Optical skyrmions and other topological quasiparticles of light

In the paper

“In the case of large values of vorticity associated with larger value of a skyrmion number, the skyrmions are designated as higher-order skyrmions [29] (Fig. 2).”

What the sources say

• Disputed

  In Results, under “Theoretical modeling and design of LSP skyrmions” (page unavailable), the paper describes higher-order modes as having multiple radial twists, but says their total skyrmion number is 1 for odd modes and 0 for even modes—not a larger number. The cited passage does not identify large vorticity as the criterion for calling them higher-order skyrmions. (LLM, conf=0.88)

  Checked by a reasoning model — may be wrong.

  cites [29] Deng, Z.-L., Shi, T., Krasnok, A., Li, X. & Alù, A. Observation of localized magnetic plasmon skyrmions. Nat. Commun. 13, 8 (2022). sourceExperimental — accuracy not yet measured

In the paper

“Based on the generalized topological transformation, the bimeron has the texture composed by two merons with opposite polarities [34].”

What the sources say

• ?Could not verify

  Section 2 discusses photonic skyrmion spin textures and reversals of spin orientation at an optical interface, but does not describe a bimeron as two merons with opposite polarities. Searches for “bimeron,” “meron,” and “generalized topological transformation” found no passage addressing that claim in our copy. (LLM, conf=0.72)

  cites [34] Shi, P., Du, L. & Yuan, X. Strong spin–orbit interaction of photonic skyrmions at the general optical interface. Nanophotonics 9, 4619–4628 (2020). sourceExperimental — accuracy not yet measured

In the paper

“While optical field-skyrmions which can be switched between Néel-and Bloch-types were reported [43], the existence of Bloch-type skyrmions was promptly disproved [44,45].”

What the sources say

• ?Could not verify

  The paper reports second-order meron and antimeron polarization textures in an optical microcavity (Abstract; no page given). The passages found for “Bloch-type,” “Néel,” and switching describe meron textures, not a report of switchable Néel- and Bloch-type optical skyrmions or a disproof of Bloch-type skyrmions. The citing sentence attaches separate citations to the report and the disproof, but neither point is established by our copy of this source. (LLM, conf=0.76)

  cites [43] Król, M. et al. Observation of second-order meron polarization textures in optical microcavities. Optica 8, 255–261 (2021). sourceExperimental — accuracy not yet measured
• Partly supported

  In Results, under “Simulating the topological Hall effect from single skyrmions with light” (page not provided), the paper describes Néel- and Bloch-type synthetic magnetization textures using different phase parameters. It does not report optical field-skyrmions being switched between those types; it says the model can be changed to accommodate them. The separate disproval claim is attributed to [44,45], not this source. (LLM, conf=0.84)

  cites [44] Karnieli, A., Tsesses, S., Bartal, G. & Arie, A. Emulating spin transport with nonlinear optics, from high-order skyrmions to the topological hall effect. Nat. Commun. 12, 1092 (2021). sourceExperimental — accuracy not yet measured
• ?Could not verify

  The discussion on p. 12301-14 describes proposed nonlinear-optical skyrmionic textures and their calculated effects, but does not address whether Bloch-type optical field-skyrmions exist. Searches for “Bloch-type skyrmions,” “disproved,” and “Néel” found no passage in our copy supporting the disproof attributed to this source. (LLM, conf=0.76)

  cites [45] Karnieli, A., Li, Y. & Arie, A. The geometric phase in nonlinear frequency conversion. Front. Phys. 17, 12301 (2022). sourceExperimental — accuracy not yet measured

In the paper

“Plasmonic spin field has recently been also used to tailor more complex skyrmionic structures, such as the merons with fractional topological charges [51,52], whereby a novel quasiparticle triplet-meron structure were designed and generated (Fig. 4c), with nanometric and femtosecond space-time resolution [51].”

What the sources say

• ?Could not verify

  The Introduction says optical skyrmions have been observed through interference of plasmon polaritons, but does not discuss merons or fractional topological charges. Searches for merons, triplet-meron structures, and nanometric or femtosecond resolution found no supporting passage in our copy; the Conclusions instead discuss paraxial vector vortex beams and say related experiments will be reported elsewhere. (LLM, conf=0.78)

  cites [51] Gao, S. et al. Paraxial skyrmionic beams. Phys. Rev. A 102, 053513 (2020). sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [52] Beckley, A. M., Brown, T. G. & Alonso, M. A. Full Poincaré beams. Opt. Express 18, 10777–10785 (2010). source

In the paper

“A natural generalization of skyrionium is a kπ-skyrmion with the raidal multi-(kπ-)twist structure [32], also known as a target skyrmion [33], which replaces the radial 2π-twist structure with kπ-twist structure and controls the skyrmion number between 0 and 1 (or -1).”

