Topological robustness of optical skyrmions through a real-world free-space link

Technical Summary: Topological Robustness of Optical Skyrmions Through a Real-World Free-Space Link

Problem Statement
Structured light offers significant potential for increasing channel capacity in modern optical networks by utilizing additional degrees of freedom (DoFs) such as space, wavelength, and polarization. However, the practical implementation of these high-dimensional states in free-space optical communication (FSOC) is severely hindered by real-world distortions, particularly atmospheric turbulence. Turbulence induces non-uniform refractive index profiles that cause rapid, evolving phase perturbations, altering the amplitude, phase, and vectorial polarization structure of the beam. This leads to crosstalk in classical links and entanglement loss in quantum channels. While mitigation strategies like adaptive optics and machine learning exist, they often require complex pre- or post-correction or channel probing. There is a need for information carriers that are inherently robust to these distortions without requiring active compensation.

Methodology
The authors experimentally demonstrated the transmission of optical skyrmions—a form of topological light—through a 270-meter free-space optical link located on the University of the Witwatersrand campus in Johannesburg, South Africa.

• Generation: Optical skyrmions were generated using a 532 nm laser shaped into vector beams via a spatial light modulator (SLM) and a modified Mach-Zehnder interferometer. The beams were constructed as a superposition of two Laguerre-Gaussian (LG) modes: $U(r) = LG^0_{l_1}(r)e_R + LG^0_{l_2}(r)e_L$, where $e_R$ and $e_L$ are right and left circular polarization unit vectors. By setting the radial index $p=0$ and modulating the azimuthal indices ($l_1 = 1, 2, 3$ and $l_2 = 0$), the authors created skyrmions with topological wrapping numbers (skyrmion numbers) of $N = 1, 2,$ and $3$.
• Transmission: The beams were transmitted over a 270 m round-trip path (135 m to a mirror and back) to simulate a free-space link. Measurements were taken at three distinct times of day to capture varying turbulence strengths: morning (calm), midday (high turbulence), and late afternoon (moderate turbulence).
• Detection: A single-shot, spatially resolved Stokes polarimetry setup was used. A 50:50 beam splitter directed the beam to a polarization-sensitive camera, allowing simultaneous measurement of all six polarization intensity projections (H, V, D, A, R, L).
• Analysis: The topological wrapping number $N$ was calculated using the Stokes vector field $S$ via the integral $N = \frac{1}{4\pi} \int_{R^2} S \cdot (\frac{\partial S}{\partial x} \times \frac{\partial S}{\partial y}) dxdy$. To account for noise and background light (e.g., sunlight), the authors employed post-processing techniques including averaging over 300 rotations of the Poincaré sphere, low-pass Gaussian filtering, and intensity-based thresholding to exclude unpolarized noise.
• Decoherence Testing: To simulate the effects of long measurement times required for quantum states, the authors averaged measurements over time scales exceeding the atmospheric coherence time ($\tau_0$), observing the effects of depolarization and decoherence on the topology.

Key Results

• Topological Preservation: Despite severe distortions in the beam's amplitude, phase, and underlying polarization structure (which rendered the vector textures unrecognizable in some cases), the topological wrapping number $N$ remained robust.
  • In the morning (scintillation index $\sigma^2_I \approx 0.007$), measured values were $N_{exp} \approx 0.81$ and $2.06$ for encoded $N=1, 2$.
  • At midday (severe turbulence, $\sigma^2_I \approx 1.4$), measured values were $N_{exp} \approx 0.95$ and $2.19$.
  • In the late afternoon ($\sigma^2_I \approx 0.23$), measured values were $N_{exp} \approx 0.97$ and $1.83$.
• Resilience to Depolarization: When averaging measurements over time scales up to 240 ms (simulating decoherence), the degree of polarization (DoP) dropped significantly from $\approx 0.84$ to $\approx 0.39$. Despite this loss of coherence and polarization, the skyrmion number remained nearly identical to the encoded values (e.g., $N=0.98$ for encoded $N=1$).
• Information Transfer: The authors encoded a 512 $\times$ 560 image of South Africa using the skyrmion number as an alphabet ($N=1, 2, 3$ corresponding to blue, orange, green).
  • Under mild distortion (morning), the reconstructed image fidelity was 98.70%.
  • Under severe distortion (midday), fidelity was 86.93%, with some color dislocation in higher-order topologies, though the image remained discernible.
  • Under moderate distortion (afternoon), fidelity was 98.60%.
  • Under depolarization conditions (240 ms averaging), fidelity reached 99.72%.

Significance and Claims
The paper claims to be the first experimental demonstration of the robustness of optical topologies through a realistic, uncontrolled atmospheric environment. The authors emphasize that this robustness is achieved without any pre- or post-correction, channel probing, or adaptive optics. The topology acts as an invariant that passes through the channel "as if it were transparent," provided the channel can be described as a smooth deformation of the map.

The work suggests that optical skyrmions offer a reliable alphabet for information transmission in both classical and quantum regimes, capable of maintaining high fidelity even when the underlying degrees of freedom are severely scrambled or depolarized. The authors note that while current measurement methods (Stokes polarimetry) are susceptible to noise, the topological nature of the signal allows for accurate retrieval even in extreme conditions. They conclude that this approach opens new avenues for robust, correction-free optical communication and motivates the development of dedicated topological detectors and optimized vectorial beam geometries for further resilience.