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Anomalous frozen evanescent phonons.

Yi Chen1,2, Jonathan L G Schneider3, Ke Wang3,4

  • 1Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany. yi.chen@partner.kit.edu.

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|October 25, 2024
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Summary
This summary is machine-generated.

We introduce frozen evanescent waves, which exhibit large spatial decay lengths in elastic metamaterials. These waves violate Saint Venant's principle, enabling potential applications in remote mechanical sensing.

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Area of Science:

  • Physics
  • Materials Science
  • Solid Mechanics

Background:

  • Evanescent waves are ubiquitous in wave phenomena, characterized by spatial decay.
  • These waves are typically studied at finite frequencies, exhibiting oscillations in time and space.
  • At zero frequency, evanescent waves
  • freeze
  • in time, leading to static solutions.

Purpose of the Study:

  • Introduce and define "frozen evanescent waves" as eigensolutions at zero eigenfrequency.
  • Investigate the connection between band structure minima and frozen evanescent phonons.
  • Explore the potential for engineering large decay lengths in static elasticity.

Main Methods:

  • Analyze the Bloch periodic problem at zero eigenfrequency.
  • Utilize Cauchy-Riemann equations in the complex plane to link band structure minima to frozen evanescent phonons.
  • Combine theoretical analysis with experimental validation for finite-size samples.

Main Results:

  • Frozen evanescent waves are identified as static eigensolutions of the Bloch periodic problem.
  • A direct link is established between band structure minima and frozen evanescent phonons.
  • Unusually large exponential decay lengths are achieved when band minima approach zero (soft modes).
  • Interference effects are observed in finite-size samples due to linear combinations of these waves.

Conclusions:

  • Frozen evanescent waves offer a mechanism to engineer large characteristic decay lengths in static elasticity.
  • The violation of Saint Venant's principle by these waves opens possibilities for remote mechanical sensing.
  • Theory and experimental results show excellent agreement, validating the findings.