NSF/DMR/-BSF: Universality and Control of Wave Propagation Inside Random Media

摘要：无论是声波、电波还是光波的散射，都是我们生活环境中不可避免的一部分。当这种环境紊乱时，电波会沿着许多不同的路径散射，这会损害我们沟通、成像或激发电子电路的能力。本项目将研究波在无序介质中的传播，采用理论与模拟相结合的实验方法。作为NSF/DMR-BSF项目的一部分，PI与Bar-Ilan大学的Patrick Sebbah小组合作开展了这项工作。这项工作将集中于发展波在有限随机介质中的传播的通用描述，并将为学生提供一个很好的训练基地。这项工作的结果也将对凝聚态物理、声学和光学等一系列跨学科问题产生广泛的影响。技术摘要：提出的研究扩展了波传播的普遍描述范围，从无序介质边界的反射波和透射波到样品内部，从比平均自由程厚许多倍的样品到传播几乎是弹道的样品。传输的现象学特性，如传输尺度所依赖的外推长度，将与通用参数（如不同传输特征信道的辅助定位长度）相关。这些参数仅依赖于样本长度与定位长度和特征通道数的比值。研究的一个重要方面是找到传输本征通道、介质中波的模式和具有位置依赖扩散系数的广义扩散方程的解之间的关系。这些方法之间的关系为控制随机介质和无序超材料中的波提供了关键线索。这种对无序介质内部波的控制为改善成像、资源勘探、体内局部加热、电信和低阈值随机激光提供了一条途径。研究了一类新的准一维散射样品的特性，其中局部态密度在样品内部消失，以了解态密度与局域化的关系。这为定位波和将区域与周围环境隔离提供了新的途径。

Nontechnical Abstract: The scattering of waves, whether acoustic, radio or optical, is an inescapable part of our environment. When this environment is disordered the wave can scatter along many different paths and this can impair our ability to communicate or to image or excite electronic circuits. This project will study the propagation of waves through disordered media using a combination of experimental approaches supplanted by theory and simulations. The effort is a collaboration between the PI and the group of Patrick Sebbah at Bar-Ilan University as part of the NSF/DMR-BSF program. The work will focus on developing a universal description of wave propagation in finite random media and will provide an excellent training ground for students. The results of this work will also have a broad impact on a range of interdisciplinary problems in condensed matter physics, acoustics and optics.Technical Abstract: The proposed research extends the range of a universal description of wave propagation from the reflected and transmitted wave at the boundaries of disordered media into the interior of the sample and from samples many times thicker than the mean free path to samples so thin that propagation is nearly ballistic. Phenomenological properties of transmission, such as the extrapolation length, upon which the scaling of transmission depends, will be related to universal parameters such as auxiliary localization lengths of different transmission eigenchannels. These parameters depend only on the ratio of sample length and the localization length and the eigenchannel number. An important aspect of the research is finding the relationship between the transmission eigenchannels, modes of waves in the medium, and solutions of a generalized diffusion equation with a position-dependent diffusion coefficient. The relationship between these approaches provides key clues to the control the wave within random media and disordered metamaterials. Such control of the wave inside disordered media provides a path towards improved imaging, resource exploration, local heating within the body, telecommunications, and low-threshold random lasing. The characteristics of a new class of quasi-one dimensional scattering sample, in which the local density of states vanishes in the interior of the sample, is investigated to understand the relationship of the density of states and localization. This provides new pathways to localizing waves and isolating regions from the surrounding environment.