Fig. 3.

Nontrivial spin texture in an elastic longitudinal wave beam. Besides the wave interference approaches, the elastic Gaussian wave beam can also induce nontrivial spin density distribution. (A) The longitudinal wave Gaussian beam in the $xOy$ plane, $\left|{\mathit{u}}_L\right|\propto \exp \left(-y^2/{\delta }^2\right)$, will carry the antisymmetric spin density around the center of the beam, $\mathit{s}\propto \frac{4y}{k_L{\delta }^2}\exp \left(-2y^2/{\delta }^2\right){\mathit{e}}_z$. The $z$ component of $\mathit{s}$ is plotted above the displacement field of the longitudinal wave Gaussian beam. (B) The real part of the displacement field behaves effectively as a circularly polarized wave profile, whose rotation reflects the nontrivial transverse spin properties along both sides of the Gaussian beam.