Intrinsic Meron Spin Textures in Generic Focused Fields

Abstract

Optical spin textures with nontrivial topology hold promise for structured light and photonic information processing, yet their generation typically relies heavily on externally structured light with care. This raises questions about their universal existence and true robustness. Here, we uncover and experimentally verify a meron-like spin texture that emerges intrinsically in focused fields, without any wavefront engineering. This intrinsic meron spin texture, unlike their externally engineered counterparts, exhibits exceptional robustness against a wide range of inputs, including partially polarized and spatially disordered pupils corrupted by decoherence and depolarization. We attribute its resilience to topological protection from phase vortices in the focal field. Our findings reveal a naturally occurring spin structure that is intrinsic to the focused field with exceptional robustness against noise, which complements the existing externally engineered ones. It offers new ingredients into topological spin textures in optics and enriches their potentials for disorder-resilient photonic applications.

Figures (5)

• Figure 1: (a) The system under study, where the spin texture at the focal plane is examined with a generic input pupil. (b-g) are schematic diagrams of three input pupils under consideration: (b,c) Fully polarized, (d,e) Partially polarized, (f,g) Spatially-randomly polarized.
• Figure 2: Spin textures and skyrmion numbers under different incident conditions. (a-c) The incident polarization ellipse and (d-f) the normalized spin textures on the focal plane are shown. (g) The partially polarized state (yellow ellipse) formed by time averaging of the fully polarized state in (a-c) and the corresponding spin texture at the focal plane. (h) The solid Poincaré sphere is naturally divided into two halves with $N_{sk}=\pm0.5$.
• Figure 3: (a-b) Decomposition of incident light into two orthogonal linearly polarized components. The orange dashed circle and orange dot represent the positions on the focal plane satisfy $\mathcal{I}_0=\mathcal{I}_2$. (c) The phase of $E_z$ in the $xy$ plane. (d) The phase of $E_\phi$ in the $rz$ plane.
• Figure 4: (a) Degree of spatial polarization randomness spanned by $\Theta_0$. (b) The polarization distribution at the input pupil when $\Theta_0=135^\circ$ and the corresponding spin texture at the focal plane. (c-e) Phase of $E_z$, $E_{\phi}$, and $E_{r}$ under the input pupil in (b). (f) $log_{10}|s_z|$ and the contour line in green highlights the positions with $|\Phi_r-\Phi_\phi|=0$ or $\pi$ (zero of $s_z$ with pure $s_\perp$). (g) Stability of $N_{sk}$ with increasing spatial randomness. The dashed gray line displays the theoretical values. The insets show the spin textures at different $\Theta_0$ with $N_{sk}$.
• Figure 5: (a) Experimental setup based on off-axis holography for measuring spin meron structure in the focal region. P, polarizer; HWP, half-wave plate; QWP, quarter-wave plate; MO, microscope objective; TL, tube lens; BS, beam splitter. (b) Stability of $N_{sk}$ as a function of the input degree of polarization $P$. Insets: Detailed distributions at the states marked by the blue dots in the red boxes, showing (c)(f)the transverse and (d)(g)longitudinal spin components and (e)(h)the $P_{3D}$ distribution at the focal plane. In the transverse spin ($s_\perp$) map, color and brightness represent its direction ($\tan^{-1}(s_y/s_x)$) and magnitude, respectively. Theoretical simulations are shown for comparison. Scale bars, 500 nm.