Optical skyrmions and other topological quasiparticles of light

In the paper

“The meron textures of the polarization Stokes field was experimentally generated by confining light into a liquid-crystal-filled microcavity (Fig. 4e) [57].”

What the sources say

• Disputed

  The main text (page unavailable) says the authors numerically modeled full Poincaré beams from a silicon microring cavity, rather than experimentally generating meron textures in a liquid-crystal-filled cavity. The cited paper’s Stokes-vector discussion concerns those modeled beams; it does not change the contrary device and method descriptions. (LLM, conf=0.90)

  Checked by a reasoning model — may be wrong.

  cites [57] Lin, W., Ota, Y., Arakawa, Y. & Iwamoto, S. Microcavity-based generation of full Poincaré beams with arbitrary skyrmion numbers. Phys. Rev. Res. 3, 023055 (2021). sourceExperimental — accuracy not yet measured

In the paper

“The first implementation of optical quasiparticles in momentum-space was demonstrated by engineering the band structure of a photonic crystal with a broken symmetry to enable meron textures formed by Stokes vectors in the Brillouin zone (Fig. 4j) [76].”

What the sources say

• Disputed

  The Abstract describes an experimental second-order skyrmionic hopfion in the polarization and phase texture of a paraxial light field in three-dimensional space. The Results describe constructing it by superimposing two structured beams, not by engineering a photonic crystal band structure to produce momentum-space merons. (LLM, conf=0.86)

  Checked by a reasoning model — may be wrong.

  cites [76] Ehrmanntraut, D. et al. Optical second-order skyrmionic hopfion. Optica 10, 725–731 (2023). sourceExperimental — accuracy not yet measured

In the paper

“Tight focusing was shown to enable optical spin skyrmions where Néel-and Bloch-type textures can be controlled by slightly tuning the input light (Fig. 4g) [63].”

What the sources say

• ?Could not verify

  The Abstract reports generating toroidal light pulses and mentions skyrmions only as a possible subject of future light–matter interaction studies. Searches for optical spin skyrmions and for skyrmions found no passage about tight focusing or controlling Néel- and Bloch-type textures by tuning the input light. The indexed passages provide no page numbers. (LLM, conf=0.76)

  cites [63] Zdagkas, A. et al. Observation of toroidal pulses of light. Nat. Photon. 16, 523–528 (2022). sourceExperimental — accuracy not yet measured

In the paper

“This results in an effective”

What the sources say

• ?Could not verify

  The Experimental demonstration and Discussion and conclusion sections address distortion and invariance of vectorial structured light, not effective magnetization. A search for magnetization and nonlinear media found no passage in our copy supporting the attributed claim. Page numbers were not available. (LLM, conf=0.76)

  cites [59] Nape, I. et al. Revealing the invariance of vectorial structured light in complex media. Nat. Photon. 16, 538–546 (2022). sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Introduction (page unavailable) discusses flying-donut pulses engaging toroidal and anapole excitations in dielectric particles, but does not describe effective magnetization in a specially designed nonlinear medium. Searches for the quoted phrase and for nonlinear-medium magnetization found no passage addressing that claim. (LLM, conf=0.74)

  cites [60] Zdagkas, A., Papasimakis, N., Savinov, V. & Zheludev, N. I. Space-time nonseparable pulses: constructing isodiffracting donut pulses from plane waves and single cycle pulses. Phys. Rev. A 102, 063512 (2020). sourceExperimental — accuracy not yet measured

In the paper

“Optical field-skyrmion lattice was first observed in the evanescent electric field of the SPP waves interfering in a resonator of a six-fold symmetry [18].”

