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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
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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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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
§ Optical skyrmions in evanescent electromagnetic fields > Discussion
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
§ Optical skyrmions in evanescent electromagnetic fields > Observation of optical skyrmions
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“and hence does not hold for propagating waves (see Supplementary).”
§ Optical skyrmions in evanescent electromagnetic fields > Formation of optical skyrmion lattices
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
§ Optical skyrmions in evanescent electromagnetic fields > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Also stated in: § Discussion · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“A more thorough explanation as to why free-space electromagnetic waves do not exhibit skyrmions can be found in the Supplementary.”
§ Optical skyrmions in evanescent electromagnetic fields > Formation of optical skyrmion lattices
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
§ Optical skyrmions in evanescent electromagnetic fields > Observation of optical skyrmions
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“we discover and observe optical skyrmion lattices that can be easily created and controlled”
§ Optical skyrmions in evanescent electromagnetic fields > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
§ Optical skyrmions in evanescent electromagnetic fields > Observation of optical skyrmions
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Moreover, they show that even guided modes with a relatively high amount of loss (decaying after 100 oscillations) can create skyrmion lattices.”
§ Optical skyrmions in evanescent electromagnetic fields > Discussion
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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).”
§ Optical skyrmions in evanescent electromagnetic fields > Observation of optical skyrmions
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes
- It may state two separate claims as one. 11
- Probably not a substantial claim. 2
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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).”
§ Optical skyrmions in evanescent electromagnetic fields > Formation of optical skyrmion lattices
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Optical skyrmions are experimentally demonstrated by interfering surface plasmon polaritons and are measured via phase-resolved near-field optical microscopy.”
§ Optical skyrmions in evanescent electromagnetic fields > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We discovered and experimentally demonstrated an optical skyrmion lattice through the interference of electromagnetic waves.”
§ Optical skyrmions in evanescent electromagnetic fields > Discussion
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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).”
§ Optical skyrmions in evanescent electromagnetic fields > Formation of optical skyrmion lattices
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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 ).”
§ Optical skyrmions in evanescent electromagnetic fields > Observation of optical skyrmions
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
§ Optical skyrmions in evanescent electromagnetic fields > Observation of optical skyrmions
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Also stated in: § Discussion · plain
In the paper
“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.”
§ Optical skyrmions in evanescent electromagnetic fields > Formation of optical skyrmion lattices
What the sources say
- Not matchedcites [39]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Not matched
In the paper
“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 .”
§ Optical skyrmions in evanescent electromagnetic fields > Formation of optical skyrmion lattices
What the sources say
- Not matchedcites [21]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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).”
§ Optical skyrmions in evanescent electromagnetic fields > Observation of optical skyrmions
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
§ Optical skyrmions in evanescent electromagnetic fields > Observation of optical skyrmions
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
§ Optical skyrmions in evanescent electromagnetic fields > Discussion
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“SPPs only exist in TM polarization and the phase difference between SPPs propagating along different directions can be easily controlled (41).”
§ Optical skyrmions in evanescent electromagnetic fields > Observation of optical skyrmions
What the sources say
- Not matchedcites [41]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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In the paper
“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.”
§ Optical skyrmions in evanescent electromagnetic fields > Formation of optical skyrmion lattices
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial 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
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