What the sources say

• ?Could not verify

  The paper’s discussion of skyrmion number (pp. 33614–33615) concerns a flat magnetic-field vortex in surface plasmon polaritons, for which it calculates a number of zero. A search for kπ-skyrmions, skyrmionium, radial multi-twists, and the claimed range of skyrmion numbers found no passage addressing those points. (LLM, conf=0.76)

  cites [32] Meiler, T., Frank, B. & Giessen, H. Dynamic tailoring of an optical skyrmion lattice in surface plasmon polaritons: comment. Opt. Express 28, 33614–33615 (2020). sourceExperimental — accuracy not yet measured
• ?Could not verify

  The supplied passages describe photonic spin-skyrmion and meron lattices, including skyrmion numbers of 1 and ±½, but do not address kπ-skyrmions as radial multi-twist generalizations of skyrmionium. Searches for “kπ-skyrmion,” “skyrmionium,” “target skyrmion,” and “2π twist” found no passage addressing that attributed point. The passages are labeled Abstract in our copy; no page number is available. (LLM, conf=0.75)

  cites [33] Lei, X. et al. Photonic spin lattices: symmetry constraints for skyrmion and meron topologies. Phys. Rev. Lett. 127, 237403 (2021). sourceExperimental — accuracy not yet measured

In the paper

“The Stokes bimerons were recently generalized into multiskyrmion structures with increasingly complex topologies [89,90].”

What the sources say

• ?Could not verify

  The paper’s discussion and conclusion describe twisted magnons driving the motion of a magnetic skyrmion (section “Twisted magnon as a magnetic tweezer”; page unavailable). Searches for “Stokes bimerons” and “multiskyrmion” found no passage about generalizing bimerons into more complex structures. (LLM, conf=0.72)

  cites [89] Jiang, Y. et al. Twisted magnon as a magnetic tweezer. Phys. Rev. Lett. 124, 217204 (2020). sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Abstract (page unavailable) describes magnetic skyrmions and a laser-based method for trapping them, but does not address Stokes bimerons or their generalization. Searches for “Stokes bimerons,” “multiskyrmion,” and related terms found no passage in our copy supporting the attributed claim. (LLM, conf=0.72)

  cites [90] Wang, X.-G. et al. The optical tweezer of skyrmions. npj Comput. Mater. 6, 140 (2020). sourceExperimental — accuracy not yet measured

In the paper

“and can be driven by the skyrmion Hall effect [61,62], spin-orbit torque [99,100], and even the light [101][102][103][104][105].”

What the sources say

• ?Not checked — no full text of the sourcecites [61] Hellwarth, R. & Nouchi, P. Focused one-cycle electromagnetic pulses. Phys. Rev. E 54, 889 (1996). source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [62] Shen, Y., Hou, Y., Papasimakis, N. & Zheludev, N. I. Supertoroidal light pulses as electromagnetic skyrmions propagating in free space. Nat. Commun. 12, 5891 (2021).
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [99] Ornelas, P., Nape, I., Koch, R. D. M. & Forbes, A. Nonlocal skyrmions as topologically resilient quantum entangled states of light. Preprint at https://arxiv.org/abs/2210.04690 (2022).
• ?Could not verify

  Section 5.2.2 (page unavailable) describes optical switching of magnetization and optical excitation of spin currents, but does not address driving skyrmions with light. Searches for skyrmion driving, the skyrmion Hall effect, and spin-orbit torque found no passage establishing the claim about skyrmions. (LLM, conf=0.72)

  cites [100] Galiffi, E. et al. Photonics of time-varying media. Adv. Photon. 4, 014002 (2022). sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [101] Ge, H. et al. Observation of acoustic skyrmions. Phys. Rev. Lett. 127, 144502 (2021). source
• ?Could not verify

