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Cited by 2Orbital Angular Momentum in OpticsTopological Materials and PhenomenaNonlinear Photonic Systems

The DOI matches its Crossref record; 52 of the 61 references it cites were found in a registry or an index, and 9 are not checked yet; 5 of the 8 sources its claims cite were checked for support.

Topological state and number transitions of optical skyrmions upon free-space beam propagation

Open access
Fan, Xinhao, Wu, Xuanguang, Ren, Kang, Zhou, Liang, Guo, Xuyue, Wei, Bingyan, Zhang, Yi, Liu, Sheng, Li, Peng, Zhao, Jianlin·2025·Communications Physics
DOI 10.1038/s42005-025-02427-0
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Abstract

Skyrmions are typical topological structures of vectorial texture that have emerged in quantum fields, magnetic systems, liquid crystals, and other contexts, showing great potential for applications in spintronics, data storage, and quantum computing. As the optical counterparts of topologically protected quasiparticles, optical skyrmions have a specific type of topological stability that skyrmion number is invariant upon light propagation in free space. Here, we demonstrate the topological state and skyrmion number transitions of two-dimensional (2D) optical skyrmions upon beam propagation in free space. By simultaneously tailoring the longitudinal intensity profiles of vortex and non-vortex Bessel components with orthogonal polarizations, 2D optical skyrmion transitions with controllable topological states and skyrmion numbers are observed in quasi-nondiffractive skyrmionic beams. Manipulating the field topologies may hold significant potential in applications related to information processing and transmission. Optical skyrmions, as topologically stable structures, offer promising applications in spintronics and quantum computing, yet their dynamic transitions remain underexplored. Here, the authors demonstrate controllable transitions of two-dimensional optical skyrmions by adjusting Bessel beam components, revealing potential for advanced information processing and transmission technologies.

Verified 2026-11-10 · 9 references not checked yet

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

The paper demonstrates controllable topological-state and skyrmion-number transitions of 2D optical skyrmions during free-space propagation by tailoring longitudinal intensity profiles of orthogonally polarized vortex and non-vortex Bessel components. Experiments and simulations show Bloch-to-Néel transitions with constant skyrmion number, and Bloch-to-Néel-to-antiskyrmion transitions with the skyrmion number jumping from about −0.9 to +0.9.

Key findings

  • A Bloch state (δ = 0, β = 0) transitions to a Néel state (δ = −π/2, β = 0) while the skyrmion number remains constant at around −0.9 over z = 0–30 cm; the transition occurs near z = 15 cm, with q = 0.999988k, N = 6, and L = 30 cm. Experimental results agree with simulations.
  • In a three-segment case, the states are Bloch at z = 0–10 cm, Néel at z = 10–20 cm, and antiskyrmion at z = 20–30 cm; the skyrmion number initially stays at −0.9 and then shifts abruptly from −0.9 to +0.9 near z = 20 cm, with topological transitions near z = 10 cm and z = 20 cm.
  • Numerical studies show arbitrary transition pathways such as Q = −2 to 2 or Q = −2 to 1, with sharp jumps near the predicted critical point at z = 15 cm; high-order Bloch states can transition to different orders of anti-skyrmion states at z = 7.5 cm, 15 cm, and 22.5 cm.
  • Designed states include Bloch (δ = 0, β = 0) with Q = −1, Néel (δ = −π/2, β = 0) with Q = −1, and antiskyrmion (δ = −π/2, β = π/2) with Q = 1; measured and computed Q values are close to but not perfectly integral.

Methods

  • Experiments used 532 nm linearly polarized light expanded and collimated, with SLM1 and SLM2 displaying computer-generated holograms to modulate horizontal and vertical polarization components; a PBS combined the beams coaxially, a 4f system filtered the +1 order, QWP1 converted horizontal/vertical polarizations to LCP/RCP, and QWP2, a polarizer, and a CMOS camera (Basler acA2040, 2048 × 2048 pixels) on a translation stage measured Stokes parameters.
  • Optical skyrmionic beams were constructed by coaxial superposition of 2N+1 Bessel beams of order l, with weights set by a longitudinal intensity envelope F(z); the authors chose l1 = 0 and l2 = −1 and applied z-segmented control of L and F(z) in both RCP and LCP components, modulating δ and β to form Stokes-vector skyrmions.
  • The skyrmion number Q was calculated by integrating the skyrmion density n·(∂n/∂x × ∂n/∂y) over region A using the normalized local Stokes vector n = [S1, S2, S3]ᵀ; experimental skyrmion numbers were obtained by integrating within the purple dashed circle.

