手渐变折射率材料光子晶体的矩形波导可以实现完整的带隙特性,而避免了二维或三维光子晶体的制造困难。此外,这种结构支持两个传播通带,一个是高于波导基模截止频率的前向波通带,一个是远低于波导基模截止频率的后向波通带,因此,该结构为支持多通带传播的小型化波导及其相关器件的设计提供了新的思路。

This paper presents a rigorous method combining the semi-analytical method and the method of moments to analyse the dispersion characteristics of rectangular waveguides containing one-dimensional(1 D)periodic photonic crystals(PC)consisted of left-handed materials(LHM)with graded-index profiles.The influence of the repetition of the periodic unit cell,the graded refractive index’s profile functions(constant,linear and parabolic),the coefficients of the profile functions on the dispersion characteristics are quantitatively analysed.The results show that a complete photonic bandgap could be achieved,avoiding the difficulty in fabricating 2 D or 3 D PCs.Moreover,such structure supports two propagation bands;one is the forward wave propagation band above the fundamental mode’s cutoff frequency;another is the backward wave propagation band dramatically lower than the cutoff frequency.Thus,such structures provide a new idea for the miniaturised waveguides’design supporting multiple propagation bands.