Optical Skyrmions: Topology in Photonic Fields

• Optical skyrmions are topologically nontrivial textures defined by vector fields mapping a two-dimensional domain onto the Poincaré sphere.
• They are realized across various platforms—including plasmonic, free-space, and integrated photonics—to enable applications in imaging, communication, and nanomagnetism.
• Experimental methods using interference and vortex beams demonstrate precise control of skyrmion number and robust topological protection under diverse conditions.

Optical skyrmion denotes a topologically nontrivial texture of a vector-like optical field over a two-dimensional domain, most commonly a normalized electric field, spin angular momentum density, polarization Stokes vector, or related pseudospin, whose spatial distribution wraps an order-parameter sphere in the optical analogue of magnetic skyrmion topology. In the unified optical view, the same concept extends across field skyrmions, spin skyrmions, Stokes skyrmions, momentum-space merons, space-time skyrmions, and three-dimensional hopfionic generalizations; it should also be distinguished from work on optically controlled magnetic skyrmions, where light manipulates a material spin texture rather than carrying the skyrmionic topology itself (Shen et al., 2022, Guan et al., 2023).

1. Topological definition and mathematical structure

For a normalized optical vector field $\mathbf{S}(x,y)\in S^2$, the standard skyrmion number is

$$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$

with equivalent notations $N_{\mathrm{sk}}$, $N$, or $Q$ depending on the realization. In different optical platforms, $\mathbf{S}$ may be the normalized electric-field vector, the direction of the local spin angular momentum, the normalized Stokes vector, or a synthetic pseudospin. The homotopy classification $\pi_2(S^2)=\mathbb{Z}$ is explicitly invoked in optical implementations where the beam cross-section is mapped to the Poincaré sphere, so integer wrapping number is the basic topological label (Lin et al., 2024).

A mathematically sharper statement is that the topological character of an optical skyrmion is not guaranteed by a visually skyrmion-like pattern alone. The degree-theoretic treatment of paraxial optical skyrmions introduces compactifiable fields, for which the optical polarization map extends smoothly to a compact oriented surface; only then does the integral above coincide with a genuine degree, and the topology is inherited from the boundary structure of the field. In that framework, topological protection follows from homotopy invariance, while failure of the relevant boundary conditions destroys the degree interpretation even if a local skyrmion-density pattern remains (Wang et al., 2024).

For paraxial optical skyrmions and skyrmion lattices, the same invariant can be reformulated purely in terms of polarization singularities and winding numbers. Using a generalized Stokes basis $\mathbf{S}_R=(S_x,S_y,S_z)^T$, the singularity-based formula

$$n = \frac{1}{2}\left( \sum_{j} S_{z}^{(j)} N_j -\bar{S}_{z}^{(\infty)} N_\infty\right)$$

expresses the global skyrmion number through the local sign of $S_z$ at singularities, integer winding numbers $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$0, and the beam-edge contribution. This formulation avoids derivative-sensitive surface integration and clarifies why the topology is robust under smooth deformations that preserve the singularity structure (McWilliam et al., 2022).

2. Order parameters, texture classes, and classification conventions

Optical skyrmions are classified first by the optical vector field that plays the role of the order parameter. The review literature distinguishes field skyrmions built from the electric field vector, spin skyrmions built from the spin angular momentum vector, Stokes skyrmions built from the polarization Stokes vector, and pseudospin skyrmions in engineered systems such as nonlinear photonic crystals. The same taxonomy extends across real space, momentum space, space-time, and three-dimensional hopfionic textures (Shen et al., 2022).

The standard 2D parameterization

$$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$1

leads to the decomposition $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$2, where $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$3 is the polarity and $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$4 the vorticity. This supports the usual texture classes. Néel-type skyrmions have hedgehog-like radial in-plane orientation; Bloch-type skyrmions have vortex-like azimuthal in-plane orientation; anti-skyrmions correspond to $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$5; merons cover only half the sphere; bimerons are related half-skyrmion composites obtained by a different pseudospin-basis unwrapping; and skyrmionium or $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$6-skyrmions have multi-twist radial structure (Shen et al., 2022).

In polarization-based realizations, an important distinction is that a full-Poincaré beam is not automatically an optical skyrmion. The free-space perspective states that “a skyrmionic beam indeed is a full Poincaré beam, while a full Poincaré beam may not be a skyrmionic one,” because the polarization field must satisfy the correct sphere-wrapping condition rather than merely visit many polarization states (Shi et al., 2024).