Limitations

  • The paper states that measured and numerically computed Q values are close to the designed integer values but not perfectly integral, mainly due to mutual coupling between longitudinal segments, non-ideal polarization/ellipticity variations within the integration region, and computational errors from finite sampling and limited integration area.
  • Evident from the text: experimental demonstrations cover a 30 cm propagation range and specific segment configurations, while broader arbitrary pathways such as Q = −2 to 2 or Q = −2 to 1 are presented as systematic numerical studies rather than experimentally verified results.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1038/s42005-025-02427-0

Cites

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Verification

Claims the paper makes

5 of 8 cited sources checked · 3 supported · 0 flagged · accuracy not yet measured

  • Premisecitation

    When 2D optical skyrmionic beams propagate in free space, the topological structure of the vector field can evolve from a Bloch type to a Néel type while the topological number remains unchanged.

    “When 2D optical skyrmionic beams propagate in free space, they possess a specific type of topological stability, during which the topological structure of the vector field can evolve from a Bloch type to a Néel type while maintaining an unchanged topological number 41,42 .”
    Quote in the paperSubstantial claim2 of 2 sources checked
    • cites [41] Gao, S. et al. Paraxial skyrmionic beams. Phys. Rev. A 102, 053513 (2020). source
    • cites [42] Zou, Y. et al. On-demand longitudinal transformations of light beams via an amplitude-phase-decoupled Pancharatnam-Berry Phase Element. Laser Photonics Rev. e02167 (2025). source

      The Figure 6 discussion reports that propagation produces periodic transitions between Néel-type and Bloch-type optical skyrmions. The longitudinally varying optical skyrmions section specifies beams prepared with a liquid-crystal q-plate, but the retrieved passages do not state that their topological number remains unchanged. (LLM, conf=0.84)

      Experimental — accuracy not yet measured
  • Premisecitation

    The construction of optical skyrmionic beams was achieved as a superposition of a vortex eigenmode and a non-vortex eigenmode with orthogonal polarizations.

    “The construction of optical skyrmionic beams was achieved as a superposition of a vortex eigenmode and a non-vortex eigenmode with orthogonal polarizations 41,43 .”
    Quote in the paperSubstantial claim2 of 2 sources checked
    • cites [41] Gao, S. et al. Paraxial skyrmionic beams. Phys. Rev. A 102, 053513 (2020). source
    • cites [43] Shen, Y. Topological bimeronic beams. Opt. Lett. 46, 3737–3740 (2021). source
  • Findingown data

    By simultaneously tailoring the longitudinal intensity profiles of vortex and non-vortex Bessel components with orthogonal polarizations, 2D optical skyrmion transitions with controllable topological states and skyrmion numbers are observed in quasi-nondiffractive skyrmionic beams.

    “By simultaneously tailoring the longitudinal intensity profiles of vortex and non-vortex Bessel components with orthogonal polarizations, 2D optical skyrmions transitions with controllable topological states and skyrmion numbers are observed in quasi-nondiffractive skyrmionic beams.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Achieving arbitrary and dynamically configurable generation of skyrmions in free space is a key challenge that must be addressed to advance the applications of optical skyrmions.
  • Findingown data

    The experimental results agree well with the simulated predictions.

    “As can be seen that the experimental results agree well with the simulated predictions.”
    Quote in the paperSubstantial claim
  • Findingown data

    The skyrmion number changes when the transition from the Néel to the antiskyrmion type is completed.

    “The skyrmion number also changes when the transition from the Néel to the antiskyrmion type is completed.”
    Quote in the paperSubstantial claim
  • It may state two separate claims as one. 13
  • Probably not a substantial claim. 1
  • The quote only partly states this claim. 1

  • It may state two separate claims as one.

    Premisecitation

    Bloch, Néel, and anti type skyrmionic beams are Poincaré beams with lemon and star structured polarization patterns, achievable as a superposition of a vortex eigenmode and a non-vortex eigenmode with orthogonal polarizations.

