Nondivergent spinning substructures near acoustic field nodes

In this work, we examine the extraordinary behavior of polarization and spin angular momentum density in the vicinity of longitudinal field zeros in three-dimensional monochromatic acoustic fields. We demonstrate that, as governed by the continuity equation, the velocity fields of arbitrary acoustic sources maintain nondiffractive elliptical polarization structures that enclose longitudinal field zeros, despite having divergent transverse spatial profiles of intensity. Furthermore, embedded in these nonparaxial field contours, for infinite distance, are threads of circular polarization singularities. We illuminate these inherent properties in acoustic vortex fields, dipole arrays, and the famous Young's double-slit experiment. Our results reveal spin characteristics of sound waves that provide a platform for future studies and applications of structured acoustic waves and chiral acoustic phenomena.

Figure 1

(a)–(c) Energy density $W$, normalized spin AM density $\left|\mathbf{S}\right|,$ and TL-alignment parameter ${\chi }_{\text{TL}}$ for an acoustic Laguerre-Gaussian beam with beam waist $w_0=\lambda$ and orders $\ell =1, p=0$ propagating in the $\widehat{\mathbf{z}}$ direction. (d)–(f) show the same quantities for non-coaxial superposition of two Laguerre-Gaussian beams ($\ell =1,p=0$), each of beam waist $w_0=\lambda$, with spacing $3\lambda$ along the $\widehat{\mathbf{x}}$ axis between their respective centers. In boxes for (a)–(f) are the amplitudes of the corresponding color-density plots at $z=0$ (blue) and $z=2z_R$ (red).

Figure 2

(a) Schematic diagram of wavelength-spaced dipoles, each with moment $\mathbf{D}=D\widehat{\mathbf{z}},$ arranged in a pentagonal geometry centered around $(x,y)=(0,0)$ in the $z=0$ plane. (b) Density plots of logarithmic energy density $log\left(W\right)$, normalized SAM density $\left|\mathbf{S}\right|,$ and TL-alignment parameter ${\chi }_{\text{TL}}$ for the superimposed fields directly above the dipole array at $z=50\lambda .$ In (c), the same quantities are shown at $z=100\lambda .$ Insets for $\left|\mathbf{S}\right|$ and ${\chi }_{\text{TL}}$ are shown around a propagating zero at $z=100\lambda .$

Figure 3

(a) Sketch of the double-slit interference geometry. The grayscale distribution represents the logarithmic intensity of $|{\mathbf{V}}^{\text{int}}|$. (b) Amplitude plots of SAM density $\left|\mathbf{S}\right|$ (red) and normalized intensity $|{\mathbf{V}}^{\text{int}}{|}^2$ (blue) at $z=40\lambda$ and $z=60\lambda ,$ whose spatial positions with respect to the slits are indicated by the red lines in (a). Pairs of circular polarization singularities or C lines ($\left|\mathbf{S}\right|=1$ corresponding to $S_y=\pm 1$) separated by $\lambda /\pi$ along $\widehat{\mathbf{x}}$ direction sandwich each intensity minimum at angle ${\alpha }_{\text{min}}$ in the far-field zone. Angular positions of C lines are offset by $\delta \alpha =\pm 1/zk$ with respect to ${\alpha }_{\text{min}}$.