无序和斐波那契序列的二进制波导阵列的安德森局域研究

Anderson localization in random and Fabonacci quasi-periodic binary waveguide array

为了研究相关性对电磁波的安德森局域现象的影响,该文根据无序序列构造了无序一维二进制波导阵列结构、根据斐波那契序列构造了准周期一维二进制波导阵列结构。利用分析转移矩阵方法分别计算了上述2种结构中横电模式的透过率、局域长度和电场的空间分布,并利用一维矩形微波波导进行了相关的实验。根据无序序列构造的无序二进制波导阵列结构的透射共振峰与周期性结构一一对应,位于带边的模式首先转为局域态;根据斐波那契序列构造的准周期二进制波导阵列结构的传输特性与组成阵列的具体单元结构无关,电磁场能量通过分布在空间中不同位置的局域态之间的耦合传输形成离散的传输态。

In order to investigate the effect of correlation on Anderson localization in electromagnetic waves,a random one-dimensional binary waveguide array is proposed based on a random binary sequence , and a quasi-periodic one-dimensional binary waveguide array is proposed based on a Fibonacci sequence .The transition, localization length and the spectra of the electrical field amplitude of tranverse electric （ TE） mode for the two one-dimensional binary waveguide arrays are calculated using transfer matrix method .Experiments are carried out using one-dimensional rectangular microwaves waveguide structure .The peaks of transmission spectrum of the random one-dimensional binary waveguide array proposed based on a random binary sequence are identical with those of periodic waveguide arrays ,the modes near the band edges become localized;the propagation characteristics of the quasi-periodic one-dimensional binary waveguide array proposed based on a Fibonacci sequence is independent of its basic unit , and electromagnetic energy is transferred discretely through the coupling between the spatial distributed localizations .