What the sources say

• ?Could not verify

  The Introduction and Concluding Remarks discuss theoretical Hopf solitons in the Skyrme-Faddeev model, not an optical observation. Searches for optical skyrmion lattices, surface-plasmon polaritons, evanescent electric fields, and six-fold resonators found no passage addressing the claimed first observation. (LLM, conf=0.78)

  cites [18] Ward, R. S. Hopf solitons on $${{\mathscr{S}}}^{3}$$ and $${{\mathscr{S}}}^{3}$$. Nonlinearity 12, 241–246 (1999). sourceExperimental — accuracy not yet measured

In the paper

“Bloch-type spin-skyrmions were theoretically proposed in a designer multilayer chiral liquid crystal structure [56], in which chirality-dependent twisted features occur in the spin vector field.”

What the sources say

• Partly supported

  The Introduction reports Bloch-type optical skyrmions in optical chiral multilayers, so it supports that part of the claim. It does not describe a designer multilayer chiral liquid-crystal structure or chirality-dependent twisting of a spin vector field; its mention of spin-field skyrmions concerns a separate, tightly focused vortex beam. Page numbers are unavailable in our copy. (LLM, conf=0.86)

  cites [56] Shen, Y., Mart´ınez, E. C. & Rosales-Guzm´an, C. Generation of optical skyrmions with tunable topological textures. ACS Photon. 9, 296–303 (2022). sourceExperimental — accuracy not yet measured

In the paper

“In parallel, a stable, individual skyrmions formed by the spin distribution of a SPP field in the presence of spin-orbit coupling was demonstrated [19].”

What the sources say

• ?Could not verify

  The Introduction (page unavailable) discusses stable magnetic hopfions in materials with competing exchange interactions, not a demonstrated skyrmion in a surface-plasmon polariton field. Searches for SPP, optical spin textures, and spin-orbit coupling found no passage in our copy addressing the claimed demonstration. (LLM, conf=0.78)

  cites [19] Rybakov, F. N. et al. Magnetic hopfions in solids. APL Mater. 10, 111113 (2022). sourceExperimental — accuracy not yet measured

In the paper

“The above topological classification is also applicable to merons and bimerons [35,36] (Fig. 2).”

What the sources say

• ?Could not verify

  The Results and Discussion describes topological invariants of structured electromagnetic waves and compares a spin-variation pattern to a topological soliton. Our copy does not discuss merons or bimerons or say that the classification applies to them (searched: “merons and bimerons,” “topological classification,” and related spin-texture terms). The indexed passages provide no page numbers. (LLM, conf=0.72)

  cites [35] Shi, P., Du, L., Li, C., Zayats, A. V. & Yuan, X. Transverse spin dynamics in structured electromagnetic guided waves. Proc. Natl Acad. Sci. USA 118, e2018816118 (2021). sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Introduction mentions photonic merons as topological structures, and §2.2 defines a skyrmion number for photonic skyrmions. Neither passage says that this classification applies to merons, and a search for bimerons found no discussion of them in our copy. No page numbers were provided. (LLM, conf=0.72)

  cites [36] Lei, X., Du, L., Yuan, X. & Zayats, A. V. Optical spin–orbit coupling in the presence of magnetization: photonic skyrmion interaction with magnetic domains. Nanophotonics 10, 3667–3675 (2021). sourceExperimental — accuracy not yet measured

In the paper

“The experimental generation of toroidal pulses can be achieved using a radially polarised pulse interaction with a gradient metasurface designed to achieve space-time coupling [81].”

What the sources say

• ?Could not verify

  The Spin-orbit torque switching section discusses electrical current pulses used to switch antiferromagnetic moments, not toroidal pulses. Searches for radially polarised pulses, gradient metasurfaces and space-time coupling found no passage addressing the claimed generation method. No page numbers are available in our copy. (LLM, conf=0.77)

  cites [81] Železný J., Wadley, P., Olejník, K., Hoffmann. A. & Ohno, H. Spin transport and spin torque in antiferromagnetic devices. Nat. Phys. 14, 220–228 (2018). sourceExperimental — accuracy not yet measured

In the paper

“Optical plasmonic field-and spin-skyrmions were verified to possess deep-subwavelength features with sufficient light intensities [19,40], which meets the emerging requirements of superresolution imaging and metrology.”

