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Folding a focalized acoustical vortex on a flat holographic transducer: Miniaturized selective acoustical tweezers

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Science Advances  12 Apr 2019:
Vol. 5, no. 4, eaav1967
DOI: 10.1126/sciadv.aav1967
  • Fig. 1 Archimedes-Fermat acoustical tweezers: Principle.

    (A) Scheme illustrating the composition of the Archimedes-Fermat acoustical tweezers: A focalized acoustical vortex is synthesized by spiraling metallic electrodes deposited at the surface of a piezoelectric substrate. The vortex propagates and focalizes inside a glass slide (sealed with the piezoelectric substrate) and a mobile glass coverslip before reaching the liquid contained in a polydimethylsiloxane (PDMS) chamber, wherein the particle is trapped. The mobility of the microfluidic chip (glass coverslip and sealed PDMS chamber) is enabled by a liquid couplant and a manual precision displacement setup represented in (E). (B) Spiraling pattern of the electrodes obtained from approximated Eq. 2 with z=55.4 and m = 1. (C) Scheme introducing the spherical (r, θ, φ) and cylindrical coordinates (ρ, φ, z) used for the demonstration of Eq. 2. (D) Comparison of the compactness of the transducer array of (5) (left) to the Archimedes-Fermat acoustical tweezers presented in this paper (right). This figure also shows the transparency of the Archimedes-Fermat acoustical tweezers (particles are trapped on the central axis of the transducer). Photo credit: Jean-Louis Thomas, CNRS (left) and Michael Baudoin, Université de Lille (right). (E) Image showing the integration of the Archimedes-Fermat acoustical tweezers into a Leica Z16 macroscope. Four tweezers have been patterned on a 3-inch LiNbO3 wafer. Photo credit: Jean-Claude Gerbedoen, SATT Nord.

  • Fig. 2 Field synthesized by an Archimedes-Fermat acoustical tweezers: Theory versus experiments.

    (A) Numerical predictions with the angular spectrum method and (B) experimental measurements with a UHF-120 Polytec laser interferometer of the normalized intensity of the vibration at the surface of the glass coverslip (focal plane, z = 0). The maximum amplitude measured experimentally (on the first ring) is 10 nm. (C) Numerical predictions with the angular spectrum method and (D) experimental measurements with the laser interferometer of the phase of the acoustic wave at the surface of the glass coverslip. (E) Radial evolution of the normalized intensity of the acoustic wave from the center of the vortex to the side, as a function of the lateral radius r in millimeters. Black solid line: Average over all angles φ of the intensity measured experimentally. Red dashed line: Evolution expected for a cylindrical vortex (cylindrical Bessel function). Blue dashed-dotted line: Evolution expected for a spherical vortex (spherical Bessel function). Red dotted line: Asymptotic evolution in 1/r. Blue dotted line: Asymptotic evolution in 1/r2. (F) Evolution of the field intensity (top) and phase (bottom) in the z direction. The direction of the arrow indicates the wave propagation direction. Left to right: Distances z = 6, 4, 2, and 0 mm, respectively (z = 0 corresponds to the focal plane). Top: Localization of the acoustic energy and formation of a localized trap. Bottom: Transition from a Hankel to a Bessel spherical beam.

  • Fig. 3 Microparticles’ selective displacement in a standard microscopy environment.

    (A) Selective manipulation of a polystyrene particle having a radius of 75 ± 2 μm with the 4.4-MHz selective acoustical tweezers based on Archimedes-Fermat spirals. This figure shows that only the particle trapped at the center of the vortex (located just above the lowest arrow, as shown in movie S3) is moved, while the other particles remain still. The particles at rest have been colored to improve the readability of the figure (see also movie S2). (B and C) Patterning of 18 polystyrene particles with a radius of 75 ± 2 μm into prescribed position to form the letters M, O, and V (moving object with vortices). (B) Randomly dispersed particles (initial state). (C) Organized particles (final state).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/4/eaav1967/DC1

    Fig. S1. Comparison of the shape of the electrodes obtained by approximated Eq. 2 and exact Eq. 1.

    Fig. S2. Image illustrating movie S1 showing an animation of the vortex measured experimentally with a UHF-120 Polytec laser interferometer.

    Fig. S3. Image illustrating movie S2 showing the selective manipulation of polystyrene particle having a radius of 75 ± 2 μm with the 4.4-MHz selective acoustical tweezers based on Archimedes-Fermat spirals.

    Fig. S4. Image illustrating movie S3 showing the vortex center located at the tip of the bottom arrow where the particle is trapped.

    Movie S1. Movie showing an animation of the vortex measured experimentally with a laser interferometer.

    Movie S2. Movie showing the selective manipulation of polystyrene particle having a radius of 75 ± 2 μm with the 4.4-MHz selective acoustical tweezers based on Archimedes-Fermat spirals.

    Movie S3. Movie showing the localization of the vortex core compared to the localization of the arrows.

  • Supplementary Materials

    The PDF file includes:

    • Fig. S1. Comparison of the shape of the electrodes obtained by approximated Eq. 2 and exact Eq. 1.
    • Fig. S2. Image illustrating movie S1 showing an animation of the vortex measured experimentally with a UHF-120 Polytec laser interferometer.
    • Fig. S3. Image illustrating movie S2 showing the selective manipulation of polystyrene particle having a radius of 75 ± 2 μm with the 4.4-MHz selective acoustical tweezers based on Archimedes-Fermat spirals.
    • Fig. S4. Image illustrating movie S3 showing the vortex center located at the tip of the bottom arrow where the particle is trapped.

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Movie showing an animation of the vortex measured experimentally with a laser interferometer.
    • Movie S2 (.mp4 format). Movie showing the selective manipulation of polystyrene particle having a radius of 75 ± 2 μm with the 4.4-MHz selective acoustical tweezers based on Archimedes-Fermat spirals.
    • Movie S3 (.mp4 format). Movie showing the localization of the vortex core compared to the localization of the arrows.

    Files in this Data Supplement:

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