    “Since 2D optical skyrmions are special vector projection textures from S 2 Poincaré sphere to R 2 plane, as shown in Figs.1(a), Bloch, Néel, and anti type skyrmionic beams are Poincaré beams with lemon and star structured polarization patterns 47 , which can be achieved as a superposition of a vortex eigenmode and a non-vortex eigenmode with orthogonal polarizations.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [47] Cardano, F. et al. Generation and dynamics of optical beams with polarization singularities. Opt. Express 21, 8815–8820 (2013). source

      The Introduction identifies these polarization-singular beams as also called Poincaré beams, and the Conclusion describes lemon and star polarization patterns. Section 2 describes their construction from orthogonally polarized Laguerre–Gauss modes with zero and nonzero orbital angular momentum. The paper does not identify the beams or patterns as Bloch, Néel, or anti-type skyrmions, so that classification is not supported by this source. (LLM, conf=0.88)

      Experimental — accuracy not yet measured

  • It may state two separate claims as one.

    Findingown data

    The polarization rotates clockwise during propagation, driving the topological state to transition sequentially from the Bloch to the intermediate state and finally to the Néel type, with one transition near z= 15 cm within z= 0-30 cm.

    “Experimental results show that the polarization rotates clockwise during propagation, driving the topological state to transition sequentially from the Bloch to the intermediate state and finally to the Néel type.With the range of z= 0-30 cm, the topological state undergoes one transition near z= 15 cm.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    By designing the parameters, multiple transition pathways such as Q = -2 to 2 or Q = -2 to 1 can be realized, with sharp jumps in the skyrmion number observed near the predicted critical point at z = 15 cm.

    “It can be seen that by designing the parameters, multiple transition pathways such as Q = -2 to 2 or Q = -2 to 1 can be realized, and sharp jumps in the skyrmion number are observed near the predicted critical point at z = 15 cm.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    The skyrmionic beam presents a quasi-nondiffraction intensity profile, while the Stokes skyrmion orderly changes from Bloch to Néel and anti types, with transitions of skyrmion number Q from -1 to 1.

    “As shown in Fig.1(b), the skyrmionic beam presents quasi-nondiffraction intensity profile, but the Stokes skyrmion orderly changes from Bloch to Néel and anti types, with the transitions of skyrmion number Q from -1 to 1.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingreasoning

    The numerically computed and experimentally measured skyrmion numbers are both very close to the theoretically designed integer values, yet not perfectly integral.

    “It is worth noting that the numerically computed and experimentally measured skyrmion number (Q values) are both very close to the theoretically designed integer values, yet not perfectly integral.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingown data

    In the three-segment case, the skyrmion number remains constant at -0.9 initially and near 20 cm undergoes a transition, shifting abruptly from -0.9 to +0.9.

    “Initially, the skyrmion number remains constant at -0.9.Near 20 cm, the skyrmion number undergoes a transition, shifting abruptly from -0.9 to +0.9.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    Within a range of 30 cm, the topological state undergoes two transitions, from the Bloch to the Néel and finally to the antiskyrmion type, occurring near z= 10 cm and z= 20 cm respectively.

    “The experimental results show that within a range of 30 cm, the topological state undergoes two transitions, from the Bloch to the Néel and finally to the antiskyrmion type.These two transitions occur near z= 10 cm and z= 20 cm respectively.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    The topological state undergoes a transition from a Bloch (δ= 0, β= 0) to a Néel type (δ=-π/2, β= 0) while the skyrmion number remains constant.

    “We first validated that the topological state undergoes a transition from a Bloch (δ= 0, β= 0) to a Néel type (δ=-π/2, β= 0), while the skyrmion number remains constant.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisecitation

    In the case of antiskyrmions, the vector field does not undergo changes during propagation and the topological number remains unchanged.

    “However, in the case of antiskyrmions, the vector field does not undergo changes during propagation, and the topological number remains unchanged 43 .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [43] Shen, Y. Topological bimeronic beams. Opt. Lett. 46, 3737–3740 (2021). source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper may give no reason why it holds.

    Premisenone given

    Optical skyrmions have a specific type of topological stability such that the skyrmion number is invariant upon light propagation in free space.

    “As the optical counterparts of topologically protected quasiparticles, optical skyrmions have a specific type of topological stability that skyrmion number is invariant upon light propagation in free space.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    Because the orbital angular momentum of the two orthogonal eigenmodes remains invariant during propagation, the polarization texture structure and skyrmion number of the superimposed fields are preserved, so Bloch and Néel type skyrmions with the same polarization texture structure mutually transition while antiskyrmions and other states with different skyrmion numbers cannot transition upon light

    “This phenomenon stems from the fact that the orbital angular momentum of the two orthogonal eigenmodes remains invariant during propagation.”
    • Also stated in: § Introduction · plain
      “Therefore, the polarization texture structure and the skyrmion number of the superimposed fields are preserved, which leads to the mutual transition of Bloch type and Néel type skyrmions with the same polarization texture structure, while anti-skyrmions and other states that have completely different skyrmion numbers cannot undergoes transition upon light propagation.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one. The quote only partly states this claim.