Classification is also convention-dependent in some platforms. In the silicon microring realization, the topological number is written as $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$7, with polarity $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$8 set by the sign change of $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$9 and vorticity $N_{\mathrm{sk}}$0 by the in-plane winding; the authors call the $N_{\mathrm{sk}}$1 and $N_{\mathrm{sk}}$2 states anti-skyrmions because they define anti-skyrmion by negative vorticity $N_{\mathrm{sk}}$3, not by negative $N_{\mathrm{sk}}$4 (Lin et al., 2024).

3. Evanescent and plasmonic optical skyrmions

The first experimentally established optical skyrmion platform was evanescent plasmonic light. In the six-wave surface-plasmon-polariton construction, optical skyrmion lattices are formed by interfering six TM guided waves of equal amplitude at an air/gold interface, producing a hexagonal lattice of normalized electric-field textures. The skyrmion number per unit cell is

$N_{\mathrm{sk}}$5

with $N_{\mathrm{sk}}$6 the normalized field. The experiment used a $N_{\mathrm{sk}}$7 nm Au layer on a $N_{\mathrm{sk}}$8 mm glass substrate, a $N_{\mathrm{sk}}$9 nm laser, and phase-resolved s-NSOM with $N$0 nm spatial resolution, yielding $N$1 for a lattice site. The same platform also established the bubble-to-Néel transition controlled by $N$2: just above the evanescence threshold $N$3, the texture is bubble-like, while larger $N$4 smooths it toward a Néel-type skyrmion (Tsesses et al., 2018).

A later plasmonic field-skyrmion study on a $N$5 nm silver film generated an isolated Néel-type skyrmion by tightly focusing a left-handed circularly polarized vortex beam with $N$6, $N$7, $N$8 nm, and $N$9. Because $Q$0, the azimuthal field component is nearly absent and the in-plane texture becomes radial, giving a hedgehog-like electric-field configuration with $Q$1. The same work used square and hexagonal apertures to generate a meron lattice and a skyrmion lattice, then demonstrated continuous transformations among isolated skyrmion, meron lattice, and skyrmion lattice using circular-fourfold, circular-sixfold, and fourfold-sixfold symmetry apertures (Shen et al., 2024).

Plasmonic optical skyrmions have also been used functionally rather than only topologically. In a thin gold film in Kretschmann geometry, a focused first-order radially polarized vortex beam generates a plasmonic Néel skyrmion whose local spin angular momentum texture at $Q$2 nm above the surface has $Q$3. Because this excitation is a pure axisymmetric TM state, it maximizes plasmon-enhanced inverse-Faraday-type drift currents and produces a stationary optomagnetic field. At resonance, the total optomagnetic energy generated with the radially polarized vortex beam is $Q$4 larger than with a focused circularly polarized beam, and the study identifies pure TM coupling plus constructive current circulation as the relevant design rule for optomagnetic nanophotonics (Karakhanyan et al., 2024).

Moiré engineering has extended plasmonic optical skyrmions beyond elementary $Q$5 cells. In twisted dual-hexagonal SPP nanostructures, the normalized real electric-field texture over a moiré supercell supports moiré plasmonic skyrmion clusters with higher total charge, including $Q$6 at $Q$7. The same system exhibits crystallized clusters at $Q$8 and $Q$9, quasi-crystallized states at $\mathbf{S}$0 and $\mathbf{S}$1, a skyrmion displacement of roughly $\mathbf{S}$2 nm for a one-degree twist change, and rapid inversion of skyrmion number under specific lateral alignment deviations, making the topological state a candidate nanoscale alignment beacon (Zhang et al., 2024).

4. Free-space, accelerating, nonlinear, and ultra-high-order realizations

Free-space optical skyrmions were first established in paraxial structured beams by treating the local polarization state as a Poincaré-vector texture. In the Laguerre–Gaussian superposition

$\mathbf{S}$3

the local Poincaré vector $\mathbf{S}$4 becomes skyrmionic, and for the beam family used experimentally the skyrmion number is $\mathbf{S}$5. With states $\mathbf{S}$6, the measured topological charges were $\mathbf{S}$7, $\mathbf{S}$8, $\mathbf{S}$9, $\pi_2(S^2)=\mathbb{Z}$0, $\pi_2(S^2)=\mathbb{Z}$1, and $\pi_2(S^2)=\mathbb{Z}$2 for nominal charges $\pi_2(S^2)=\mathbb{Z}$3 (Zhu et al., 2021).

