Speckle Evolution and Modes in Random Media

*非技术抽象*我们探索和控制我们的环境，并通过光、声、量子力学电子波和微波辐射等波保持联系。这样的波在空旷的空间或有序的结构中自由流动，但在我们周围世界普遍存在的无序中被散射所阻碍。在无序样品中传播的波由于散射而在空间中剧烈起伏。它们产生强度的唯一随机斑纹图案，这是随机样本的唯一指纹。然而，对于任何类型的波，在传输过程中都有共同的要素。微波和光学测量表明，输运的每个统计性质都可以用一个参数来表征，并且所有这些参数都是简单相关的。这些参数的值反映了在自由扩散波和被样品内无序捕获的局域波之间的过渡中波的空间范围的变化。该奖项支持一个项目，该项目将使用微波和光学测量来获得不同频率的辐射散斑图案。这些模式将被分析，以找到波的潜在振荡模式，类似于小提琴弦的基本振动，以及允许通过不透明样本传输的通道。从不同的角度对波的传播进行研究，将使我们对波的传播及其在电信、纳米电子、光子学和成像等领域的应用有更全面的了解。此外，微波和光学测量将由高中生、本科生和研究生以及博士后进行。因此，该项目将为年轻研究人员提供一个激动人心的培训场所。*技术摘要*无序样品中波传播的性质反映了介质中模式的空间和频谱变化。当模式被光谱隔离时，样品内部的强度以指数形式达到峰值。但是，在光谱上重叠的模式可能会延伸到整个样本。但随机样本内部的波是看不见的。该奖项支持一个项目，该项目将试图通过使用微波和光学测量传输的散斑图案与频移的转换来揭示从局域传输到扩散传输的过渡过程中随机系统的基本电磁模式和传输通道，从而克服这一限制。散斑图案的分析将使计算波通过随机介质的所有传输特性成为可能。如果成功，局域波的动力学或散斑演化的统计等问题将得到解决，这些问题由于偶尔涉及重叠模式而无法进行全面的理论分析。将找到传输矩阵的特征信道和相关联的传输系数。这将给出本地化转变的另一种描述，并将促进允许适当相移的光通过不透明样品的强透射率的策略。这项工作将加强为加强纽约大都会地区的技术基础而建立的城市大学光子中心。来自当地高中和本科生的学生以及研究生和更多的高级研究人员将积极参与到实验室中来。他们的职业生涯将通过研究来促进，研究将微波和光学技术结合起来，探索一系列基本和应用感兴趣的问题。

****NON-TECHNICAL ABSTRACT****We explore and control our environment and stay in touch with one another via waves such as light, sound, quantum mechanical electron waves, and microwave radiation. Such waves flow freely through empty space or ordered structures but are impeded by scattering in the pervasive disorder of the world around us. Waves transmitted through disordered samples fluctuate wildly in space due to the scattering. They produce a unique random speckle pattern of intensity, which is a unique fingerprint of the random sample. Nevertheless, there are common elements in the transport for any kind of wave. Microwave and optical measurements demonstrate that each statistical property of transport can be characterized by a single parameter and all such parameters are simply related. The value of these parameters reflects the changing spatial extent of the wave in a transition between freely diffusing and localized waves trapped by disorder within the sample. This award supports a project that will use microwave and optical measurements to obtain the speckle pattern of radiation for different frequencies. The patterns will be analyzed to find the underlying modes of oscillation of the wave, which are akin to the fundamental vibrations of a violin string, as well as the allowed channels for transmission through opaque samples. Approaching the study of wave propagation from different perspectives will lead to a more complete understanding of wave propagation with applications to telecommunications, nano-electronics, photonics and imaging. In addition the microwave and optical measurements will be carried out by high school students, undergraduates and graduate students, and by a postdoctoral fellow. Thus, this project will provide a stimulating training ground for young researchers. ****TECHNICAL ABSTRACT****The nature of wave propagation in disordered samples reflects the spatial and spectral variation of the modes within the medium. When modes are spectrally isolated, the intensity inside the sample is exponentially peaked. However, modes that overlap spectrally may extend throughout the sample. But the wave in the interior of a random sample is hidden from view. This award supports a project that will attempt to overcome this limitation by using microwave and optical measurements of the transformation of transmitted speckle patterns with frequency shift to reveal both the underlying electromagnetic modes and the transmission channels of random systems in the transition from localized to diffusive transport. Analysis of the speckle patterns will enable the calculation of all transmission properties of the waves through the random media. If successful, problems such as the dynamics of localized waves or the statistics of speckle evolution, which have eluded a full theoretical analysis because they involve occasionally overlapping modes, will be resolved. The eigenchannels of the transmission matrix and associated transmission coefficients will be found. This will give an alternate description of the localization transition and will facilitate strategies that will allow for strong transmission of properly phased light though opaque samples. This work will strengthen the CUNY Photonic Center established to enhance the technological base of the New York metropolitan area. Students from local high schools and undergraduates, as well as graduate students and more senior researchers will be actively engaged in the laboratory. Their careers will be fostered by research, which combines microwave and optical techniques to probe a diverse set of problems of fundamental and applied interest.