  The citation is attached to the claim that skyrmions can be driven by light. The main-text passage on three-wave interference reports a skyrmion lattice in propagating sound waves, while the References list mentions optical skyrmions; neither says that light drives skyrmions. Searches for light-driven skyrmions and the cited sentence found no supporting passage in our copy. (LLM, conf=0.76)

  cites [102] Muelas-Hurtado, R. D. et al. Observation of polarization singularities and topological textures in sound waves. Phys. Rev. Lett. 129, 204301 (2022). sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [103] Hu, P. et al. Observation of localized acoustic skyrmions. Appl. Phys. Lett. 122, 022201 (2023). source
• Partly supported

  For this source, the relevant part of the citing sentence is the claim that skyrmions can be driven by light. The Discussion mentions optomechanical coupling with light as a possible route to future skyrmion systems, but the Results describe moving the observed phononic skyrmion lattice by changing excitation-source phases, not by light. The source therefore supports a possible connection to light, not the stated light-driven motion. (LLM, conf=0.82)

  cites [104] Cao, L., Wan, S., Zeng, Y., Zhu, Y. & Assouar, B. Observation of phononic skyrmions based on hybrid spin of elastic waves. Sci. Adv. 9, eadf3652 (2023). sourceExperimental — accuracy not yet measured
• Partly supported

  The Introduction and Section II (page unavailable) describe using structured light to create skyrmionic optical excitations in atomic ensembles. This supports the light-related part for skyrmion formation, but the passages do not show light driving the motion of an existing skyrmion. The Hall effect and spin-orbit torque have separate citations in the citing sentence and are not attributed to this source. (LLM, conf=0.82)

  cites [105] Parmee, C. D., Dennis, M. R. & Ruostekoski, J. Optical excitations of skyrmions, knotted solitons, and defects in atoms. Commun. Phys. 5, 54 (2022). sourceExperimental — accuracy not yet measured

In the paper

“The optical hopfions were recently extended to higher-order quasiparticles and their topologically protected transport in free space was demonstrated [92].”

What the sources say

• ?Could not verify

  The Introduction and Discussion describe laser-controlled rotation of a magnetic skyrmion crystal, not optical hopfions. Searches for optical hopfions, higher-order quasiparticles, and protected transport in free space found no passage addressing the cited claim. (LLM, conf=0.78)

  cites [92] Tengdin, P. et al. Imaging the ultrafast coherent control of a skyrmion crystal. Phys. Rev. 12, 041030 (2022). sourceExperimental — accuracy not yet measured

In the paper

“Optical skyrmions can interact with magnetic skyrmions allowing for a route to manipulate these magnetic particles [103][104][105].”

What the sources say

• ?Not checked — no full text of the sourcecites [103] Hu, P. et al. Observation of localized acoustic skyrmions. Appl. Phys. Lett. 122, 022201 (2023). source
• ?Could not verify

  The Introduction mentions magnetic skyrmions and the extension of skyrmions to photonics, but does not describe an interaction between them. The Discussion addresses coupling between elastic and electromagnetic waves, not using optical skyrmions to manipulate magnetic skyrmions. Searches for optical–magnetic interaction and manipulation found no supporting passage in our copy. (LLM, conf=0.76)

  cites [104] Cao, L., Wan, S., Zeng, Y., Zhu, Y. & Assouar, B. Observation of phononic skyrmions based on hybrid spin of elastic waves. Sci. Adv. 9, eadf3652 (2023). sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Baby-Skyrmions section describes optical fields used to prepare skyrmionic textures in an atomic ensemble, and the 3D Skyrmions section discusses light–matter coupling. Neither the supplied passages nor searches for magnetic-skyrmion interaction and manipulation address optical skyrmions interacting with magnetic skyrmions to manipulate them. No page numbers were provided in our copy. (LLM, conf=0.76)

  cites [105] Parmee, C. D., Dennis, M. R. & Ruostekoski, J. Optical excitations of skyrmions, knotted solitons, and defects in atoms. Commun. Phys. 5, 54 (2022). sourceExperimental — accuracy not yet measured

In the paper

“Similarly, bimeronium is a quasiparticle which can be obtained by adding radial kπ twist structure to a fundamental bimeron (akin to the concept of skyrmionium) [38].”

What the sources say

• ?Could not verify

  The discussion on p. 4 describes merons and their half-integer topological charge, but does not address bimeronium or its proposed construction. Searches for “bimeronium,” “radial kπ twist,” “bimeron,” and “skyrmionium” found no passage in our copy supporting the attributed claim. (LLM, conf=0.76)

  cites [38] Xiong, L. et al. Polaritonic vortices with a half-integer charge. Nano Lett. 21, 9256–9261 (2021). sourceExperimental — accuracy not yet measured

In the paper

“While the optical bimerons were only recently first proposed in paraxial vector beams [69].”

