Speckle Evolution and Modes in Random Media

****非技术摘要****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与彼此保持联系。这样的波在空旷的空间或有序的结构中自由流动，但在我们周围无处不在的无序世界中被散射所阻碍。由于散射，通过无序样本传输的波在空间中波动很大。它们产生一种独特的随机散斑强度模式，这是随机样本的独特指纹。然而，在任何一种波的输运中都有共同的要素。微波和光学测量表明，输运的每一个统计性质都可以用一个参数来表征，而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无序捕获的局部波之间转换的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模式。将对这些模式进行分析，以找到波的潜在振荡模式，这类似于小提琴弦的基本振动，以及通过不透明样品的允许传输通道。从不同的角度对波的传播进行研究，将使我们对波的传播有更全面的了解，并将其应用于电信、纳米电子、光子学和成像等领域。此外，微波和光学测量将由高中生、本科生和研究生以及一名博士后进行。因此，这个项目将为年轻的研究人员提供一个令人兴奋的训练场地。****技术摘要****波在无序样品中的传播性质反映了介质内模态的空间和频谱变化。当模态被光谱隔离时，样品内部的强度呈指数峰值。然而，频谱重叠的模式可能会延伸到整个样品。但是随机样本内部的波是隐藏在视线之外的。该奖项支持一个项目，该项目将尝试克服这一限制，通过使用微波和光学测量传输散斑模式的转换与频移，揭示从局域传输到扩散传输的随机系统的潜在电磁模式和传输通道。对散斑模式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，诸如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的传输系数。这将给出定位转变的另一种描述，并将促进将允许适当相控光通过不透明样品的强传输的策略。这项工作将加强为提高纽约大都会地区的技术基础而建立的纽约市立大学光子中心。来自当地高中和本科生的学生，以及研究生和更高级的研究人员将积极参与实验室。他们的事业将通过研究来促进，这些研究结合了微波和光学技术来探索各种各样的基础和应用兴趣问题。

****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.