What the sources say

• ?Could not verify

  The Introduction and Results and discussions sections address magnetic hopfions and magnetic skyrmions, not optical plasmonic field- or spin-skyrmions. Searches for deep-subwavelength features, light intensity, and plasmonic skyrmions found no passage in our copy that verifies the attributed claim. (LLM, conf=0.76)

  cites [19] Rybakov, F. N. et al. Magnetic hopfions in solids. APL Mater. 10, 111113 (2022). sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [40] Zhang, Q. et al. Optical topological lattices of Bloch type skyrmion and meron topologies. Photon. Res. 10, 947–957 (2022). source

In the paper

“(iv) topological protection-the topology of a photonic skyrmion texture can be very stable and resilient to disorder and perturbation in complex media unless catastrophic events [64,73]”

What the sources say

• ?Could not verify

  The passage labeled “Photonic toroidal vortex > Abstract” describes a toroidal vortex’s phase structure and possible applications in photonic topology, but not a photonic skyrmion texture. Searches for skyrmions, topological protection, disorder, perturbations, and catastrophic events found no passage addressing the claimed resilience in complex media. (LLM, conf=0.76)

  cites [64] Wan, C., Cao, Q., Chen, J., Chong, A. & Zhan, Q. Toroidal vortices of light. Nat. Photon. 16, 519–522 (2022). sourceExperimental — accuracy not yet measured
• Partly supported

  Section IV (page not provided) says the optical skyrmion’s polarization singularity persists under external perturbation and that its main feature can be topologically protected. It does not establish resilience to disorder in complex media or identify catastrophic events as the exception; it leaves a detailed analysis of dynamical stability for future work. (LLM, conf=0.86)

  cites [73] Kuratsuji, H. & Tsuchida, S. Evolution of the stokes parameters, polarization singularities, and optical skyrmion. Phys. Rev. A 103, 023514 (2021). sourceExperimental — accuracy not yet measured

In the paper

“Using a hypersphere as a higher-dimensional generalization of a Poincaré sphere, the unwrapping of the vector field structure results in a skyrmionic texture in 3D which was termed an optical hopfion [77].”

What the sources say

• ?Could not verify

  The paper’s Abstract describes three-dimensional magnetic skyrmion bundles in FeGe, not an optical hopfion. Searches for “optical hopfion,” “hypersphere,” and “Poincaré sphere” found no passage addressing the claimed construction; the shared reference to a 3D skyrmionic texture does not establish it. (LLM, conf=0.75)

  cites [77] Tang, J. et al. Magnetic skyrmion bundles and their current-driven dynamics. Nat. Nanotechnol. 16, 1086–1091 (2021). sourceExperimental — accuracy not yet measured

In the paper

“The Stokes skyrmions can also be generated directly in lasers with skyrmion numbers controlled by the resonator grating [71] (Fig. 4h).”

What the sources say

• Partly supported

  Section 4 (Multi-Skyrmions; page not given) says skyrmion number can be increased by changing phase vortices or the topological charge of a Laguerre–Gaussian mode. The copy does not support the more specific claim that Stokes skyrmions are generated directly in lasers or that a resonator grating controls their number. (LLM, conf=0.83)

  cites [71] Cisowski, C., Ross, C. & Franke-Arnold, S. Building paraxial optical skyrmions using rational maps. Adv. Photon. Res. 4, 2200350 (2023). sourceExperimental — accuracy not yet measured

In the paper

“This topological protection was demonstrated as a salient property of vectorial structured light due to its polarization inhomogeneity, in contrast to scalar structured light [73].”