What the sources say

• ?Could not verify

  The paper’s skyrmion and meron passages discuss momentum-space spin textures in superconductors, not optical bimerons. Searches for optical bimerons and paraxial vector beams found no passage addressing where optical bimerons were first proposed. (LLM, conf=0.76)

  cites [69] Loder, F., Kampf, A. P., Kopp, T. & Braak, D. Momentum-space spin texture in a topological superconductor. Phys. Rev. B 96, 024508 (2017). sourceExperimental — accuracy not yet measured

In the paper

“In condensed matter physics, skyrmions can be formed due to the Dzyaloshinskii-Moriya interaction (DMI) [97], dipole-dipole interaction [98]”

What the sources say

• ?Could not verify

  The paper’s ‘Polarization and vector vortices’ section discusses optical vortex structures, not the formation of condensed-matter skyrmions. Searches for ‘skyrmion,’ ‘Dzyaloshinskii,’ and ‘dipole-dipole’ found no passage in our copy addressing either proposed interaction. No page numbers are available in the indexed passages. (LLM, conf=0.77)

  cites [97] Shen, Y. et al. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities. Light Sci. Appl. 8, 90 (2019). sourceExperimental — accuracy not yet measured
• ?Could not verify

  The cited paper’s Ray-Wave Structured Light section discusses optical skyrmions, but does not address how skyrmions form in condensed matter. Searches for dipole–dipole and Dzyaloshinskii–Moriya interactions found no passage stating the claimed mechanisms; the returned passages concern structured light and references (pages unavailable). (LLM, conf=0.76)

  cites [98] Wan, Z., Wang, H., Liu, Q., Fu, X. & Shen, Y. Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photon. 10, 2149–2164 (2023). sourceExperimental — accuracy not yet measured

In the paper

“The most important applications of magnetic skyrmions are the high-density information storage in modern spintronics [98].”

What the sources say

• ?Could not verify

  The Ray-Wave Structured Light section discusses optical skyrmions, and the cited passages on information capacity concern structured light and optical communication. Searches for magnetic skyrmions, spintronics, and high-density information storage found no passage addressing the claimed application. (LLM, conf=0.75)

  cites [98] Wan, Z., Wang, H., Liu, Q., Fu, X. & Shen, Y. Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photon. 10, 2149–2164 (2023). sourceExperimental — accuracy not yet measured

In the paper

“The momentum-space magnetic skyrmions were previously studied to demonstrate anomalous Hall effect in magnets [86,87].”

What the sources say

• ?Could not verify

  The Introduction discusses momentum-space chiral textures in photonic structures and separately describes magnetic skyrmions, but it does not connect momentum-space magnetic skyrmions to the anomalous Hall effect. Searches for “anomalous Hall effect in magnets” and “momentum-space magnetic skyrmions” found no passage addressing that claim. (LLM, conf=0.72)

  cites [86] Shi, P., Du, L., Li, M. & Yuan, X. Symmetry-protected photonic chiral spin textures by spin–orbit coupling. Laser Photon. Rev. 15, 2000554 (2021). sourceExperimental — accuracy not yet measured
• Partly supported

  The “Optical Skyrmions” passage in section C says skyrmions have previously been studied in magnetic materials. It does not say those studies concerned momentum-space magnetic skyrmions or demonstrated the anomalous Hall effect. (LLM, conf=0.78)

  cites [87] Wu, H.-J. et al. Conformal frequency conversion for arbitrary vectorial structured light. Optica 9, 187–196 (2022). sourceExperimental — accuracy not yet measured

In the paper

“The skyrmionium has zero total skyrmion number and a radial 2π-twist structure (”

What the sources say

• ?Not checked — no full text of the sourcecites [31] Bai, C., Chen, J., Zhang, Y., Zhang, D. & Zhan, Q. Dynamic tailoring of an optical skyrmion lattice in surface plasmon polaritons. Opt. Express 28, 10320–10328 (2020). source

In the paper

“A skyrmion with opposite vorticity m = -1, termed anti-skyrmion, has a very different to conventional skyrmion saddle texture (Fig. ??c).”

