****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.
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.
We explore and control our environment and stay in touch with one another via waves such as light, sound, microwave radiation and quantum mechanical electron waves. Such waves flow freely through empty space or ordered structures but are impeded by scattering in the disorder of the world around us. We have broken wave transmission into its components seen from a number of different perspectives, which taken separately and together give a rich picture of wave transport. These perspectives are (1) the speckle patterns of the field that fluctuate rapidly in space, (2) the modes of wave oscillation within of random media that are like the harmonics of a violin string, and (3) the natural transmission channels through random systems. Working with high school students, undergraduate and graduate students and postdoctoral fellows we have determined the spatial structure and evolution with frequency shift of speckle patterns, found the frequencies and width of modes of oscillation of the field and the variation of the field of each mode in space, and discovered greatly enhanced transmission and sharp focusing of waves utilizing the transmission channels of the wave. We have found that the spatial patterns of modes in random systems are highly correlated. This explains a wide range of puzzling characteristics of steady-state and pulsed transmission. For example, the delayed onset of transmission through a scattering medium following an incident pulse is due to modes which are close in frequency adding together in such a way that the total wave nearly disappears at early times. At later times, the decay rate of transmitted energy is explained by the decay of increasingly prominent long-lived modes inside the medium. We also determined the values of transmission of individual channels of the transmission matrix and achieved nearly complete transmission in opaque diffusive samples. Modal properties hold the key to molding the absorption and emission of light from materials while channel properties control transmission and focusing. Thus, understanding the fundamental basis of propagation in terms of modes and channels will find a wide array of applications. The students and postdoctoral fellows in our group obtain the training that enables them to enter a wide variety of careers in research. The two students that received their Ph.D. degrees with the support of this grant, have taken jobs in a photonics firm, Chiral Photonics, and at the Wellman Center at Harvard, where they are respectively, developing new approaches coupling to optical fibers to photonic integrated circuits and new speckle imaging modalities. The high school student who went on to work in our lab as an undergraduate is continuing to study waves in random systems and patterns as a graduate student in computer science at Yale. The postdocs have gone on to research positions at JDS Uniphase and Argonne National Labs and as an Assistant Professor in Engineering at University of Rennes. Many high school students have gotten their first taste of research in our group.
