The DOI matches its Crossref record; 48 of the 49 references it cites were found in a registry or an index; none of the 4 sources its claims cite is checked for support yet.
Optical skyrmion lattice in evanescent electromagnetic fields
Open accessAbstract
Generating a lattice of optical skyrmions: The topological properties of systems can be robust to defects and imperfections. Skyrmions are one such topological entity, which resemble “hedgehog-like” structures. Tsesses et al. controlled the interference of plasmon polaritons on a patterned metallic surface to generate a lattice of optical skyrmions. Such control could potentially optically mimic complex condensed matter systems or help in the development of robust optical communications and circuits. Science , this issue p. 993
Overview
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Written from the paper’s full text.
TL;DR
The paper predicts and experimentally observes an optical skyrmion lattice formed by interfering evanescent electromagnetic waves, specifically surface plasmon polaritons. It shows that the electric-field vector can form Néel-type or bubble-type skyrmions and that the topological invariant is robust to losses and imperfections.
Key findings
- An optical skyrmion lattice is theoretically described using six interfering TM guided waves, with each lattice site forming a Néel-type skyrmion and calculated skyrmion number \(S = 1\).
- The skyrmion domain walls can be tuned from bubble-type to Néel-type by changing the transverse wave vector; the skyrmion number density contrast converges to 0.5 for the Néel-type case.
- Experimentally, surface plasmon polaritons on an air–gold interface produce a plasmonic skyrmion lattice with measured skyrmion number \(S = 0.997 \pm 0.058\).
- Loss robustness is quantified: 49 unit cells can exhibit \(S > 0.99\) if the waves persist for roughly 400 periods before decaying; the experimental sample had 37 lattice sites.
Methods
- Theory: six equal-amplitude TM guided waves propagating in the transverse plane with transverse wave vectors of similar magnitude create three standing waves at 0°, 60°, and 120°; the axial electric field is expressed as a sum of three cosine functions, and the skyrmion number is computed from the normalized three-component electric field.
- Experiment: SPPs are excited at an air–gold interface using a hexagonally shaped coupling slit and 660 nm circularly polarized light; the sample consists of six gratings on a 200 nm Au layer on a 1 mm glass substrate, with grating periodicity corresponding to the plasmonic wavelength of 636 nm.
- Measurement: phase-resolved near-field optical microscopy (s-NSOM) with pseudo-heterodyne interferometric detection measures the axial electric field at 20 nm resolution; spatial Fourier filtering is used to remove noise before extracting transverse field components and skyrmion number.
Limitations
- Stated: losses distort the unit vector \(e = E/|E|\) and create an unwanted phase difference between components; in the small-loss regime the real part still yields a well-defined skyrmion lattice, but \(S\) deviates slightly from its quantized value due to weak breaking of lattice translation symmetry, increasingly for unit cells farther from the origin.
- Stated: the finite structure and unequal SPP amplitudes—caused by different propagation lengths of SPPs generated by two slit edges and propagation loss—distort the skyrmion lattice.
- Evident from the text: the experiment demonstrates a bubble-type lattice at the center of the sample, while the full tuning from bubble-type to Néel-type skyrmions is shown theoretically; TE-polarized magnetic-field skyrmions are proposed but not experimentally demonstrated.
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Claims the paper makes
0 of 4 cited sources checked · 0 supported · 0 flagged
- Findingnone given
Once the electromagnetic waves gain evanescence in free-space, the skyrmion number jumps to the value of 1, independent of the change in the transverse wave vector.
“Once the electromagnetic waves gain evanescence in free-space, the skyrmion number jumps to the value of 1, independent of the change in the transverse wave vector.”
Quote in the paperSubstantial claim - Findingreasoning
In the small-loss regime, the skyrmion number S deviates slightly from its quantized value at zero losses due to the weak breaking of the lattice translation symmetry, increasingly more so for unit cells farther away from the point of origin.
“In this regime, the skyrmion number S deviates slightly from its quantized value at zero losses due to the weak breaking of the lattice translation symmetry, increasingly more so for unit cells which are farther away from the point of origin.”
Quote in the paperSubstantial claim - Findingreasoning
The property that all electric field components are real for evanescent waves does not hold for propagating waves.
“and hence does not hold for propagating waves (see Supplementary).”
