Topological Control of Chirality and Spin with Structured Light

Abstract

Structured light beams with engineered topological properties offer a powerful means to control spin angular momentum (SAM) and optical chirality, key quantities shaped by spin-orbit interaction (SOI) in light. Such effects are typically regarded as emerging only through light-matter interactions. Here, we show that higher-order Poincaré modes, carrying a tunable Pancharatnam topological charge $\ell_p$, enable precise control of SOI purely from the intrinsic topology of the light field, without requiring any material interface. In doing so, we reveal a free-space paraxial optical Hall effect, where modulation of $\ell_p$ drives spatial separation of circular polarization states - a direct signature of SOI in a regime previously thought immune to such behaviour. Our analysis identifies two propagation-induced topological mechanisms underlying this effect: differential Gouy phase shifts between orthogonal components, and radial divergence of the beam envelope. These results overturn the common view that spin-orbit effects in free space require non-paraxial conditions, and establish a broadly tunable route to generating and controlling chirality and SAM without tight focusing. This approach provides new opportunities for optical manipulation, chiral sensing, and high-dimensional photonic information processing.

Figures (6)

• Figure 1: Concept of spin-separation in vectorial fields. (a) Spin-dependent separation resulting from a vectorial field interacting with an anisotropic medium, therefore resulting in a photonic spin-Hall effect. Lateral transverse shifts are observed depending on the spin components of the incident field. (b) Spin separation induced by tight focusing of a radially polarized vectorial beam carrying a PT phase with a corresponding topological charge, $\ell_p$, and (c) reproduced by propagating the same field but through freespace without any interactions with matter. In each case, spin separation is observed in the evolved vector beam, showing regions dominated by right-handed and left-handed circular polarizations.
• Figure 2: Revealing the origin of orbit-dependent spin dynamics in paraxial light. (a) A horizontally polarized LG mode (with $\ell_p = 1$ and $p = 0$) incident on a $q$-plate, produces a vector mode with a radially polarized field pattern (in the near field) but carrying a net OAM charge of $\ell_p$. Initially, the field contains zero spin density as it is populated by linear polarization states. On propagation, the beam shows a varying chirality and spin density ($S_3$), shown via the polarization ellipses, at various propagation planes. These propagation planes are marked by the ratio $\zeta = z/z_R$, with $\zeta=0$ corresponding to the image plane. The spin density ($S_3$, top panel) and the relative phase ($\phi_{12}$, bottom inset) are shown at each propagation plane. (b) Spin textured fields represented by spin unit vectors for the various corresponding propagation planes, with selected zoomed-in regions. Initially, the spin vectors point in the transverse plane, then gradually accumulate upward right-circular (RC) and downward left-circular (LC) spin components at the center and away from the origin, respectively. In the far field, there is a clear boundary that separates the LC and RC spin components, indicative of the Hall effect - orbit dependent spin separation. (c) The population of polarization states is shown at each plane on the Poincaré sphere. Initially, only the equator is covered at the waist plane, since the field contains only linear polarization states. Eventually, full coverage is shown, illustrating that the field evolves into a full Poincaré beam.
• Figure 3: Experimental stokes parameter analysis. (a) Measured Stokes parameters, $S_j$, for $\ell_p=1$ at various propagation planes, labeled here as the ratio $\zeta = z/z_R$ with $\zeta=0$ corresponding to the image plane. The last row shows the relative phases, $\phi_{12}$, showing a winding number $2 \Delta \ell \approx 2$ for all propagation planes. (b) The measured $z$ component of the Stokes parameter $S_3(\mathbf{r})$, characterizing the spin density of the field at different planes, $\zeta$ and the corresponding relative phase ($\phi_{12}$, see inset). This is shown for $\ell_p = -1, 2$ and $-2$.
• Figure 4: Observing orbit induced spin induction upon propagation. Reconstructed Poincaré sphere coverage and polarization ellipses for Pancharatnam topological indexes (a) $\ell_p = -1$ and (b) $\ell_p = 1$ at various propagation planes ($\zeta = z/z_R$). The same plots are shown for topological phases (c) $\ell_p=-2$ and (d) $\ell_p=2$, illustrating the emergence of spin from a vectorial field that initially has zero spin density in the paraxial regime.
• Figure 5: Emergent orbit-induced Hall effect. Experimental spin textures for the farfield modes given the Pancharatnam topological charge, $\ell_p =$ of (a) $0$, (b) $-1$, (c) $-2$, (d) 1 and (e) 2, illustrating an orbit-induced Hall effect. The transverse spin separation is visualized by the spin-current insets, which reveal an azimuthal flow that reverses direction as it approaches the field’s origin. This behaviour shows that the polarization handedness is well-defined near the center and changes beyond a certain radial distance, indicative of an optical spin-Hall effect. The insets show the spin currents ($\bar{J}$) which reveal the azimuthal spin currents due to the spin-Hall effect.