Anderson Localization of Classical Waves in Weakly Scattering Metamaterials
Ara A. Asatrian, Sergey A. Gredeskul, Lindsay C. Botten, Michael A. Byrne, Valentin D. Freilikher, Ilya V. Shadrivov, Ross C. McPhedran, Yuri S. Kivshar
We study the propagation and localization of classical waves in one-dimensional disordered structures composed of alternating layers of left- and right-handed materials (mixed stacks) and compare them to the structures composed of different layers of the same material (homogeneous stacks). For weakly scattering layers, we have developed an effective analytical approach and have calculated the transmission length within a wide region of the input parameters. When both refractive index and layer thickness of a mixed stack are random, the transmission length in the long-wave range of the localized regime exhibits a quadratic power wavelength dependence with the coefficients different for mixed and homogeneous stacks. Moreover, the transmission length of a mixed stack differs from reciprocal of the Lyapunov exponent of the corresponding infinite stack. In both the ballistic regime of a mixed stack and in the near long-wave region of a homogeneous stack, the transmission length of a realization is a strongly fluctuating quantity. In the far long-wave part of the ballistic region, the homogeneous stack becomes effectively uniform and the transmission length fluctuations are weaker. The crossover region from the localization to the ballistic regime is relatively narrow for both mixed and homogeneous stacks. In mixed stacks with only refractive-index disorder, Anderson localization at long wavelengths is substantially suppressed, with the localization length growing with the wavelength much faster than for homogeneous stacks. The crossover region becomes essentially wider and transmission resonances appear only in much longer stacks. All theoretical predictions are in an excellent agreement with the results of numerical simulations.
Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials
我们总结了我们的全面的分析和数值研究的结果，极化的安德森局域化的经典波在一维随机堆栈的影响。我们考虑完全由正常材料或超材料组成的均匀堆叠，以及由正常材料和超材料的交替层组成的混合堆叠。我们推广了以前对正入射情况的理论研究[A. A. Asatryan等人，Phys.Rev.B81，075124（2010）]中的方法与离轴入射的情况相比较。对于一般情况下，折射率和层厚度都是随机的，我们得到的长波和短波渐近的本地化长度在很宽的入射角范围内（包括布鲁斯特“异常”角）。在布鲁斯特角，我们表明，长波本地化长度是成比例的波长的平方，为正常入射的情况下，但与比例系数大大大于正常入射。在只有折射率无序的混合堆栈中，我们证明了p-偏振波是强烈本地化的，而对于s-偏振的本地化基本上被抑制，在正常入射的情况下。在只有厚度无序的情况下，我们还研究了从本地化到离域在布鲁斯特角的过渡。