What the sources say

• Partly supported

  Section IV (page unavailable) says the modeled optical skyrmion’s main feature can be topologically protected against external disturbance, supporting the protection aspect. It does not establish this as a general property of vectorial structured light, attribute it specifically to polarization inhomogeneity, or compare it with scalar structured light. (LLM, conf=0.86)

  cites [73] Kuratsuji, H. & Tsuchida, S. Evolution of the stokes parameters, polarization singularities, and optical skyrmion. Phys. Rev. A 103, 023514 (2021). sourceExperimental — accuracy not yet measured

In the paper

“Such topological protection was recently theoretically and experimentally demonstrated for different kinds of perturbations in complex media such as liquid and atmosphere turbulence, laying the base for applying free-space skyrmions as a nextgeneration robust carrier for information transfer [73,74].”

What the sources say

• Partly supported

  Section IV says the optical skyrmion’s main feature can be topologically protected against external disturbance. It does not report experimental demonstrations or test protection in liquid or atmospheric turbulence; Section V describes a possible experimental realization instead. (LLM, conf=0.88)

  cites [73] Kuratsuji, H. & Tsuchida, S. Evolution of the stokes parameters, polarization singularities, and optical skyrmion. Phys. Rev. A 103, 023514 (2021). sourceExperimental — accuracy not yet measured
• Partly supported

  The Discussion (page unavailable) says the paper’s experiments and theory demonstrate topological invariances in structured light and may lead to robust designs for free-space optics. It does not report tests of protection against different perturbations in liquids or atmospheric turbulence; those conditions are unsupported. (LLM, conf=0.86)

  cites [74] Sugic, D. et al. Particle-like topologies in light. Nat. Commun. 12, 6785 (2021). sourceExperimental — accuracy not yet measured

In the paper

“In such optical hopfion, each fibre in the Hopf fibration corresponds to the trajectory of a certain polarization ellipse [77] (Fig. 4k).”

What the sources say

• ?Could not verify

  The supplied Abstract passages describe magnetic skyrmion bundles in FeGe and their current-driven motion, not optical hopfions. Searches for Hopf-fibration fibres and polarization-ellipse trajectories found no passage in our copy addressing the claimed correspondence. (LLM, conf=0.76)

  cites [77] Tang, J. et al. Magnetic skyrmion bundles and their current-driven dynamics. Nat. Nanotechnol. 16, 1086–1091 (2021). sourceExperimental — accuracy not yet measured

In the paper

“Such skyrmionic beams were identified considering superposition of a vortex beam and a non-vortex beam with orthogonal polarizations, i.e. a nonseparable state between spatial mode of polarization, where the two modal components must have a fixed ratio of the Gouy phase and aligned at the beam waist [65,66,69].”

What the sources say

• ?Could not verify

  The Introduction (page unavailable) mentions optical skyrmions but does not describe how the claimed beams are formed. Results and discussion (page unavailable) describes generating scalar hopfions by manipulating poloidal and toroidal spiral phases. Searches for the Gouy-phase ratio, beam-waist alignment, and superposition of orthogonally polarized vortex and non-vortex beams found no passage addressing those conditions. (LLM, conf=0.72)

  cites [65] Wan, C., Shen, Y., Chong, A. & Zhan, Q. Scalar optical hopfons. eLight 2, 22 (2022). sourceExperimental — accuracy not yet measured
• ?Could not verify

  The paper’s opening section describes skyrmionic configurations in supertoroidal pulses, and its ‘Singularities and topological properties’ section discusses their evolution. Neither addresses the claimed construction by superposing vortex and non-vortex beams with orthogonal polarizations, a fixed Gouy-phase ratio, and alignment at the beam waist; searches for those terms found no supporting passage. (LLM, conf=0.73)

  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). sourceExperimental — accuracy not yet measured
• ?Could not verify

  Section III discusses momentum-space spin textures and pairing in a superconductor, while Section B defines a skyrmion number for a Bloch-vector field. Searches for Gouy phase, orthogonally polarized vortex and non-vortex beams, and beam-waist alignment found no passage addressing the optical-beam claim. The different subject matter does not itself contradict the claim. (LLM, conf=0.78)

