Bridging Three Orders of Magnitude: Multiple Scattered Waves Sense Fractal Microscopic Structures via Dispersion

Wave scattering provides profound insight into the structure of matter. Typically, the ability to sense microstructure is determined by the ratio of scatterer size to probing wavelength. Here, we address the question of whether macroscopic waves can report back the presence and distribution of micro...

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Bibliographic Details
Published in:Physical review letters 2015-08, Vol.115 (9), p.094301-094301, Article 094301
Main Authors: Lambert, Simon A, Näsholm, Sven Peter, Nordsletten, David, Michler, Christian, Juge, Lauriane, Serfaty, Jean-Michel, Bilston, Lynne, Guzina, Bojan, Holm, Sverre, Sinkus, Ralph
Format: Article
Language:English
Subjects:
Biomechanics
Coherence length
Coherent scattering
Computer Science
Computer Simulation
Dispersions
Fingerprints
Fractal analysis
Fractals
Mechanics
Medical Imaging
Microstructure
Models, Theoretical
Physics
Reflection
Sound
Wavelengths
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Summary:Wave scattering provides profound insight into the structure of matter. Typically, the ability to sense microstructure is determined by the ratio of scatterer size to probing wavelength. Here, we address the question of whether macroscopic waves can report back the presence and distribution of microscopic scatterers despite several orders of magnitude difference in scale between wavelength and scatterer size. In our analysis, monosized hard scatterers 5  μm in radius are immersed in lossless gelatin phantoms to investigate the effect of multiple reflections on the propagation of shear waves with millimeter wavelength. Steady-state monochromatic waves are imaged in situ via magnetic resonance imaging, enabling quantification of the phase velocity at a voxel size big enough to contain thousands of individual scatterers, but small enough to resolve the wavelength. We show in theory, experiments, and simulations that the resulting coherent superposition of multiple reflections gives rise to power-law dispersion at the macroscopic scale if the scatterer distribution exhibits apparent fractality over an effective length scale that is comparable to the probing wavelength. Since apparent fractality is naturally present in any random medium, microstructure can thereby leave its fingerprint on the macroscopically quantifiable power-law exponent. Our results are generic to wave phenomena and carry great potential for sensing microstructure that exhibits intrinsic fractality, such as, for instance, vasculature.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.115.094301