In the paper

“The radial kπ-twist structures of the spin-skyrmion possess deep-subwavelength features, opening a new pathway for super-resolution imaging and microscopy [19].”

What the sources say

• Not checked yetcites [19] Rybakov, F. N. et al. Magnetic hopfions in solids. APL Mater. 10, 111113 (2022). source

In the paper

“A skyrmion can be divided into two merons with a half skyrmion number, each corresponding to a half unwrapping from the parameter sphere.”

In the paper

“In paraxial beams, the electromagnetic field is a purely transverse in non-absorbing media, therefore, the field vectors always lie in a plane normal to the propagation direction.”

In the paper

“If the sphere is unwrapped not from the pole but from a point on the equator, a bimeron quasiparticle is obtained (Fig. ??d).”

In the paper

“The spin vectors in a tightly focused vortex beam may look like a Néel-type skyrmion-like texture in the focal plane near the beam axis, however, it is not a rigorous analogue of a skyrmion and a skyrmion number can not be assigned [19].”

What the sources say

• Not checked yetcites [19] Rybakov, F. N. et al. Magnetic hopfions in solids. APL Mater. 10, 111113 (2022). source

In the paper

“The reason is that a diffraction-free propagating beam is boundary-free and, therefore, is unable to form a well-defined topological structure, in contrast to an evanescent optical vortexes.”

In the paper

“They exist in the evanescent fields carry-ing orbital angular momentum (OAM), and can be realised by exciting a waveguided mode with a light having OAM.”

In the paper

“The propagation direction of a guided mode and the direction of its transverse spin (due to the longitudinal field component) are intimately locked, and one cannot be changed without the other.”

In the paper

“Such optical skyrmions are most closely related to their magnetic counterparts and can exist as individual isolated quasiparticles [19] as well as form hexagonal lattices [46].”

What the sources say

• Not checked yet

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

  cites [19] Rybakov, F. N. et al. Magnetic hopfions in solids. APL Mater. 10, 111113 (2022). source
• ?Not checked — no full text of the sourcecites [46] Karnieli, A. & Arie, A. All-optical stern-gerlach effect. Phys. Rev. Lett. 120, 053901 (2018). source

In the paper

“Each pair of gratings on opposite sides of the hexagon supports a standing wave and the skyrmion textures are formed by superposition of the electric fields of the standing waves along variant spatial directions (Fig. 4a).”

In the paper

“Skyrmions have many generalized forms in the quasiparticle family, a typical example of which is skyrmionium, a coupled state connecting two skyrmions with opposite polarities and resulting into skyrmion number of s = 1 -1 = 0 [30].”

What the sources say

• Not checked yet

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

  cites [30] Yang, J. et al. Symmetry-protected spoof localized surface plasmonic skyrmion. Laser Photon. Rev. 16, 2200007 (2022). source

In the paper

“Physical realisation of different unwrapping styles is related to a particular system properties.”

In the paper

“In contrast to the skyrmion representation with a fixed spiny sphere, a bimeron can be obtained by switching the coordinates of longitude and latitude or tilting the sphere.”

In the paper

“For optical skyrmions, symmetry breaking is one of the factors that defines an unwrapping style.”

In the paper

“A bimeron can similarly be described by a unit sphere mapping but with a more general wrapping style (Box 1).”

In the paper

“Geometrically, the distinction of an anti-skyrmion is a counter-clockwise vector distribution along the perimeter encircling a skyrmion center; the vectors of an anti-skyrmion wrap around the center clockwise (-2π), while the vectors of a skyrmion wrap around the centre counter-clockwise (2π) (Fig. 2).”

In the paper

“The described above topological classifications can be extended to considerations of any quasiparticle, for example, the kπ-bimeron with additional radial multi-twist structure in bimeronium (fourth plot in the fourth row of Fig. 2), which yet to be found experimentally.”

In the paper

“Spoof SPP, the surface electromagnetic waves that propagate along planar interfaces with sign-changing permittivities were also reported to generate skyrmion-like structures for the fields in a resonator [41,42], but their topological protection needs to be further investigated.”