  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

“(i) ultrasmall-the spatial size of a spin-skyrmion features can be realized on a deep-subwavelength scale as the spin is not subject to diffraction [19,40,51]”

What the sources say

• ?Could not verify

  The Results and discussions section describes hopfions as small three-dimensional spin textures and discusses a characteristic scale of inhomogeneity. Our copy does not say that spin-skyrmion features can be deep-subwavelength or that spin is exempt from diffraction; searches for diffraction and subwavelength size found no supporting passage. (LLM, conf=0.72)

  cites [19] Rybakov, F. N. et al. Magnetic hopfions in solids. APL Mater. 10, 111113 (2022). sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [40] Zhang, Q. et al. Optical topological lattices of Bloch type skyrmion and meron topologies. Photon. Res. 10, 947–957 (2022). source
• ?Could not verify

  Section II describes skyrmion patterns formed by spatially varying polarization or spin, but does not address their minimum spatial size. Searches for deep-subwavelength features and a diffraction limit found no passage saying that spin is exempt from diffraction or that this permits deep-subwavelength skyrmion features. (LLM, conf=0.75)

  cites [51] Gao, S. et al. Paraxial skyrmionic beams. Phys. Rev. A 102, 053513 (2020). sourceExperimental — accuracy not yet measured

In the paper

“In contrast to time-varying fieldskyrmion lattices, static optical skyrmions can be constructed from the spin vectors (spin angular momentum, SAM) of the evanescent electromagnetic field, with out-of-plane and radial components of”

In the paper

“However, the tight focusing may introduce a longitudinal field component in the field structure.”

In the paper

“The main challenge in achieving optical skyrmions is the ability to twist the optical field vectors in 3D in on-demand structured fields [39], which requires to break the prevailing paradigm to treat electromagnetic field as a transverse field.”

What the sources say

• ?Not checked — no full text of the sourcecites [39] Ghosh, A. et al. A topological lattice of plasmonic merons. Appl. Phys. Rev. 8, 041413 (2021). source

In the paper

“Very recently, skyrmionic structures were observed in optics [18,19].”

What the sources say

• Not checked yet

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

  cites [18] Ward, R. S. Hopf solitons on $${{\mathscr{S}}}^{3}$$ and $${{\mathscr{S}}}^{3}$$. Nonlinearity 12, 241–246 (1999). source
• 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

In the paper

“A lattice of skyrmion-shaped distributions of the evanescent electric field, oscillating in time but preserving their topology, was realised in the especially shaped surface-plasmon polariton (SPP) resonator [18].”

What the sources say

• Not checked yet

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

  cites [18] Ward, R. S. Hopf solitons on $${{\mathscr{S}}}^{3}$$ and $${{\mathscr{S}}}^{3}$$. Nonlinearity 12, 241–246 (1999). source

In the paper

“The topological classification of Néel-, Bloch-, and anti-types of skyrmions is also applicable for skyrmionium (Fig. 2).”

In the paper

“Similar topological considerations apply to the field-skyrmion lattices as the propagation of the guided modes and spins are linked with the additional requirement for the field symmetry, restricting the existence of individual field skyrmions.”

In the paper

“Therefore, 2D guided electromagnetic modes, such as surface plasmon polaritons or other planar waveguides are obvious candidates for realisation of 2D topological structures.”

In the paper

“These topological numbers determine classification of quasiparticle types.”

In the paper

“The field-skyrmion topologies in such propagating beams may theoretically exhibit strong stability against scattering in disordered media [64].”

What the sources say

• Not checked yet

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

  cites [64] Wan, C., Cao, Q., Chen, J., Chong, A. & Zhan, Q. Toroidal vortices of light. Nat. Photon. 16, 519–522 (2022). source

In the paper

“One of the implementations is to use pseudospin vectors in nonlinear photonic crystals [58].”

