Universal nondiffractive topological spin textures in vortex cores of light and sound

TL;DR

The paper uncovers a universal, nondiffracting spin texture—a skyrmionic meron—embedded in the cores of optical and acoustic vortex beams, described within a Laguerre–Gaussian framework. It derives analytic core spin expressions and a subwavelength, propagation-invariant structure with Skyrme numbers $N=\mathrm{sign}(l)/2$ for sound and $N=-\sigma/2=\mathrm{sign}(l)/2$ for light (under the spin–orbit helicity condition), and introduces a truncated Skyrme number to quantify the texture extent. An acoustic experiment in water provides full 3D measurements of the velocity field confirming the predicted meron cores and their near-field robustness, while a discrete-channel analytic model explains how near-field nondiffracting textures emerge from a finite aperture. The work also shows that universality is basis-dependent: optical Bessel beams yield different core topologies (e.g., $N=-\sigma/2$ for $|l|=1$ versus $N=-\sigma$ for $|l|>1$) due to spin–orbit coupling, whereas acoustic cores remain at $N=\pm1/2$ for all $|l|\ge1$, highlighting the role of modal basis in topological spin textures with potential implications for imaging and spin–orbit interactions at subwavelength scales.

Abstract

We report universal skyrmionic spin textures in the cores of optical and acoustic vortex beams, described within the framework of Laguerre-Gaussian modes. We analytically demonstrate nondiffractive propagating spin merons, independent of whether the field is transverse or longitudinal, with their sign controlled by the wavefront helicity. Experimental confirmation is provided in acoustics through full three-dimensional measurements of the velocity vector field. Although these phenomena are intrinsic to vortex cores, we also show that the claimed universality breaks down for higher-order topological charges, depending on the carrier mode, here exemplified using the Bessel framework.

Figures (7)

• Figure 1: Analytical core spin textures $\{{\mathbf{\widetilde{s}}}\}$ for unit-charge vortices of light (for $\sigma l<0$) and sound, over a $\lambda^2$ area centered on the $z$ axis from Eqs. (\ref{['eq:s_sound_core']}) and (\ref{['eq:s_light_core']}). See Supplemental Materials, Sec. II, for an alternative visualization emphasizing the sphere-to-plane stereographic projection of the spin texture.
• Figure 2: (a) Diffracting intensity pattern $|f_l(\mathbf{r})|^2$ of a vortex beam with $l=\pm1$ whatever the nature of the wave, from Eq.(\ref{['eq:LG']}). (b) Calculated maps of $\chi_{\rm TL}(\mathbf{s})$ in the meridional plane $(z,\rho)$ and in the transverse plane at $z=0$ (insets), for light and sound, for $|l|=1$ with $\sigma l < 0$ for optics. All plots calculated for $w_0=\lambda$.
• Figure 3: (a) Photograph of the acoustic experimental setup. (b) Experimental normalized transverse pressure magnitude of a vortex beam with $l=1$, $\bar{p}=|p|/\max(|p|)$, at focus ($z=0$), over a $2.6 \lambda \times 2.6 \lambda$ area. Inset: simulation. (c) Corresponding pressure phase map, $\varphi = \arg(p)$. Inset: simulation. (d) Simulated meridional distribution of $\bar{p}$. Simulations are made using Eqs. (\ref{['eq:p_s']}) and (\ref{['eq:p']}).
• Figure 4: Experimental transverse-to-longitudinal alignment parameter for the spin vector, $\chi_{\rm TL}(\mathbf{s})$, for an acoustic vortex beam with $l=1$ over a $4 \lambda^2$ area centered on the $z$ axis, in the range $-10~{\rm mm} < z < 35$ mm, with 5 mm increments. Insets: corresponding simulations from Eqs. (\ref{['eq:p_s']}) and (\ref{['eq:p']}).
• Figure 5: Experimentally reconstructed textures $\{{\mathbf{s}}\}$ of spin core merons of the Bloch type for unit-charge acoustic vortex beams with $l=\pm1$, over a $\lambda^2$ area centered on the $z$ axis, at $z=0$. Insets: corresponding simulations with half sampling density.