What the sources say

• ?Not checked — no full text of the sourcecites [41] Ghosh, A., Yang, S., Dai, Y. & Petek, H. The spin texture topology of polygonal plasmon fields. ACS Photon. 10, 13–23 (2023). source
• Not checked yet

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

  cites [42] Zhang, Q., Xie, Z., Du, L., Shi, P. & Yuan, X. Bloch-type photonic skyrmions in optical chiral multilayers. Phys. Rev. Res. 3, 023109 (2021). source

In the paper

“A skyrmion with s = 1 but with the vector structure arranged along tangent direction (Fig. ??b) represents a vortex (Bloch-type) texture with γ = π/2, which is different from a hedgehog (Néel-type) texture with γ = 0 (Fig. ??a).”

In the paper

“As discussed above, the optical skyrmions in evanescent fields are limited to Néel-type topological textures, and it is a challenge to generate optical Bloch-type skyrmions at the interface of homogeneous media.”

In the paper

“In the case of m = -1, the topology is defined as anti-skyrmion with a saddle (anti-vortex) texture [28].”

What the sources say

• ?Not checked — no full text of the sourcecites [28] Davis, T. J. et al. Ultrafast vector imaging of plasmonic skyrmion dynamics with deep subwavelength resolution. Science 368, eaba6415 (2020). source

In the paper

“Spin-skyrmion and spinmeron lattices are formed due to a broken rotational symmetry of the field with orbital angular momentum, with 6-fold symmetry being responsible for a skyrmion lattice and 4-fold symmetry for a meron lattice in the appropriately shaped resonator (Fig. 4d) [46,[53][54][55].”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [46,[53][54][55]

In the paper

“Optical skyrmions and other quasiparticles can be constructed with various 3D vector fields, which in optics can be, for example, the electric field (E x , E y , E z ), spin angular momentum (s x , s y , s z ), polarization Stokes vec-tor (S x , S y , S z ), pseudospin (k x , k y , k z ), etc.”

In the paper

“A Stokes skyrmion was introduced corresponding to a spatial variation of a polarization pattern in a vector beam [65,66].”

What the sources say

• Not checked yet

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

  cites [65] Wan, C., Shen, Y., Chong, A. & Zhan, Q. Scalar optical hopfons. eLight 2, 22 (2022). source
• Not checked yet

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

  cites [66] Shen, Y., Papasimakis, N. & Zheludev, N. I. Non diffracting supertoroidal pulses: optical "Kármán vortex streets". Preprint at https://arxiv.org/abs/2204.05676 (2022). source

In the paper

“Recently, a new concept of bimeronium was proposed as an extension of bimeron [38], similar to skyrmionium evolved from skyrmion, with similar topological classification.”

What the sources say

• Not checked yet

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

  cites [38] Xiong, L. et al. Polaritonic vortices with a half-integer charge. Nano Lett. 21, 9256–9261 (2021). source

In the paper

“The spin-skyrmion and spin-meron textures correspond to the lowest energy of the electromagnetic field configuration, therefore, energetically stable.”

In the paper

“The related skyrmions in the pulse always exhibit a constant vorticity of 1, while the polarity alternates between +1 and -1 due to the optical cycle evolution.”

In the paper

“More complex cases of topological quasiparticles are also possible, such as a skyrmionium, which requires a radial twisting number, a bimeron obtained with a tilted parameter sphere and unwrapping from the equator, as well as 3D quasiparticles (Box 1).”

In the paper

“An optical bimeronium can be realized by replacing the scalar mode bases of a bimeronic beam with higher-order vortex modes or Bessel beams.”

In the paper

“Similar topology-based protocols of information encoding, processing and transport can be envisaged in optics.”

In the paper

“The topological approaches developed for optical skyrmions can also be transferred to other wave fields such as acoustic (sound) waves [122][123][124], elastic waves [125], and atomic waves [126].”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [122]
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [123]
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [124]
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [125]
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [126]

In the paper

“The diversity and stability of particlelike topologies allows consideration of the particle physics and condensed matter physics effects in optics in order to study and tailor light-matter interactions for quantum and topological technologies.”

In the paper

“(ii) ultrafast-the skyrmion texture can be resolved on femtosecond scales and at optical single-cycle field level [51,75]”

What the sources say

• Not checked yet

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

  cites [51] Gao, S. et al. Paraxial skyrmionic beams. Phys. Rev. A 102, 053513 (2020). source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [75] Shen, Y. et al. Topological transformation and freespace transport of photonic hopfons. Adv. Photon. 5, 015001 (2023).

