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This study presents universal expressions for wave momentum, spin, and angular momentum in elastic media, differing from prior work. It reveals quantized total angular momentum for cylindrical elastic modes, highlighting the importance of all contributions.

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Area of Science:

  • Solid Mechanics
  • Wave Physics
  • Acoustics

Background:

  • Recent theoretical and experimental interest in spin and orbital angular momenta of elastic waves.
  • Existing models for wave momentum and angular momentum in elastic media.

Purpose of the Study:

  • To revisit and derive canonical expressions for wave momentum, spin, and orbital angular momentum in isotropic elastic media.
  • To clarify the contributions of different wave components to angular momentum.
  • To investigate the quantization of angular momentum in specific elastic wave modes.

Main Methods:

  • Derivation of universal expressions for wave momentum and angular momentum.
  • Analysis of cylindrical elastic modes.
  • Calculation of transverse spin angular momentum for surface Rayleigh waves.

Main Results:

  • Established simple universal expressions for wave momentum, spin, and orbital angular momentum in isotropic elastic media.
  • Demonstrated that these expressions differ from previous results and do not require separation of wave field components.
  • Showed that the normalized z component of total angular momentum for cylindrical elastic modes is quantized and equals the azimuthal quantum number.
  • Identified that orbital and spin parts are not quantized due to spin-orbit geometric-phase effects.
  • Calculated the transverse spin angular momentum of a surface Rayleigh wave.

Conclusions:

  • The derived universal expressions offer a simplified and comprehensive description of angular momentum in elastic waves.
  • All contributions (longitudinal, transverse, and hybrid) to angular momenta are shown to be equally important.
  • The quantization of total angular momentum in cylindrical modes provides new insights into the behavior of elastic waves.