What the sources say

• ?Not checked — no full text of the sourcecites [58] Dennis, M. R., O’Holleran, K. & Padgett, M. J. Singular optics: optical vortices and polarization singularities. Prog. Optics 53, 293–363 (2009). source

In the paper

“The interaction between a light beam and the pseudospin skyrmion with controlled higher-order texture in a nonlinear crystal can be used to emulate properties of magnetic skyrmions in materials, i.e. spin transport and topologically protected skyrmion Hall effect, promising a powerful tool for applications of new photonic Hall devices [58,61,62].”

What the sources say

• ?Not checked — no full text of the sourcecites [58] Dennis, M. R., O’Holleran, K. & Padgett, M. J. Singular optics: optical vortices and polarization singularities. Prog. Optics 53, 293–363 (2009). source
• ?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).

In the paper

“Topological protection for spin-skyrmion quasiparticles is ensured by spin-orbit coupling in the evanescent field.”

In the paper

“SPP field-skyrmions have the topological texture limited to Néel-type topology.”

In the paper

“The same as the field-skyrmions, optical spin-skyrmions also allow only Néel-type textures in the isotropic medium (Fig. 4b) [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 symmetry considerations completely determine the topology of the evanescent electromagnetic field either through interference or spin-orbit coupling in the case of OAM carrying beams [46].”

What the sources say

• ?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

“Anti-skyrmions cannot be classified by anti-Néel or anti-Bloch types due to the intrinsic symmetry of a saddle structure, which is only wholly rotate itself by tuning helicity.”

In the paper

“In the case of m = 1, the skyrmions of γ = 0 or γ = π are classified as Néel-type and exhibit a hedgehog texture around the quasiparticle [26].”

What the sources say

• ?Not checked — no full text of the sourcecites [26] Yu, X. et al. Transformation between meron and skyrmion topological spin textures in a chiral magnet. Nature 564, 95–98 (2018). source

In the paper

“In the absence of the spin-orbit coupling, in the case when the field is not carrying OAM, instead of spin-skyrmions, fieldskyrmion lattices are formed, thus connecting two types of optical skyrmion manifestations.”

In the paper

“For γ = ±π/2, the skyrmions are classified as Bloch-type with a vortex texture around the center [27].”

What the sources say

• Not checked yet

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

  cites [27] Zhang, X. et al. A frustrated bimeronium: static structure and dynamics. Appl. Phys. Lett. 118, 052411 (2021). source

In the paper

“However, a skyrmion number cannot uniquely determine the spin texture.”

In the paper

“2D surface or 3D space or 4D space-time physical representations can be used to obtain various kinds of optical quasiparticles, fulfilling the appropriate mapping (Fig. 3).”

In the paper

“Longitudinal components naturally appear due to the evanescent field present in guided modes of planar or confined waveguides.”

In the paper

“Photonic field-skyrmions, which are dynamic field textures with the electric field oscillating in time, exist only in a six-fold lattice.”

In the paper

“In the evanescent field carrying OAM, this results in the topological protection of of a skyrmionic spin distribution, in the absence of catastrophic events, such as out of plane scattering in the propagating waves in the adjacent media.”

In the paper

“Dynamics of such skyrmionic SPP standing wave can be observed using photoemission electron microscopy [40].”

What the sources say

• ?Not checked — no full text of the sourcecites [40] Zhang, Q. et al. Optical topological lattices of Bloch type skyrmion and meron topologies. Photon. Res. 10, 947–957 (2022). source

In the paper

“In particular, the digital hologram method can be used to generate tuneable skyrmions with all the textures of Néel-, Bloch, and anti-types [70] (Fig. 4g).”

What the sources say

• ?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

“A 3D analysis of the Stokes vector field of a paraxial full-Poincaré vector beam reveals an analogue of a skyrmion tube [91].”

