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Special Camp: Mesoscopic Correlations of Diffusing Light: Controlling Transmission of Radiation in Strong Scattering Media

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Doug Stone, Yale University
16 September 2016 from 11:15 AM to 12:15 PM
339 Davey Laboratory
Contact Name
Jainendra Jain and Mikael Rechtsman
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A key discovery of the 1980’s was the unexpected fluctuation properties of the
transmission matrix for disordered electrons in mesoscopic conductors, determined
through low-temperature transport measurements. Particularly surprising was the
theoretical prediction of Universal Conductance Fluctuations in the metallic (diffusive)
regime: the standard deviation of the conductance was found to be independent of the
mean free path and order e2/h. This result implied the existence of previously unknown
correlations in the transmission matrix of any diffusing classical wave, including
electromagnetic waves. In the language of optics, the diffusive speckle pattern is not
uncorrelated beyond the speckle size, as believed since Lord Rayleigh; this was later
verified by various experimental and numerical studies. A related and equally surprising
discovery was that for purely elastic scattering there always exist certain input states
known as “open channels” which allow transmission with probability unity through a
disordered medium with average transmission <T> <<1. This result was not testable with
electronic transport due to the inability to control the input electronic state. Moreover
how or if open channels might exist in optics was an unresolved question until recently.
However the invention of the spatial light modulator about a decade ago renewed interest
in such questions, as it became possible to exert a high degree of control over the
wavefront of incident light and search for optimal inputs. I will review recent theoretical
and experimental work at Yale related to these questions [1-3]. The theory provides a
random matrix description of coherent control of transmission of diffusive light and
predicts the maximum transmission enhancement possible for a given experimental
geometry. The experiments demonstrate order of magnitude coherent control of diffusive
transmission and very recently have confirmed in detail the predictions of the random
matrix theory for the geometry-dependent eigenvalue density. The mesoscopic
correlations of diffusing waves are found to play a critical role in enhancing the dynamic
range of control.

[1] “Filtering random matrices: The effect of imperfect channel control in multiple-scattering”, A.Goetschy and A. D. Stone, Physical Review Letters, 111, 063901 (2013).
[2] “Coherent control of transmission of light through disordered media”, S. M. Popoff, A. Goetschy, S. F.Liew, A. D. Stone, and H. Cao, Physical Review Letters, 112, 133903 (2014).
[3] “Correlation effects in focused transmission through disordered media”, C. W. Hsu, S.-F. Liew, A.Goetschy, H. Cao and A. D. Stone, submitted to Nature Physics.