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Transport through modes in random media

Nature volume 471, pages 345–348 (2011)Cite this article

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Abstract

Excitations in complex media are superpositions of eigenstates that are referred to as ‘levels’ for quantum systems and ‘modes’ for classical waves. Although the Hamiltonian of a complex system may not be known or solvable, Wigner conjectured1 that the statistics of energy level spacings would be the same as for the eigenvalues of large random matrices. This has explained key characteristics of neutron scattering spectra2. Subsequently, Thouless and co-workers argued3,4 that the metal–insulator transition in disordered systems4,5,6 could be described by a single parameter, the ratio of the average width and spacing of electronic energy levels: when this dimensionless ratio falls below unity, conductivity is suppressed by Anderson localization5 of the electronic wavefunction. However, because of spectral congestion due to the overlap of modes7,8,9, even for localized waves, a comprehensive modal description of wave propagation has not been realized. Here we show that the field speckle pattern10 of transmitted radiation—in this case, a microwave field transmitted through randomly packed alumina spheres—can be decomposed into a sum of the patterns of the individual modes of the medium and the central frequency and linewidth of each mode can be found. We find strong correlation between modal field speckle patterns, which leads to destructive interference between modes. This allows us to explain complexities of steady state and pulsed transmission of localized waves and to harmonize wave and particle descriptions of diffusion.

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Figure 1: Measurements of transmission through random media.
Figure 2: Total transmission and mode speckle patterns.
Figure 3: Time–frequency analysis.
Figure 4: Dynamics of localized waves.
Figure 5: Localization parameters.

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Acknowledgements

This research was supported by the National Science Foundation (DMR0907285).

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Authors and Affiliations

  1. Department of Physics, Queens College of the City University of New York, Flushing, New York 11367, USA,

    Jing Wang & Azriel Z. Genack

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  1. Jing Wang
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  2. Azriel Z. Genack
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Contributions

J.W. improved the apparatus, took the data, developed the modal decomposition and the time–frequency analysis algorithms, analysed the data and contributed to writing the paper. A.Z.G. largely conceived and directed the research and wrote the paper.

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Correspondence to Azriel Z. Genack.

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The authors declare no competing financial interests.

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Wang, J., Genack, A. Transport through modes in random media. Nature 471, 345–348 (2011). https://doi.org/10.1038/nature09824

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