A distinct free-space mechanism does not require vector-beam synthesis at all. Gauss-Stokes skyrmions arise around the phase singularity of a single uniformly polarized optical vortex because Gauss’s law, $\pi_2(S^2)=\mathbb{Z}$4, enforces a longitudinal field

$\pi_2(S^2)=\mathbb{Z}$5

Near the vortex core, the transverse field vanishes but the axial field need not, so the phase singularity is concealed by a longitudinal component and the relevant order parameter becomes the transverse-axial Stokes vector. For the experimentally observed focused $\pi_2(S^2)=\mathbb{Z}$6 vortex, the reconstructed transverse-axial skyrmion number was $\pi_2(S^2)=\mathbb{Z}$7, in agreement with the theoretical $\pi_2(S^2)=\mathbb{Z}$8 (Mata-Cervera et al., 28 Jan 2025).

Propagation engineering has introduced nontrivial skyrmion transport. Accelerating optical skyrmion lattices are generated by embedding a skyrmion-forming vector beam in an Airy-beam framework,

$\pi_2(S^2)=\mathbb{Z}$9

so that the whole lattice follows a parabolic trajectory. In experiment, the skyrmion unit cell maintained $\mathbf{S}_R=(S_x,S_y,S_z)^T$0 over $\mathbf{S}_R=(S_x,S_y,S_z)^T$1, with $\mathbf{S}_R=(S_x,S_y,S_z)^T$2 mm, while the meron core remained $\mathbf{S}_R=(S_x,S_y,S_z)^T$3 over $\mathbf{S}_R=(S_x,S_y,S_z)^T$4. The same work attributes the Bloch-to-Néel evolution during propagation to Gouy-phase accumulation between Airy-structured components (Wu et al., 9 Jan 2025).

Nonlinear plasma optics provides a different route. In second-harmonic generation from a linearly polarized optical vortex in underdense plasma, the nonlinear free-electron polarization spontaneously generates right- and left-circular second-harmonic components whose effective topological charges differ by $\mathbf{S}_R=(S_x,S_y,S_z)^T$5. For homogeneous plasma this yields a confined near-field Stokes skyrmion with $\mathbf{S}_R=(S_x,S_y,S_z)^T$6, which evolves after propagation into a second-order meron with whole-plane $\mathbf{S}_R=(S_x,S_y,S_z)^T$7; in inhomogeneous plasma an extra term proportional to $\mathbf{S}_R=(S_x,S_y,S_z)^T$8 deforms the skyrmionic texture and suggests a route to topological diagnosis of plasma density (Barriopedro et al., 4 May 2026).

The high-order regime has been pushed much further by ring-shaped skyrmions built from two orthogonally polarized vortex modes with unequal nonzero OAM. This avoids the radial-overlap failure of the usual Gaussian-plus-vortex construction and enabled nominal $\mathbf{S}_R=(S_x,S_y,S_z)^T$9th, $$n = \frac{1}{2}\left( \sum_{j} S_{z}^{(j)} N_j -\bar{S}_{z}^{(\infty)} N_\infty\right)$$0th, $$n = \frac{1}{2}\left( \sum_{j} S_{z}^{(j)} N_j -\bar{S}_{z}^{(\infty)} N_\infty\right)$$1th, $$n = \frac{1}{2}\left( \sum_{j} S_{z}^{(j)} N_j -\bar{S}_{z}^{(\infty)} N_\infty\right)$$2th, $$n = \frac{1}{2}\left( \sum_{j} S_{z}^{(j)} N_j -\bar{S}_{z}^{(\infty)} N_\infty\right)$$3th, and $$n = \frac{1}{2}\left( \sum_{j} S_{z}^{(j)} N_j -\bar{S}_{z}^{(\infty)} N_\infty\right)$$4th-order optical skyrmions with measured charges $$n = \frac{1}{2}\left( \sum_{j} S_{z}^{(j)} N_j -\bar{S}_{z}^{(\infty)} N_\infty\right)$$5, $$n = \frac{1}{2}\left( \sum_{j} S_{z}^{(j)} N_j -\bar{S}_{z}^{(\infty)} N_\infty\right)$$6, $$n = \frac{1}{2}\left( \sum_{j} S_{z}^{(j)} N_j -\bar{S}_{z}^{(\infty)} N_\infty\right)$$7, $$n = \frac{1}{2}\left( \sum_{j} S_{z}^{(j)} N_j -\bar{S}_{z}^{(\infty)} N_\infty\right)$$8, $$n = \frac{1}{2}\left( \sum_{j} S_{z}^{(j)} N_j -\bar{S}_{z}^{(\infty)} N_\infty\right)$$9, and $S_z$0. Perfect-vortex implementations then decoupled beam width from topological order, with only about $S_z$1 mm fluctuation in measured ring width over orders $S_z$2, and experiments showed topological stability upon propagation over $S_z$3 cm (Zeng et al., 6 May 2025).

