By controlling the many degrees of freedom in the incident wavefront, one can manipulate wave propagation in complex structures. Such wavefront-shaping methods have been used extensively for controlling light transmitted into wavelength-scale regions (speckles), a property that is insensitive to correlations in the speckle pattern. Extending coherent control to larger regions is of great interest both scientifically and for applications such as optical communications, photothermal therapy, and the imaging of large objects within or behind a diffusive medium. However, waves diffusing through a disordered medium are known to exhibit non-local intensity correlations, and their effect on coherent control has not been fully understood. Here, we demonstrate the effects of correlations with wavefront-shaping experiments on a scattering sample of zinc oxide microparticles. Long-range correlations substantially increase the dynamic range of coherent control over light transmitted onto larger target regions, far beyond what would be achievable if correlations were negligible. This and other effects of correlations emerge when the number of speckles targeted, M2, exceeds the dimensionless conductance g. Using a filtered random matrix ensemble appropriate for describing coherent diffusion and the lateral spreading in an open geometry, we show analytically that M2/g appears as the controlling parameter in universal scaling laws for several statistical properties of interest---predictions that we quantitatively confirm with experimental data. Our work elucidates the roles of speckle correlations and provides a general theoretical framework for modeling open systems in wavefront-shaping experiments.
Chia Wei Hsu, Seng Fatt Liew, Arthur Goetschy, Hui Cao, and A. Douglas Stone, "Correlation effects in focused transmission through disordered media (Conference Presentation)," Proc. SPIE 10073, Adaptive Optics and Wavefront Control for Biological Systems III, 100730P (Presented at SPIE BiOS: January 29, 2017; Published: 24 April 2017); https://doi.org/10.1117/12.2250352.5380600096001.
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