Quote in the paperSubstantial claim - Findingown data
Optical skyrmion lattices are robust to imperfections.
“while illustrating their robustness to imperfections”
- Also stated in: § Discussion · plain
“We have also explored, theoretically and experimentally, the robustness of the topological properties of the system to losses, finiteness and other imperfections.”
Quote in the paperSubstantial claim - Also stated in: § Discussion · plain
- Findingreasoning
Free-space electromagnetic waves do not exhibit skyrmions.
“A more thorough explanation as to why free-space electromagnetic waves do not exhibit skyrmions can be found in the Supplementary.”
Quote in the paperSubstantial claim
- Findingown data
The interference of the SPPs in the middle of the coupling slit creates a plasmonic skyrmion lattice with characteristics typical to bubbles.
“The interference of the SPPs in the middle of the coupling slit creates a plasmonic skyrmion lattice with characteristics typical to bubbles, as portrayed in Fig. 5.”
Quote in the paperSubstantial claim - Findingown data
Optical skyrmion lattices can be easily created and controlled.
“we discover and observe optical skyrmion lattices that can be easily created and controlled”
Quote in the paperSubstantial claim - Findingown data
A configuration in which 49 sites exhibit S>0.99 is obtained if the electromagnetic waves creating it persist for roughly 400 periods before decaying.
“For example, a configuration in which 49 sites exhibit 0.99 S is obtained if the electromagnetic waves creating it persist for roughly 400 periods before decayingan easily achieved goal in many photonic systems.”
Quote in the paperNot a substantial claim - Findingnone given
Even guided modes with a relatively high amount of loss (decaying after 100 oscillations) can create skyrmion lattices.
“Moreover, they show that even guided modes with a relatively high amount of loss (decaying after 100 oscillations) can create skyrmion lattices.”
Quote in the paperNot a substantial claim - Findingown data
The extracted skyrmion number density at the center of the lattice resembles that of the bubble-type skyrmion lattice shown in the inset of Fig. 2 (point A).
“Fig. 5E depicts the extracted skyrmion number density at the center of the lattice, which resembles that of the bubble-type skyrmion lattice shown in the inset of Fig. 2 (point A).”
Quote in the paperNot a substantial claim - Premisereasoning
Surface plasmon polaritons are by design an imperfect system, due to the ohmic losses generated by the metal.
“Furthermore, they are by design an imperfect system, due to the ohmic losses generated by the metal.”
Quote in the paperSubstantial claim - Study design and conductcitation
The experimental setup enables phase-resolved measurement of the electric field normal to the surface by means of pseudo-heterodyne interferometric detection.
“The experimental setup used to detect optical skyrmions is depicted in Fig. 4 a scattering nearfield scanning optical microscope (s-NSOM), which enables phase-resolved measurement of the electric field normal to the surface by means of pseudo-heterodyne interferometric detection (42).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [42]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationnone given
The optical skyrmions presented are entirely engineered by the boundary conditions of a linear system.
“whereas the optical skyrmions we present are entirely engineered by the boundary conditions of a linear system.”
Quote in the paperSubstantial claim - Interpretationreasoning
The bubble-like characteristics are a result of the relatively small transverse wave vector, leading to an axial field component 5 times larger than the transverse ones.
“This is a result of the relatively small transverse wave vector, leading to an axial field component 5 times larger than the transverse ones.”
Quote in the paperSubstantial claim - Interpretationreasoning
The transition from bubble-type to Néel-type skyrmions stems directly from the scaling factor k_z/k, which can be tuned by varying the effective index of a guided mode.
“This stems directly from the scaling factor / z kk , which can be tuned by varying the effective index (normalized propagation constant) of a guided mode.”
Quote in the paperSubstantial claim - Interpretationreasoning
The results are ubiquitous to any photonic system exhibiting evanescence, e.g. planar waveguide modes and waves undergoing total internal reflection (TIR).
“Our results are ubiquitous to any photonic system exhibiting evanescence, e.g.planar waveguide modes and waves undergoing total internal reflection (TIR).”
Quote in the paperSubstantial claim - Premisereasoning
The skyrmion number S, being an integer, is robust to deformations of the field e as long as e remains non-singular and maintains the periodicity of the lattice.
