Speckle Evolution and Modes in Random Media

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****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.