We also reveal information about the local direction of the polarization in the proximity of subwavelength scattering elements, and find nonuniversal correlations between its components. For a simple scattering medium made of dielectric nanoparticles in an aqueous environment, we find that the size of the speckle that is formed inside the random sample is almost two times smaller than that expected from existing theories-a result which we can attribute to a combination of polarization and near-field effects. The experimental results for both scattering and non-scattering media are compared to full-wave 3D numerical calculations which allows to unveil several unexpected phenomena. We use a new technique (also introduced in this paper) that allows to measure such correlations at a nm-controlled distance, based on embedded emitters separated by DNA strings of calibrated length. In this work, we present an experimental study, supported by numerical calculations, on two-point intensity correlations of the optical fields inside bulk 3D random media. More importantly, it will allow us to relate the optical properties that we observe from the outside to what is happening inside a photonic medium, which can help the design of new materials and devices with tailored photonic functionalities. Connecting the spatial and polarimetric properties of bulk light fields to the structural information of a sample will deepen our understanding of optical transport phenomena, effective-medium theories, intensity, and polarization correlations. Gaining access to the distribution of light inside complex photonic media is important for a series of reasons. As a result, certain optical properties of complex media remain particularly hard to investigate even numerically, which explains why we have only recently started to unveil several unexpected aspects of light propagation and transmission inside disordered media 23, 24, 25, 26, 27. In addition to the experimental difficulties, also the theoretical description of light propagation inside 3D nanostructured material is a challenging task, requiring to address a broad range of length scales (from subwavelength resonances to the scaling of transport properties to increasing system size), coupling of vector-wave components in three dimensions, nonuniversal, and possibly even nonlocal effects 14, 21, 22. As a matter of fact, even nonspatially resolved information available to date is limited to lifetime statistics studies 19, 20. While the advent of near-field microscopy has pushed the limits of such measurements down to the immediate vicinity of the outer surface of a scattering material 13, 14, 15, 16, most information about the nature of spatial intensity fluctuations inside a three-dimensional (3D) medium remains precluded due to the invasive nature of conventional near-field detection techniques 17, 18. The key features of speckle patterns are the length scales over which they fluctuate, which can be measured looking at the decay of the intensity spatial correlation function \(C_2)\rangle\). The existence of these granular structures became apparent since the invention of laser 1, 2 and yet up to these days we still keep learning about their fundamental properties 3, 4, 5 and the range of applications they enable, spanning from imaging 6, 7, 8, 9, 10 to spectroscopy 11 and cryptography 12, to name a few. When subject to multiple scattering, propagating electromagnetic waves will, in general, accumulate random and uncorrelated phase delays resulting in a fluctuating profile known as speckle pattern. The deviations are explained, by comparison with rigorous numerical calculations, in terms of correlations among polarization components and non-universal near-field contributions at the nanoscale. Our method provides in situ access to fundamental properties of bulk speckles as their size and polarization degrees of freedom, both of which are found to deviate significantly from theoretical predictions. Here we report on the first direct measurements of spatially resolved intensity correlations of light inside a disordered medium, using embedded DNA strings decorated with emitters separated by a controlled nanometric distance. Furthermore, its proper theoretical description poses enormous challenges. While speckle formed outside a sample is easily measured and analysed, true bulk speckle, as formed inside random media, is difficult to investigate directly due to the obvious issue of physical access. Speckle is maybe the most fundamental interference effect of light in disordered media, giving rise to fascinating physical phenomena and cutting edge applications.
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