    Interpretationreasoning

    The deviation of the measured skyrmion numbers from integer values stems from mutual coupling between different longitudinal segments of the beam, non-ideal polarization states within the numerical integration region, and computational errors from finite sampling points and limited integration area size.

    “This minor deviation primarily stems from two factors.First, in our longitudinal segment modulation method, mutual coupling exists between different longitudinal segments of the beam, introducing slight perturbations in the actual light field evolution compared to the ideal case.Second, within the numerical integration region, the polarization state does not achieve ideal conditions at all”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisereasoning

    Once the eigenmodes in the orthogonal polarization components are selected, they remain unchanged during propagation in free space, so the skyrmion number of the skyrmionic beam remains invariant, making the transition of Q from -1 to 1 impossible.

    “However, once the eigenmodes in the orthogonal polarization components are selected, they remain unchanged during propagation in free space.Consequently, the skyrmion number of the skyrmionics beam remains invariant, making it impossible to achieve the transition of the Q from -1 to 1 as illustrated in Figure 1(b).”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisenone given

    By modulating δ and β, the spatial distribution of the Stokes vector forms 2D optical skyrmions whose texture can be controlled as Bloch (δ=0, β=0) with Q=-1, Néel (δ=-π/2, β=0) with Q=-1, and antiskyrmion (δ=-π/2, β=π/2) with Q=1.

    “By modulating δ and β, the spatial distribution of the Stokes vector forms 2D optical skyrmions, which has a skyrmionics texture that can be controlled as Bloch (δ =0, β =0) with Q=-1, Néel (δ =-π/2, β =0) with Q=-1 and antiskyrmion (δ =-π/2, β =π/2) with Q=1.”
    Quote in the paperSubstantial claim
14 of 14

  • The paper relies on this without support.

    Achieving arbitrary and dynamically configurable generation of skyrmions in free space is a key challenge that must be addressed to advance the applications of optical skyrmions.

    “To further advance these applications, it is crucial to address the key challenge of achieving arbitrary and dynamically configurable generation of skyrmions in free space.”

  • The paper relies on this without support.

    The dynamic transitions of optical skyrmions remain underexplored.

    “Optical skyrmions, as topologically stable structures, offer promising applications in spintronics and quantum computing, yet their dynamic transitions remain underexplored.”
2 of 2

Citations

Cites

Flagged first, then by citations

Research works printed but not linked: 3

  1. Pisljar, J. et al. Blue Phase III: Topological Fluid of Skyrmions,. Phys. Rev. X 12, 011003 (2022).
  2. Zhang, X. et al. Skyrmion-skyrmion and skyrmion-edge repulsions in skyrmion-based racetrack memory. Sci. Rep. 5, 7643 (2015). · DOI
  3. Wu, X. et al. Wavelength-insensitive snapshot Stokes polarimetric imaging based on cascaded metasurfaces. Adv. Photonics 7, 016008 (2025). · DOI

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Metadata

Authors
Fan, X., Wu, X., Ren, K., Zhou, L., Guo, X., Wei, B., Zhang, Y., Liu, S., Li, P., & Zhao, J.
Affiliations
  • Northwestern Polytechnical University (CN)
  • Tsinghua University (CN)
Corresponding author
  • Guo, Xuyue
  • Li, Peng
ORCID
Venue
Communications Physics
Publisher
Springer Science and Business Media LLC
Published
2025-11-26
Volume
8
Issue
1
ISSN
2399-3650 (ISSN-L)
DOI
10.1038/s42005-025-02427-0
OpenAlex
W4416722711
Cited by
2
References
52
Citations by year
2026: 2
FWCI
0.58
Type
journal article
Language
en
Open access
Licence
Locations
  • Communications Physics (publishedVersion, cc-by-nc-nd)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
  • Northwestern University
  • National Natural Science Foundation of China (12174309, 12474298)
  • Northwestern Polytechnical University
  • National Key Research and Development Program of China (2022YFA1404800)
  • Fundamental Research Funds for the Central Universities (5000230111)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Photonic Systems
Keywords
optical skyrmions, skyrmion number, topological charge, free-space beam propagation, Bessel beams, optical vortices, polarization, topological stability, spintronics, optical information processing

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