准光光束的安德森局域化

IF 0.7 4区 地球科学 Q4 ENGINEERING, ELECTRICAL & ELECTRONIC
V. A. Mironov, D. A. Fadeev
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引用次数: 0

摘要

本文分析研究了波束在具有随机参数的均匀波导结构中传播的统计(安德森)局域化。我们详细探讨了在连续介质极限下随机非均匀介质中波场衍射展宽的抑制。对亥姆霍兹方程进行统计平均,得到了平均场的色散方程。色散方程的结构与抛物线色散定律(准光学近似中均匀介质的典型)有很大的不同。由这个方程定义的波矢量的表面(折射率表面)有曲率改变符号的点。在波过程理论中,这表明在所谓的空间特殊方向上传播的波束的衍射受到抑制,这与安德森局域化相对应。在将场表示为横波数上初始分布谱的傅里叶积分的基础上,考虑了这种波束的演化。积分的渐近计算表明,安德森局域化是由艾里光束描述的。对过渡区进行了数值研究。在离散问题的情况下也可以得出类似的结论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On Anderson Localization of Quasi-Optical Wave Beams

We study analytically the statistical (Anderson) localization of the wave beam propagating in a structure of evenly placed waveguides with random parameters. We explore in detail the suppression of the diffraction broadening of the wave field in a randomly inhomogeneous medium in the continuum limit. A dispersion equation for the mean field is obtained from statistical averaging of the Helmholtz equation. The structure of the dispersion equation considerably differs from the parabolic dispersion law (typical of homogeneous media in the quasioptical approximation). The surface of the wave vectors defined by this equation (the refractive-index surface) has points where the curvature changes sign. In the theory of wave processes, this indicates that the diffraction is suppressed for the wave beams propagating in the so-called special directions in space, which corresponds to the Anderson localization. Evolution of such wave beams is considered on the basis of presenting the field as the Fourier integral of the spectrum of initial distribution over the transverse wave number. The asymptotic evaluation of the integral shows that the Anderson localization is described by the Airy beams. The transition region is studied numerically. Similar conclusions are also drawn in the case of a discrete problem.

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来源期刊
Radiophysics and Quantum Electronics
Radiophysics and Quantum Electronics ENGINEERING, ELECTRICAL & ELECTRONIC-PHYSICS, APPLIED
CiteScore
1.10
自引率
12.50%
发文量
60
审稿时长
6-12 weeks
期刊介绍: Radiophysics and Quantum Electronics contains the most recent and best Russian research on topics such as: Radio astronomy; Plasma astrophysics; Ionospheric, atmospheric and oceanic physics; Radiowave propagation; Quantum radiophysics; Pphysics of oscillations and waves; Physics of plasmas; Statistical radiophysics; Electrodynamics; Vacuum and plasma electronics; Acoustics; Solid-state electronics. Radiophysics and Quantum Electronics is a translation of the Russian journal Izvestiya VUZ. Radiofizika, published by the Radiophysical Research Institute and N.I. Lobachevsky State University at Nizhnii Novgorod, Russia. The Russian volume-year is published in English beginning in April. All articles are peer-reviewed.
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