Mondal Sandip, Mujumdar Sushil
Opt Lett. 2020 Feb 15;45(4):997-1000. doi: 10.1364/OL.383748.
We report on the relation between the localization length and level-spacing characteristics of two-dimensional (2D) optical localizing systems. Using the tight-binding model over a wide range of disorder, we compute spectro-spatial features of Anderson localized modes. The spectra allow us to estimate the level-spacing statistics while the localization length $ \xi $ξ is computed from the eigenvectors. We use a hybrid interpolating function to fit the level-spacing distribution, whose repulsion exponent $ \beta $β varies continuously between 0 and 1, with the former representing Poissonian statistics and the latter approximating the Wigner-Dyson distribution. We find that the $ (\xi ,\beta ) $(ξ,β) scatter points occupy a well-defined nonlinear locus that is well fit by a sigmoidal function, implying that the localization length of a 2D disordered medium can be estimated by spectral means using the level-spacing statistics. This technique is also immune to dissipation since the repulsion exponent is insensitive to level widths, in the limit of weak dissipation.
我们报告了二维（2D）光学定位系统的局域长度与能级间距特性之间的关系。在广泛的无序范围内使用紧束缚模型，我们计算了安德森局域模的光谱空间特征。光谱使我们能够估计能级间距统计量，而局域长度$\xi$则从特征向量计算得出。我们使用混合插值函数来拟合能级间距分布，其排斥指数$\beta$在0和1之间连续变化，前者代表泊松统计，后者近似维格纳 - 戴森分布。我们发现$(\xi,\beta)$散点占据了一个明确的非线性轨迹，该轨迹可以很好地用一个S形函数拟合，这意味着二维无序介质的局域长度可以通过使用能级间距统计量的光谱方法来估计。由于在弱耗散极限下排斥指数对能级宽度不敏感，所以该技术也不受耗散影响。
