Optical skyrmion lattices accelerating in free space

Technical Summary: Optical Skyrmion Lattices Accelerating in Free Space

Problem Statement
While optical skyrmions—vectorial structured light with nontrivial topologies—have been successfully generated and shown to propagate in free space, existing experimental observations are limited to straight-line propagation. A significant gap exists in controlling these topological structures to spatially accelerate along curved trajectories. Such control is identified as crucial for advanced applications in information sorting and transfer, yet it remains a challenge to achieve while maintaining topological stability.

Methodology
The study addresses this gap by generating accelerating skyrmion lattices using paraxial beams. The core methodology involves the non-separable superposition of orthogonally polarized Airy beams and vortex Airy beams.

• Theoretical Construction: The researchers utilize the unique properties of Airy beams, which exhibit non-diffracting, self-accelerating intensity distributions. By applying cubic phase modulation to Gaussian beams, they create finite-energy Airy beams. Introducing vortex phases during this process generates complementary vortex Airy beams. The superposition of these orthogonally polarized components (Right-Circular and Left-Circular polarization) creates a normalized Stokes vector distribution that forms periodic skyrmion lattices.
• Experimental Setup: The experiment employs a self-locking polarization Mach-Zehnder interferometer. A 532 nm laser is split into two orthogonally polarized beams and directed to a Spatial Light Modulator (SLM). The SLM modulates the beams with complex amplitude holograms corresponding to the Fourier transforms of the desired Airy and vortex Airy beams. A beam displacer recombines the beams, and a quarter-wave plate and Fourier lens reconstruct the vector beam at the Fourier plane.
• Measurement: Propagation tomographies are recorded using a digital propagation technique integrated into the holograms, eliminating the need for physical camera translation. Spatial Stokes tomography is performed using a camera combined with polarizers to capture the lattice structures in Stokes space.

Key Contributions

1. First Demonstration of Accelerating Skyrmion Lattices: The paper presents the first experimental realization of skyrmion lattices that accelerate along parabolic trajectories in free space, conveyed by Airy structured light.
2. Topological Stability Analysis: The study quantifies the topological stability of these lattices during propagation. It demonstrates that the skyrmion unit cells maintain a Skyrme number $|N_{sk}| > 0.9$ within a propagation range of $\pm 1.22 z_R$ (where $z_R$ is the Rayleigh length).
3. Discovery of Enhanced Meron Robustness: A notable finding is the superior stability of the meron structures (occupying the core regions of the skyrmion textures). These meron lattices maintain a stable Skyrme number of approximately $-0.5$ (with $|N_{sk}|$ stable within $0.5 \pm 0.02$) over a significantly extended range of $\pm 3.06 z_R$, despite the degradation of the surrounding lattice.
4. Mechanism Elucidation: The work clarifies that the transition between Bloch-type and Néel-type textures at different propagation planes is attributed to the accumulation of Gouy phase, while the self-accelerating behavior is inherited from the underlying Airy beam components.

Results
Experimental results show that while the periodic intensity profiles of the constituent Airy and vortex Airy beams degrade with propagation distance (particularly the vortex lattices becoming indistinguishable at $z = 100$ mm), the topological structures exhibit resilience.

• Skyrmion Lattices: At the Fourier plane ($z=0$), perfect periodic Stokes vector and skyrmion density distributions are observed. As propagation increases, the lattices deform, and the $S_3=1$ area shrinks, leading to the emergence of abnormal positive skyrmion density values. However, the topological integrity remains robust ($|N_{sk}| > 0.9$) for $\pm 1.22 z_R$.
• Meron Lattices: The meron structures demonstrate greater resilience, maintaining their topological identity over $\pm 3.06 z_R$. This stability is achieved at the expense of the outer regions of the skyrmion structure, which degrade more rapidly.

Significance
The authors claim that this work provides a new potential carrier for topologically robust information distribution, particle sorting, and manipulation. By demonstrating that optical skyrmions can be controlled to accelerate along curved trajectories while retaining topological stability, the study opens new directions in structured light research. The findings suggest that these accelerating lattices are suitable for practical applications in nontrivial light-matter interactions, leveraging their self-healing properties and intricate topological structures. The work establishes a foundation for future exploration in advanced microscopy, plasma channel induction, and electron beam manipulation, though the paper specifically frames these as potential future applications enabled by the demonstrated platform.