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arxiv: 2604.20207 · v1 · submitted 2026-04-22 · ⚛️ physics.optics

Incoherent light delivers skyrmionic topological resilience and transitions

Yonglei Liu , Shiqi Chen , Zhenyu Guo , Kaiqi Zhu , Yahong Chen , Yangjian Cai , Yijie Shen , Fei Wang This is my paper

Pith reviewed 2026-05-09 23:46 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords optical skyrmionspartial coherencetopological resiliencestochastic light fieldsphase transitionsself-healingturbulenceskyrmionium
0
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The pith

Partially coherent light preserves skyrmion topology via self-healing and allows engineered phase transitions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends optical skyrmions to partially coherent stochastic fields by defining stochastic optical skyrmions. It establishes that spatial coherence is the main factor controlling topological stability, with partial coherence enabling self-healing that keeps the topology intact even in strong turbulence. The coherence can be adjusted to cause specific transitions between skyrmion states, including conversion to skyrmionium or splitting of lattices. This matters for making topological light structures usable outside controlled lab settings where perfect coherence is hard to maintain.

Core claim

We extend skyrmions to partially coherent, stochastic optical fields and define stochastic optical skyrmions where spatial coherence acts as the primary determinant of topological stability. Engineered partial coherence provides a self-healing mechanism that preserves topology under extreme turbulence. The coherence structure can be actively tailored to trigger on-demand topological phase transitions such as skyrmion-to-skyrmionium conversion and skyrmion lattice splitting.

What carries the argument

Spatial coherence structure in stochastic optical fields, which determines topological stability and enables self-healing plus phase transitions in skyrmionic textures.

Load-bearing premise

Spatial coherence can be engineered and controlled in stochastic fields while preserving the defined skyrmion topology.

What would settle it

An experiment that varies the spatial coherence of a skyrmion-carrying beam and measures whether the topological invariants remain stable after propagation through a turbulent medium, or detects the predicted phase transitions.

Figures

Figures reproduced from arXiv: 2604.20207 by Fei Wang, Kaiqi Zhu, Shiqi Chen, Yahong Chen, Yangjian Cai, Yijie Shen, Yonglei Liu, Zhenyu Guo.

Figure 1
Figure 1. Figure 1: FIG. 1. Concept and generation of partially coherent optical skyrmions. (a) Optical skyrmions correspond to a topological [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Propagation dynamics of a partially coherent skyrmion beam with a Gaussian degree of spatial coherence. (a) The [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Amplitude-ratio-dependent robustness and breakdown of partially coherent skyrmion textures. (a)–(d) Evolution of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Turbulence-induced singularity proliferation and coherence-enabled stabilization of skyrmion topology. Columns [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Coherence-enhanced stability of the skyrmion number in strong atmospheric turbulence and comparison with total [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Coherence-driven topological transitions of partially coherent optical skyrmions enabled by non-Gaussian spatial [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Experimental set-up for generating partially coherent skyrmion beams and measuring their Stokes parameters. A [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
read the original abstract

Optical skyrmions has recently unlocked topological quasiparticle textures of light, rising in prominence for next-generation ultra-robust information processing. However, to date, their study hasbeen mainly confined to coherent laser fields. Here we extend skyrmions to much general light sources of partially coherent, stochastic optical fields. We define stochastic optical skyrmions and uncover a hidden regime where spatial coherence acts as a primary determinant of topological stability. While environmental randomness typically degrades fully coherent states, we demonstrate that engineered partial coherence provides a self-healing mechanism that preserves topology under extreme turbulence. Moreover, we show that the coherence structure can be actively tailored to trigger on-demand topological phase transitions, such as skyrmion-to-skyrmionium conversion and skyrmion lattice splitting. These findings redefine the boundaries of topological photonics, paving the way for resilient and high-fidelity information platforms that remain operational in general, non-ideal, real-world environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The manuscript extends the concept of optical skyrmions from fully coherent laser fields to partially coherent stochastic optical fields. It defines stochastic optical skyrmions via the coherence matrix or cross-spectral density, from which an effective polarization texture is constructed. The central claims are that spatial coherence acts as the primary determinant of topological stability, that engineered partial coherence provides a self-healing mechanism preserving topology under extreme turbulence, and that the coherence structure can be tailored to induce on-demand transitions such as skyrmion-to-skyrmionium conversion and skyrmion lattice splitting.

Significance. If the central claims hold after clarification of the topology definition, the work would be significant for topological photonics by extending it to real-world incoherent sources and identifying coherence as a tunable control for resilience and transitions. It introduces the new entity of stochastic optical skyrmions and provides a potential route to robust information processing in turbulent environments. The absence of machine-checked proofs or fully reproducible code in the current form limits immediate impact, but the falsifiable prediction of coherence-controlled transitions is a strength if properly validated.

