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Register a new userObservation of Intensity Statistics of Light Transmitted Through 3D Random Media
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We experimentally observe the spatial intensity statistics of light transmitted through three-dimensional isotropic scattering media. The intensity distributions measured through layers consisting of zinc oxide nanoparticles differ significantly from the usual Rayleigh statistics associated with speckle, and instead are in agreement with the predictions of mesoscopic transport theory, taking into account the known material parameters of the samples. Consistent with the measured spatial intensity fluctuations, the total transmission fluctuates. The magnitude of the fluctuations in the total transmission is smaller than expected on the basis of quasi-one-dimensional (1D) transport theory, which indicates that quasi-1D theories cannot fully describe these open three-dimensional media.
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Waves propagating through a weakly scattering random medium show a pronounced branching of the flow accompanied by the formation of freak waves, i.e., extremely intense waves. Theory predicts that this strong fluctuation regime is accompanied by its own fundamental length scale of transport in random media, parametrically different from the mean free path or the localization length. We show numerically how the scintillation index can be used to assess the scaling behavior of the branching length. We report the experimental observation of this scaling using microwave transport experiments in quasi-two-dimensional resonators with randomly distributed weak scatterers. Remarkably, the scaling range extends much further than expected from random caustics statistics.
We study theoretically the mutual information between reflected and transmitted speckle patterns produced by wave scattering from disordered media. The mutual information between the two speckle images recorded on an array of N detection points (pixels) takes the form of long-range intensity correlation loops, that we evaluate explicitly as a function of the disorder strength and the Thouless number g. Our analysis, supported by extensive numerical simulations, reveals a competing effect of cross-sample and surface spatial correlations. An optimal distance between pixels is proven to exist, that enhances the mutual information by a factor Ng compared to the single-pixel scenario.
We establish a fundamental relationship between the averaged density of states and the extinction mean free path of wave propagating in random media. From the principle of causality and the Kramers-Kronig relations, we show that both quantities are connected by dispersion relations and are constrained by a frequency sum rule. The results are valid under very general conditions and should be helpful in the analysis of measurements of wave transport through complex systems and in the design of randomly or periodically structured materials with specific transport properties.
Structures with heavy-tailed distributions of disorder occur widely in nature. The evolution of such systems, as in foraging for food or the occurrence of earthquakes is generally analyzed in terms of an incoherent series of events. But the study of wave propagation or lasing in such systems requires the consideration of coherent scattering. We consider the distribution of wave energy inside 1D random media in which the spacing between scatterers follow a Levy $alpha$-stable distribution characterized by a power-law decay with exponent $alpha$. We show that the averages of the intensity and logarithmic intensity are given in terms of the average of the logarithm of transmission and the depth into the sample raised to the power $alpha$. Mapping the depth into the sample to the number of scattering elements yields intensity statistics that are identical to those found for Anderson localization in standard random media. This allows for the separation for the impacts of disorder distribution and wave coherence in random media.
Apart from the difficulty of producing highly scattering samples, a major challenge in the observation of Anderson localization of 3D light is identifying an unambiguous signature of the phase transition in experimentally feasible situations. In this letter we establish a clear correspondence between the collapse of the conductance, the increase in intensity fluctuations at the localization transition and the scaling analysis results based on the Thouless number, thus connecting the macroscopic and microscopic approaches of localization. Furthermore, the transition thus inferred is fully compatible both with the results based on the eigenvalue analysis of the microscopic description and with the effective-medium Ioffe-Regel criterion.
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