In the paper

“Optical skyrmions stand at the crossroads of spintronics and structured light and may lead to new protocols in optical communications and informatics, by transferring methods from spintronics to structured light and utilising various degrees of freedom provided by topologically protected vectorial field textures.”

In the paper

“Similarly, once a optical skyrmionic pattern is designed in a free-space by the mode nonseparability and Gouy-phase locking discussed above, the topology and skyrmion number is invariant upon light propagation and resilient to perturbations, except for catastrophic events, such as strong scattering.”

In the paper

“For quantum technologies, since skyrmions are characterised by multiple topological charges, e.g.polarity and vorticity, exotic biparticle entangled states can be considered with more degrees of freedom.”

In the paper

“The realisation of optical counterparts of skyrmion quasiparticles has enabled the novel topological approach for controlling electromagnetic fields.”

In the paper

“The situation is different in the case of the few-cycle ultrafast pulses, which represent space-time nonseparable solutions of the Maxwell's equations [79].In the latter case, propagating skyrmions can be achieved with the toroidal light pulses [80].”

What the sources say

• Not checked yet

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

  cites [79] Ackerman, P. J. & Smalyukh, I. I. Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfons. Phys. Rev. 7, 011006 (2017). source
• ?Not checked — no full text of the sourcecites [80] Yang, H., Liang, J. & Cui, Q. First-principles calculations for Dzyaloshinskii–Moriya interaction. Nat. Rev. Phys. 5, 43–61 (2023). source

In the paper

“Such pulses induce multiple singularities in their electromagnetic field, which form vortex-ring-like configurations, and skyrmionic topology can be observed in their transverse cross-section.”

In the paper

“Spin textures in a momentum space provide a direct approach to visualizing the local Berry curvature, enabling robust and direct manipulation of polarization of light [76] and space-time coupling of light wave packets [85].”

What the sources say

• Not checked yet

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

  cites [76] Ehrmanntraut, D. et al. Optical second-order skyrmionic hopfion. Optica 10, 725–731 (2023). source
• ?Not checked — no full text of the sourcecites [85] Zhao, H. J., Chen, P., Prosandeev, S., Artyukhin, S. & Bellaiche, L. Dzyaloshinskii–Moriya-like interaction in ferroelectrics and antiferroelectrics. Nat. Mater. 20, 341–345 (2021). source

In the paper

“To be classified as a skyrmion, the vector texture described by a topological number must be protected upon propagation.”

In the paper

“If the modes have misaligned Gouy phases, the beam will not be topologically protected and show variant topological charge upon propagation.”

In the paper

“The bimeronic beam can be obtained by modifying a skyrmionic beam, which requires a superposition with two specially designed spatial modes with two different non-orthogonal polarizations (a skyrmionic beam requires them to be orthogonal).”

In the paper

“In turn, applying optical concepts to magnetism, magnetic skyrmions have been used as a magnetic tweezers with a similar mechanism to optical tweezers with twisted light [111][112][113].”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [111]
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [112]
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [113]

In the paper

“Momentum-space spin textures in photonic systems promise intriguing physical insights related to Dirac monopoles and photon spin quantization, whereby the magnetic monopole charge quantization in momentum space can arise from spin-1 skyrmion properties of polaritons.[88].”

What the sources say

• Not checked yet

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

  cites [88] Wätzel, J. & Berakdar, J. Topological light fields for highly non-linear charge quantum dynamics and high harmonic generation. Opt. Express 28, 19469–19481 (2020). source

In the paper

“(iii) diversity of topologies-the vector textures of skyrmions can be characterized by multiple topological numbers and extended to higher dimensional cases [69,70]”

What the sources say

• Not checked yetcites [69] Loder, F., Kampf, A. P., Kopp, T. & Braak, D. Momentum-space spin texture in a topological superconductor. Phys. Rev. B 96, 024508 (2017). source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [70] Lin, M., Du, L. & Yuan, X. Photonic pseudospin skyrmion in momentum space. IEEE Photon. J. 15, 6500106 (2022).

In the paper

“In magnetic skyrmionic racetrack memory for high-density information storage, the information is encoded in the presence and absence of skyrmions [98].”

What the sources say

• Not checked yet

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

  cites [98] Wan, Z., Wang, H., Liu, Q., Fu, X. & Shen, Y. Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photon. 10, 2149–2164 (2023). source

In the paper

“The complex topology of skyrmions may provide great potential to explore higher-dimensional quantum states for quantum technologies which are difficult to reach otherwise.”