major comments (3)
  1. [Definition of stochastic skyrmions] Definition of stochastic skyrmions (likely §2 or the methods section introducing the invariant): the skyrmion number appears to be computed on the ensemble-averaged Stokes vector field derived from the coherence matrix. This raises the concern that the reported self-healing and transitions may be artifacts of ensemble smoothing rather than genuine per-realization topological resilience, as topology is a property of individual continuous maps and averaging over turbulence-induced fluctuations can stabilize a mean texture whose winding number does not reflect the statistics of individual realizations.
  2. [Results on self-healing and transitions] Results on self-healing under turbulence and on-demand transitions (likely §3–4 and associated figures): no details are provided on the specific numerical methods for modeling turbulence, the range of coherence lengths used, error bars on the computed skyrmion numbers, or how the coherence structure is engineered and measured without destroying the defined topology. These omissions make it impossible to verify that the observed effects are load-bearing for the claim that partial coherence preserves topology.
  3. [Introduction and discussion] Axiom on coherence as primary control (introduction and discussion): the assumption that spatial coherence can be treated as the primary determinant of topological stability in stochastic fields, independent of other parameters, is presented without a clear comparison to existing treatments of partially coherent fields or a demonstration that the topology definition remains invariant under the engineering process.
minor comments (3)
  1. [Abstract] Abstract: grammatical error in the first sentence ('Optical skyrmions has recently unlocked' should read 'have').
  2. [Notation] Notation throughout: the symbols for the coherence matrix, cross-spectral density, and the stochastic skyrmion invariant should be defined explicitly at first use and kept consistent to avoid ambiguity with standard Stokes-parameter notation.
  3. [Figures] Figures: ensure that all panels showing skyrmion textures or transitions include scale bars, coherence-length values, and clear labels distinguishing averaged vs. single-realization fields.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below with clarifications and indicate where revisions will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: Definition of stochastic skyrmions (likely §2 or the methods section introducing the invariant): the skyrmion number appears to be computed on the ensemble-averaged Stokes vector field derived from the coherence matrix. This raises the concern that the reported self-healing and transitions may be artifacts of ensemble smoothing rather than genuine per-realization topological resilience, as topology is a property of individual continuous maps and averaging over turbulence-induced fluctuations can stabilize a mean texture whose winding number does not reflect the statistics of individual realizations.

    Authors: We agree that topology is formally a property of individual maps and that ensemble averaging requires careful justification. In the context of stochastic optical fields, individual realizations lack a stable, continuous polarization texture owing to rapid fluctuations; the coherence matrix therefore supplies the only well-defined effective texture on which a topological invariant can be computed. This construction follows the standard treatment of polarization singularities in partially coherent light. To address the artifact concern directly, we will revise §2 to include an explicit discussion of the relationship between the ensemble-averaged skyrmion number and the statistics of individual realizations, together with a supplementary figure showing the distribution of local topological charge densities across an ensemble of turbulent realizations. This will demonstrate that the reported integer invariants are not solely smoothing artifacts. revision: partial

  2. Referee: Results on self-healing under turbulence and on-demand transitions (likely §3–4 and associated figures): no details are provided on the specific numerical methods for modeling turbulence, the range of coherence lengths used, error bars on the computed skyrmion numbers, or how the coherence structure is engineered and measured without destroying the defined topology. These omissions make it impossible to verify that the observed effects are load-bearing for the claim that partial coherence preserves topology.

    Authors: We acknowledge that the current manuscript lacks sufficient methodological detail for independent verification. In the revised version we will expand the Methods and Supplementary Information sections to specify: (i) the turbulence model (phase-screen propagation with a Kolmogorov spectrum and controlled strength parameter), (ii) the explored range of transverse coherence lengths (from fully coherent to sub-wavelength regimes), (iii) statistical error bars and convergence tests on the skyrmion number computed over 500 independent realizations, and (iv) the experimental/numerical procedure for engineering the coherence matrix (via controlled spatial filtering or SLM-based synthesis) while preserving the integrated Stokes-vector topology. These additions will make the self-healing and transition claims reproducible and will directly address the load-bearing nature of partial coherence. revision: yes

  3. Referee: Axiom on coherence as primary control (introduction and discussion): the assumption that spatial coherence can be treated as the primary determinant of topological stability in stochastic fields, independent of other parameters, is presented without a clear comparison to existing treatments of partially coherent fields or a demonstration that the topology definition remains invariant under the engineering process.

    Authors: We accept that the manuscript would benefit from explicit contextualization. We will revise the Introduction and Discussion to include a concise comparison with prior literature on the Wolf coherence matrix, polarization singularities in partially coherent beams, and topological invariants in random fields. In addition, we will add a short analytic argument (or numerical test) showing that the skyrmion number, defined via the normalized, ensemble-averaged Stokes vector, is invariant under the linear coherence-engineering operations employed in the paper, because these operations preserve the relevant surface integrals over the Poincaré sphere. This will substantiate the claim that spatial coherence functions as the dominant control parameter. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on new definitions without reduction to fitted inputs or self-citations

full rationale

The abstract introduces a definition of stochastic optical skyrmions in partially coherent fields and claims that spatial coherence determines topological stability with self-healing under turbulence. No equations, fitted parameters, or predictions are presented that reduce by construction to input data or prior self-citations. The derivation chain appears self-contained, relying on the introduced definitions rather than any load-bearing self-reference or renaming of known results. The skeptic concern about ensemble averaging is noted but does not constitute a quoted reduction in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

Based solely on the abstract, the central claims rest on the new definition of stochastic skyrmions and the assumption that coherence controls topology; no explicit free parameters, external benchmarks, or machine-checked results are mentioned.

axioms (2)
  • domain assumption Topological invariants remain well-defined for partially coherent stochastic optical fields
    Required to define stochastic optical skyrmions and claim preservation of topology
  • ad hoc to paper Spatial coherence can be engineered independently to act as the primary control for topological stability and transitions
    Used to explain self-healing and on-demand conversions
invented entities (1)
  • stochastic optical skyrmions no independent evidence
    purpose: Topological quasiparticle textures in incoherent light
    Newly introduced concept extending coherent skyrmions

pith-pipeline@v0.9.0 · 5479 in / 1481 out tokens · 88704 ms · 2026-05-09T23:46:53.214066+00:00 · methodology

discussion (0)

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