“The skyrmion number S, being an integer, is robust to deformations of the field e as long as e remains non-singular and maintains the periodicity of the lattice.”
Quote in the paperSubstantial claim - Study design and conductreasoning
The phase information, filtering ability and high spatial resolution of the measurement enable the correct extraction of the transverse field components and thus of the skyrmion number.
“The phase information, filtering ability and high spatial resolution of the measurement enable the correct extraction of the transverse field components and thusof the skyrmion number.”
Quote in the paperSubstantial claim - Interpretationown data
The electric field vector of electromagnetic waves can be structured to meet all requirements needed to create a skyrmion lattice, similarly to the magnetization vector of skyrmion lattices in chiral magnets.
“Interestingly, we find that the electric field vector of electromagnetic waves can be structured so as to meet all the requirements needed to create a skyrmion lattice, similarly to the magnetization vector of the skyrmion lattices in chiral magnets.”
Quote in the paperSubstantial claim
- It may state two separate claims as one. 11
- Probably not a substantial claim. 2
It may state two separate claims as one.
FindingreasoningFor k slightly larger than k0, the skyrmions are spatially confined (density contrast close to 1), with clear domain walls separating between two specific field states, effectively creating bubble-type skyrmions.
“For k slightly larger than 0 k , the skyrmions are spatially confined (density contrast close to 1), with clear domain walls separating between two specific field states, effectively creating bubble-type skyrmions (point A).”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingown dataOptical skyrmions are experimentally demonstrated by interfering surface plasmon polaritons and measured via phase-resolved near-field optical microscopy.
“Optical skyrmions are experimentally demonstrated by interfering surface plasmon polaritons and are measured via phase-resolved near-field optical microscopy.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingown dataWe discovered and experimentally demonstrated an optical skyrmion lattice through the interference of electromagnetic waves.
“We discovered and experimentally demonstrated an optical skyrmion lattice through the interference of electromagnetic waves.”
Quote in the paperSubstantial claimIt may state two separate claims as one.
FindingreasoningAs k grows, the domain walls start to smear, creating skyrmions with increasingly uniform skyrmion number density, converging to the Néel-type field formation shown in Fig. 1 (point C, density contrast of 0.5).
“As k grows, the domain walls start to smear (point B), creating skyrmions with increasingly uniform skyrmion number density, converging to the Néel-type field formation shown in Fig. 1 (point C, density contrast of 0.5).”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingnone givenIn the specific system used here, SPPs are excited at the interface of air and gold, resulting in both a small propagation decay and a transverse wave vector just slightly larger than the free-space wavenumber (k = (1.038+0.003i)k0).
“In the specific system used here (inset Fig. 4), SPPs are excited at the interface of air and gold, resulting in both a small propagation decay and a transverse wave vector just slightly larger than the free-space wavenumber ( 0 1.038 0.003 k i k ).”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingown dataThe measured skyrmion number in each lattice site is S=0.997±0.058, demonstrating the robustness of the optical skyrmions.
“Calculating the skyrmion number in each lattice site, we reach the result 0.997 0.058 S , demonstrating the robustness of the optical skyrmions.”
- Also stated in: § Discussion · plain
“The measured skyrmion number of a single lattice site was 0.997 0.058 S , which, together with the figures, shows a good match to the theoretical prediction.”
Quote in the paperSubstantial claim- Also stated in: § Discussion · plain
It may state two separate claims as one.
FindingcitationFor waves evanescently decaying in one dimension, all electric field components are entirely real (up to a global phase), allowing definition of a real unit vector e=E/|E| and enabling description of the field configuration as an optical skyrmion lattice.
“Namely, for waves evanescently decaying in one dimension, all electric field components are entirely real (up to a global phase), allowing to define a real unit vector e= EE associated with the electric field and enabling a description of the field configuration as an optical skyrmion lattice.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [39]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
It may state two separate claims as one.
Findingown dataThe normalized three-dimensional electric field confirms the formation of a skyrmion lattice, with each lattice site exhibiting the distinct features of a Néel-type skyrmion and a calculated skyrmion number S=1.
“The normalized three-dimensional electric field (Fig. 1D) confirms the formation of a skyrmion latticeeach lattice site exhibits the distinct features of a Néel-type skyrmion (21), with their calculated skyrmion number, using Eq. ( 1), being 1 S .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [21]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
It may state two separate claims as one.