What the sources say

• Not checked yet

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

  cites [91] Poy, G. et al. Interaction and co-assembly of optical and topological solitons. Nat. Photon. 16, 454–461 (2022). source

In the paper

“The plasmonic field skyrmions were also applied for frequency sensing, achieving high sensitivity (> 4.82%) and extreme accuracy (≈ 99.99%) in the deep-subwavelength areas 26× 10 -5 λ 2 [116], which is a milestone for ultracompact highly sensitive sensors.”

What the sources say

• ?Not matched

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

  cites [116]

In the paper

“In contrast to intensity variations, the local spin distribution in the skyrmions varies at the deep-subwavelength scales, down to λ/60 level or ∼ 10 nm [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

“With the increasing supertoroidal order parameter, multiple propagating skyrmions can be obtained with different topological textures (polarity and helicity) within the pulse [75] (Fig. 4i).”

What the sources say

• ?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

“By combining a pair of ±1st-order spin skyrmions with an accurately controlled separation, a structured spin field akin to the field of an electron-positron pair can be constructed”

What the sources say

• ?Not matched

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

  cites [119]

In the paper

“Recently, an electric analogue of the DMI was demonstrated [106,107], which inspires exploration of the optical DMI.”

What the sources say

• ?Not matched

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

  cites [106]
• ?Not matched

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

  cites [107]

In the paper

“For isolated spin-skyrmions, optical analog of the exchange energy and the DMI terms are related to conservation of the total angular momentum and the spin texture stability is protected by the optical spin-Hall effect and symmetry of the optical system in the presence of OAM [108].”

What the sources say

• ?Not matched

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

  cites [108]

In the paper

“This would be especially advantageous for imaging the material properties influencing optical polarisation, such as magnetic or ferroelectric domain distributions [50].”

What the sources say

• ?Not checked — no full text of the sourcecites [50] Liu, C., Zhang, S., Maier, S. A. & Ren, H. Disorder induced topological state transition in the optical skyrmion family. Phys. Rev. Lett. 129, 267401 (2022). source

In the paper

“the localization can be achieved by measuring the spin degree of such a structured spin distribution [119].”

What the sources say

• ?Not matched

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

  cites [119]

In the paper

“More complex skyrmion textures can be involved in the entanglement, such as the skyrmionium or kπ skyrmion described by additional topological numbers, to access hybrid-entangled states with multiple degrees of freedom, beyond spin or OAM entangled photons.”

In the paper

“Recently, it has also been experimentally demonstrated that the interactions between light and topological quasiparticles in liquid crystals can enable local transfer of momentum between light and matter, revealing a new mechanism to develop advanced applications such as solitonic tractors and nonlinear photonic devices [114].”

What the sources say

• ?Not matched

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

  cites [114]

In the paper

“Free-space skyrmions possess topological protection in analogy to the topological protection of skyrmions in magnetic materials.”

In the paper

“Skyrmion Hall effect recently found its optical counterpart in pseudospin skyrmions in nonlinear media, which lays foundation to design novel topological photonic devices [58].”

What the sources say

• ?Not checked — no full text of the sourcecites [58] Dennis, M. R., O’Holleran, K. & Padgett, M. J. Singular optics: optical vortices and polarization singularities. Prog. Optics 53, 293–363 (2009). source

In the paper

“a displacement sensing technology with sensitivity down to angstrom/picometer and effective linear range exceeding hundreds of nanometer was successfully realized”

What the sources say

• ?Not matched

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

  cites [119]

In the paper

“For instance, a skyrmion of polarity-up and vorticity of ℓ can be entan-gled with another skyrmion of polarity-up and vorticity of -ℓ.”

In the paper

“The kπ skyrmions were reported in free-space skyrmionic vector beams with reconfigurable topological textures, including higher-order vorticity and kπ radial twist [70].”

What the sources say

• ?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

“Such momentum-space meron was used for generating space-time light bullets, i.e. the 3D localized wave packets with complex space-time coupling and nondiffracting propagation.”

