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Correlation-enhanced control of wave focusing in disordered media


A fundamental challenge in physics is controlling the propagation of waves in disordered media despite strong scattering from inhomogeneities. Spatial light modulators enable one to synthesize (shape) the incident wavefront, optimizing the multipath interference to achieve a specific behaviour such as focusing light to a target region. However, the extent of achievable control is not known when the target region is much larger than the wavelength and contains many speckles. Here we show that for targets containing more than g speckles, where g is the dimensionless conductance, the extent of transmission control is substantially enhanced by the long-range mesoscopic correlations among the speckles. Using a filtered random matrix ensemble appropriate for coherent diffusion in open geometries, we predict the full distributions of transmission eigenvalues as well as universal scaling laws for statistical properties, in excellent agreement with our experiment. This work provides a general framework for describing wavefront-shaping experiments in disordered systems.

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Figure 1: Experimental set-up and representative output patterns.
Figure 2: Correlation effects in wavefront shaping and their universal scaling.
Figure 3: Allowed and achieved range of focused transmission as a function of the target size.
Figure 4: Full distributions of transmission eigenvalues.


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We thank S. Popoff, Y. Bromberg, S. Knitter, R. Sarma, W. Xiong, F. Scheffold, E. Akkermans and I. M. Vellekoop for helpful discussions. This work is supported by the National Science Foundation under grant No. DMR-1307632 and ECCS-1068642, the US Office of Naval Research under grant No. N00014-13-1-0649, and the US–Israel Binational Science Foundation (BSF) under grant no. 2015509. A.G. acknowledges the support of LABEX WIFI (Laboratory of Excellence ANR-10-LABX-24) within the French Program ‘Investments for the Future’ under reference ANR-10-IDEX-0001-02 PSL.

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C.W.H. and S.F.L. performed the experiment. C.W.H. analysed the data. C.W.H. developed the theory descriptions. A.G. proposed the effective MP model. H.C. and A.D.S. supervised the project. All authors discussed and interpreted the results. C.W.H. and A.D.S. wrote the manuscript with input from all authors.

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Correspondence to Chia Wei Hsu.

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The authors declare no competing financial interests.

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Hsu, C., Liew, S., Goetschy, A. et al. Correlation-enhanced control of wave focusing in disordered media. Nature Phys 13, 497–502 (2017).

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