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6CCVD Research

Three-dimensional acoustic lensing with a bubbly diamond metamaterial

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2021-06-25
JournalJournal of Applied Physics
AuthorsMaxime Lanoy, Fabrice Lemoult, Geoffroy Lerosey, Arnaud Tourin, Valentin Leroy
InstitutionsCentre National de la Recherche Scientifique, Laboratoire MatiĂšre et SystĂšmes Complexes
Citations7
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”
  • 3D Acoustic Flat Lens Design: A three-dimensional acoustic flat metalens is numerically demonstrated, utilizing a crystalline metamaterial composed of air bubbles in water.
  • Diamond Lattice Structure: The material employs a diamond lattice arrangement of monopolar resonant air bubbles (radius r = 1 mm), which introduces a bi-periodic structure necessary for generating a negative-slope optical branch.
  • Negative Refractive Index (NIM): The structure achieves an effective refractive index of n = -1 at the operating frequency of 2929 Hz, enabling all-angle negative refraction, confirmed by Gaussian beam simulations.
  • Isotropic Propagation: The diamond structure ensures highly isotropic propagation across a large portion of the Brillouin zone, a critical feature for minimizing aberration effects in 3D imaging.
  • Super-Resolution Focusing: By slightly tuning the frequency (e.g., to 2917 Hz, where n ≈ -3.2), the focus is shifted into the near field, allowing evanescent waves to contribute, resulting in super-resolution focusing (FWHM 0.4λ0), significantly beating the standard Rayleigh diffraction limit (0.72λ0).
  • 3D Imaging Capability: The metalens is shown capable of imaging extended objects in three dimensions, demonstrating its potential for practical volumetric acoustic imaging.
  • Practical Feasibility: The design leverages recent advances in 3D printed frames for creating stable, ordered air bubble assemblies in water.

Technical Specifications

Section titled “Technical Specifications”
ParameterValueUnitContext
Scatterer TypeAir bubble (Monopolar)N/AHosted in water; potentially C6F14 enriched for stability.
Bubble Radius (r)1mmUsed for Minnaert resonance calculations.
Lattice StructureDiamond (Bi-periodic)N/ADerived from fcc lattice with two scatterers per unit cell.
Lattice Constant (a)11.8cmAverage separation distance between unit cells.
Air Volume Fraction (φ)0.001%Highly diluted concentration.
Minnaert Resonance (fm)2890HzFundamental resonance frequency of the isolated bubble.
Target Frequency (n = -1)2929HzFrequency for all-angle negative refraction.
Wavelength in Water (λ0)51.2cmWavelength corresponding to the n = -1 frequency.
Slab Thickness (n = -1 test)1.5λ0N/AThickness used for refraction and focusing simulations.
Near-Field Refractive Index~ -3.2N/AAchieved at 2917 Hz to enable super-resolution focusing.
Super-Resolution FWHM0.4λ0N/AFull Width at Half Maximum achieved in the near field.
Diffraction Limit (Rayleigh)0.72λ0N/AStandard limit for comparison; the metalens beats this.

Key Methodologies

Section titled “Key Methodologies”
  1. Metamaterial Design: The acoustic metamaterial was designed based on the Minnaert resonance of air bubbles, selecting the diamond lattice structure (fcc lattice with a two-scatterer basis) to introduce the necessary bi-periodicity for a negative-slope optical branch.
  2. Band Structure Computation: The eigenvalue problem for the infinite crystal was solved numerically using COMSOL Multiphysics, applying periodic boundary conditions to the unit cell to map the dispersion relations along main crystal directions.
  3. Isotropy Verification: Dispersion curves for various directions were overlaid to confirm that the equifrequency surface was essentially spherical (isotropic) near the operating frequency (2929 Hz), ensuring minimal aberration.
  4. Negative Refraction Simulation: The full multiple scattering problem was solved for a Gaussian acoustic beam obliquely incident (45°) on a slab of the bubbly diamond material (thickness 1.5λ0) to verify the n = -1 behavior and negative refraction angle.
  5. Focusing and Lensing Simulation: The multiple scattering problem was solved for a point source excitation placed near the slab interface to demonstrate focusing capabilities and measure the transverse profile of the focal spot.
  6. Near-Field Super-Resolution: The operating frequency was tuned slightly lower (e.g., 2917 Hz) to increase the effective refractive index (n ≈ -3.2), shifting the focus into the near field of the slab where evanescent waves contribute to the image, thereby achieving subwavelength resolution.
  7. 3D Imaging Demonstration: The three-dimensional imaging capability was illustrated by simulating an extended object (92 incoherent point sources forming “3D”) and tilting the slab by 18° to break rotational invariance and engage all three spatial dimensions in the imaging process.

Commercial Applications

Section titled “Commercial Applications”
  • Underwater Sonar and Sensing: Enables the creation of compact, flat acoustic lenses for high-resolution underwater imaging and detection systems, replacing traditional bulky curved lenses.
  • Non-Destructive Evaluation (NDE): Provides subwavelength acoustic focusing for inspecting internal structures of materials, allowing detection of defects smaller than half the operating wavelength in liquid or soft media.
  • Medical Diagnostics (Ultrasound): Potential for developing next-generation ultrasound probes capable of near-field super-resolution imaging, offering enhanced detail for clinical diagnostics.
  • Acoustic Microscopy: Used in laboratory settings for high-precision acoustic metrology and characterization of materials and fluid dynamics at subwavelength scales.
  • Transferable Metamaterial Technology: The underlying principle (bi-periodic structure generating a negative optical branch) is transferable to other wave systems, such as airborne acoustics (using spherical Helmholtz resonators) or elastic waves, expanding applications beyond water.
View Original Abstract

A sound wave travelling in water is scattered by a periodic assembly of air bubbles. The local structure matters even in the low frequency regime. If the bubbles are arranged in a face-centered cubic (fcc) lattice, a total bandgap opens near the Minnaert resonance frequency. If they are arranged in the diamond structure, which one obtains by simply adding a second bubble to the unit cell, one finds an additional branch with a negative slope (optical branch). For a single specific frequency, the medium behaves as if its refractive index (relative to water) is exactly n=−1. We show that a slab of this material can be used to design a three-dimensional flat lens. We also report super-resolution focusing in the near field of the slab and illustrate its potential for imaging in three dimensions.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 1967 - Electrodynamics of substances with simultaneously negative values of ɛ and ÎŒ [Crossref]
  2. 2001 - Experimental verification of a negative index of refraction [Crossref]
  3. 2000 - Negative refraction makes a perfect lens [Crossref]
  4. 1998 - Low frequency plasmons in thin-wire structures [Crossref]
  5. 1996 - Extremely low frequency plasmons in metallic mesostructures [Crossref]
  6. 1999 - Magnetism from conductors and enhanced nonlinear phenomena [Crossref]
  7. 2000 - Locally resonant sonic materials [Crossref]
  8. 2006 - Ultrasonic metamaterials with negative modulus [Crossref]
  9. 2004 - Double-negative acoustic metamaterial [Crossref]
  10. 2015 - Soft 3D acoustic metamaterial with negative index [Crossref]

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