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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。
The differential transfer matrix method (DTMM) can solve the wave equation in a one-dimensional inhomogeneous medium. With this method, bandgap analysis of several one-dimensional photonic crystals with continuous and periodic distribution of refractive index has been carried out. The results show that the one-dimensional periodic structure with continuous change of refractive index also has obvious band gap characteristics. The more gradual the change of refractive index, the smaller the width of optical bandgap. For a one-dimensional photonic crystal with a sinusoidally changing refractive index, the refractive index changes more sharply. The smaller the central frequency of the photonic crystal, the wider the bandgap. Meanwhile, the larger the average refractive index, the smaller the center frequency, narrow. As the physical properties of materials are continuously changing, the same structure can be extended to one-dimensional periodic functionally graded materials.