In the paper

“The fine structure of spin skyrmion can be used as a tool for imaging, promising a superresolution microscopic method beyond diffraction limit.”

In the paper

“Upon the propagation of a skyrmionic beam, the vector texture can evolve from Bloch-type into Néel-type and vise versa in free space.”

In the paper

“While primarily 2D skyrmionic structures were widely considered in the electromagnetic domain, the studies of 3D skyrmions have also been recently initiated in the structured light.”

In the paper

“For isolated spin-skyrmions, optical analog of the exchange energy and the DMI terms are related to conservation of the total angular momentum and the spin texture stability is protected by the optical spin-Hall effect and symmetry of the optical system in the presence of OAM [108].”

What the sources say

• ?Not matched

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

  cites [108]

In the paper

“The ultrasmall and ultrafast features play an important role in developing applications in super-resolution imaging and metrology beyond the diffraction limit.”

In the paper

“The toroidal pulses can be generalized into supertoroidal, fractal-like configurations of singularity distributions and vortex rings [75].”

What the sources say

• ?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

“The optical spin skyrmions were also recently used in developing ultraprecise displacement sensing or metrology achieving pico-metric resolution [117].”

What the sources say

• ?Not matched

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

  cites [117]

In the paper

“This is turn promises ultraprecise detection of magnetic skyrmions [115].”

What the sources say

• ?Not matched

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

  cites [115]

In the paper

“However, in the case of an anti-skyrmion texture, the vector field texture will not change during propagation [69].”

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

In the paper

“Diffractionless propagation of supertoroidal pulses may potentially enable the skyrmion topologies to be transported over an arbitrary long distance [84].”

What the sources say

• Not checked yet

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

  cites [84] Hirosawa, T., Klinovaja, J., Loss, D. & Díaz, S. A. Laser-controlled real-and reciprocal-space topology in multiferroic insulators. Phys. Rev. Lett. 128, 037201 (2022). source

In the paper

“In this case, the degree of the nonorthogonality controls the tilt of the parameter sphere to obtain a bimeron (Box 1).”

In the paper

“When such a space-polarization nonseparable vector beam propagates in complex media, the scattering can easily distort scalar mode components and local polarization, however, the global topology related to the orthogonality and nonseparablity of spatial mode and polarization is very difficult to change [73].”

What the sources say

• Not checked yet

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

  cites [73] Kuratsuji, H. & Tsuchida, S. Evolution of the stokes parameters, polarization singularities, and optical skyrmion. Phys. Rev. A 103, 023514 (2021). source

In the paper

“Interestingly, there exist also another kind of optical toroidal pulses that belong to a scalar light field with the phase gradient lines resembling skyrmion structure rather than the real optical vector field [82,83].”

What the sources say

• ?Not checked — no full text of the sourcecites [82] Yang, S.-H., Naaman, R., Paltiel, Y. & Parkin, S. S. Chiral spintronics. Nat. Rev. Phys. 3, 328–343 (2021). source
• Not checked yet

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

  cites [83] Fujita, H. & Sato, M. Ultrafast generation of skyrmionic defects with vortex beams: printing laser profles on magnets. Phys. Rev. B 95, 054421 (2017). source

In the paper

“The resolving of fine structure of light and control of its movement also serves as basic scale mark to enable ultraprecise displacement metrology, such as the optical ruler metrology [118].”

What the sources say

• ?Not matched

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

  cites [118]

In the paper

“A nonlocal optical skyrmion as a quantum entangled state of two photons with hybrid degrees of freedom, spatial mode and polarization, fulfilling a skyrmion mapping in the correlation function of the two entangled photons has recently been introduced [78] (Fig. 4l).”

What the sources say

• Not checked yet

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

  cites [78] Tai, J.-S. B. & Smalyukh, I. I. Three-dimensional crystals of adaptive knots. Science 365, 1449–1453 (2019). source

In the paper

“Much higher resolution is possible at the expense of the reduced light intensity required for detection.”