FindingreasoningIn the regime of small losses, the configuration of the real part of the field still yields a well-defined skyrmion lattice, while being sufficiently larger than the imaginary part such that the latter is negligible.
“However, in the regime of small losses, the configuration of the real part of the field still yields a well-defined skyrmion lattice, while being sufficiently larger than the imaginary part such that the latter is negligible (see full derivation in the Supplementary).”
Quote in the paperSubstantial claimIt may state two separate claims as one.
Findingown dataThe real electric field is slightly distorted, as expected, but still shows similarity to the electric field configuration presented in Fig. 1.
“While the real electric field is slightly distorted, as expected (Fig. 5A-C), it still shows similarity to the electric field configuration presented in Fig. 1.”
Quote in the paperNot a substantial claimProbably not a substantial claim. The paper’s conclusions may not depend on it.
Premisenone givenThe optical skyrmions described in this work are in the frequency domain, i.e., formed in a physical field oscillating in time, as opposed to other skyrmions, which are field formations constant in time.
“It is worth emphasizing that the optical skyrmions described in this work are in the frequency domain, i.e., formed in a physical field oscillating in time, as opposed to other skyrmions, which are field formations constant in time.”
Quote in the paperNot a substantial claimIt may state two separate claims as one.
PremisecitationSurface plasmon polaritons only exist in TM polarization and the phase difference between SPPs propagating along different directions can be easily controlled.
“SPPs only exist in TM polarization and the phase difference between SPPs propagating along different directions can be easily controlled (41).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [41]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim.
Study design and conductreasoningThe new definition of e as the real part of the local unit vector of the electric field is completely consistent with the prior description of optical skyrmions in the ideal case.
“This new definition is completely consistent with the prior description of optical skyrmions in the ideal case, which is determined by Eqs.(2,3) in a lossless medium.”
Quote in the paperSubstantial claim
The paper relies on this without support.
The field of optical skyrmions has so far remained untapped by experimental investigation.
“However, only recently has there been any experimental investigation of optical topological domain walls (38), while the field of optical skyrmions has so far remained untapped.”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Figure 1 cites Eq. 4 for a field defined by Eq. 3
MinorThe caption attributes the transverse electric-field amplitude to Eq. 4, but the paper identifies Eqs. (2,3) as the equations describing the electric field in Figure 1; Eq. 3 is introduced as the transverse-field equation.
“(B) Amplitude of the transverse (in-plane) electric field (Eq.4).”
“Figure 1 depicts the electric field described by Eqs.(2,3)”
Figure 5 points to Figure 3 for the measurement system
MinorFigure 5 says the measurement system is described in Figure 3, whereas Figure 4 is labeled as the experimental setup and sample characterization. Figure 3 instead concerns theoretical persistence in the presence of loss.
“The complex value of the axial electric field was measured with 20 nm resolution by the system described in Fig.3”
“Fig. 4. Experimental setup and sample characterization.”
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Metadata
- Authors
- Tsesses, S., Ostrovsky, E., Cohen, K., Gjonaj, B., Lindner, N. H., & Bartal, G.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- Albanian University (AL)
- Corresponding author
- Bartal, G.
- Venue
- Science
- Published
- 2018-09-07
- Volume
- 361
- Issue
- 6406
- Pages
- 993-996
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2884207325
- Cited by
- 514
- References
- 49
- Citations by year
- 2026: 129 · 2025: 122 · 2024: 84 · 2023: 58 · 2022: 38 · 2021: 36 · 2020: 30 · 2019: 16 · 2018: 1
- FWCI
- 9.96
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Science (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Figshare (submittedVersion, public-domain)
- arXiv (Cornell University)
- Funders
- H2020 European Research Council (639172)
- “Circle of Light,” Israeli Centers for Research Excellence (Israel Science Foundation (ISF) (1802/12))
- "Circle of Light", Israeli Centers of Research Excellence (Israel Science Foundation (ISF) (1802/12))
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Plasmonic and Surface Plasmon Research
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
- Keywords
- surface plasmon polaritons, topological defects, Néel skyrmions, topological domain walls, photonic systems, optical information processing
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-11-10, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-11-10 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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