平面随机复合材料中极性本征模的安德森局域化
Anderson Localization of Polar Eigenmodes in Random Planar Composites
摘要：
无序介质中经典波的安德森局域化是近三十年来引起人们关注的一个基本物理现象。最近，在纳米结构的金属-电介质薄膜（也称为随机平面复合材料）中的极性激发的局部化已经成为深入研究的主题。平面复合材料的潜在应用包括局部近场显微镜和光谱学。许多以前的研究依赖于准静态近似和直接类比的电子在无序固体中的局域化。在这里，我考虑没有准静态近似的本地化问题。我表明，本地化的极性激发的特点是代数，而不是指数空间限制。这个结果在二维和三维中也是有效的。我还表明，以前使用的本地化标准的基础上本征模式的回转半径是不一致的指数和代数本地化。提出了一种基于偶极参与数的替代判据。给出了定域-离域转变的数值演示。最后，它表明，与以前的信念，本地化模式可以有效地耦合到运行波。
英文摘要：
Anderson localization of classical waves in disordered media is a fundamental physical phenomenon that has attracted attention in the past three decades. More recently, localization of polar excitations in nanostructured metal-dielectric films (also known as random planar composite) has been subject of intense studies. Potential applications of planar composites include local near-field microscopy and spectroscopy. A number of previous studies have relied on the quasistatic approximation and a direct analogy with localization of electrons in disordered solids. Here I consider the localization problem without the quasistatic approximation. I show that localization of polar excitations is characterized by algebraic rather than by exponential spatial confinement. This result is also valid in two and three dimensions. I also show that the previously used localization criterion based on the gyration radius of eigenmodes is inconsistent with both exponential and algebraic localization. An alternative criterion based on the dipole participation number is proposed. Numerical demonstration of a localization-delocalization transition is given. Finally, it is shown that, contrary to the previous belief, localized modes can be effectively coupled to running waves.
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