5. Integrated, fiber, and dynamically reconfigurable platforms

Optical skyrmions are no longer confined to bulk or near-field laboratory geometries. Silicon photonics has provided an integrated source platform based on microring resonators with engineered double angular gratings. In this implementation, two circularly polarized emitted components with different orbital angular momenta produce a normalized Stokes texture whose skyrmion number is set by the OAM difference. The first representative device generated a first-order optical anti-skyrmion with measured $S_z$4 for a 37-pixel domain and $S_z$5 for a 38-pixel domain; a second device generated a second-order anti-skyrmion with $S_z$6. The platform operated around the telecom C-band on a $S_z$7 nm silicon layer with $S_z$8m ring radius and $S_z$9 nm waveguide width, establishing the first experimental integrated-photonics demonstration of on-chip optical skyrmion generation (Lin et al., 2024).

Fiber integration has been achieved with a metafiber: a metasurface bonded onto the tip of an optical fiber and designed to generate a zeroth-order Bessel beam in one polarization channel and a first-order vortex Bessel beam in the orthogonal channel. The resulting normalized Stokes field formed a skyrmion with measured $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$00, very close to the simulated $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$01. The same platform was continuously tunable through the input polarization angle, maintained high-quality skyrmion generation over approximately $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$02, and experimentally verified polarization inversion widths of about $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$03 for skyrmions and $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$04 for bimerons, beyond the conventional diffraction scale $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$05 (He et al., 2024).

Dynamic switching has been realized in liquid-crystal spin-orbit devices. A patterned liquid-crystal element with fixed Pancharatnam–Berry geometric phase and voltage-controlled retardance produces the output

$$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$06

so that voltage changes only the Gaussian–vortex balance, not the written phase pattern. The result is a reversible window-collapse-window evolution of the skyrmion number, with representative first-order values $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$07, $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$08, near-zero, $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$09, $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$10, and $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$11 as voltage scans through the half-wave condition. The device achieved $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$12 ms switching from vortex to skyrmion and $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$13 ms from skyrmion to vortex, corresponding to an ideal cycling rate of approximately $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$14 Hz, and was used to encode and decode a $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$15 binary image (Tang et al., 17 Jun 2026).

Programmable integrated reconfiguration has also been proposed with a silicon microring-resonator optical phased array. Optimized inner- and outer-grating emitters provide decoupled LCP and RCP bases with polarization fractions of $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$16 and $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$17, while programmable phase control switches between Néel-type and Bloch-type skyrmions and tunes the skyrmion number from $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$18 to $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$19. In the same platform, a four-symbol free-space communication link encoded in skyrmion number maintained a lower symbol error rate over a broader turbulence range than ideal LG-OAM encoding in a Kolmogorov phase-screen channel (Cai et al., 11 May 2026).

6. Robustness, storage, and applications

Topological robustness has become a central theme in optical-skyrmion research, but the most careful formulations are conditional rather than absolute. The boundary-origin theory of optical skyrmions proves that robustness through complex media follows when the perturbation respects the compactifying boundary conditions of the unperturbed field. In that setting, spatially varying retarders, suitable spatially varying diattenuators, and Type-I depolarizers preserve the degree, whereas noncompactifiable media or Type-II depolarizers can destroy it. Experiments with paraxial skyrmion beams of target degree $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$20 to $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$21 reported maximum error about $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$22 after cascaded polarization aberrations, while numerical tests for retarders and diattenuators yielded relative errors in the $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$23 to $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$24 range (Wang et al., 2024).

Atmospheric turbulence studies support a similar conclusion for free-space channels. For optical skyrmion fields built from orthogonally polarized LG modes, the skyrmion number remained close to its ideal value $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$25 over a broad range of Kolmogorov-type turbulence. For the $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$26 state, $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$27 evolved from $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$28 at $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$29 to $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$30 at $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$31, and remained recognizable even at $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$32. The same work found that, at fixed skyrmion number, larger $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$33 gives better resilience because reduced spatial overlap between the constituent LG components makes the polarization texture less vulnerable to turbulence-induced mixing (Zhang et al., 2024).

Optical-skyrmion topology has also survived full light–matter–light conversion. In a cold-$$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$34 dual-path EIT memory, paraxial skyrmions with $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$35 were decomposed into two path-separated LG components, stored independently as spin waves, retrieved, and recombined. The skyrmion number remained close to the target value for storage times $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$36, $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$37, and $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$38, and remained largely unchanged even when the control power was varied by more than $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$39 up to $$n=\frac{1}{4\pi}\int_A \mathbf{S}\cdot \left( \frac{\partial \mathbf{S}}{\partial x}\times \frac{\partial \mathbf{S}}{\partial y} \right)\,dx\,dy,$$40 mW. This was reported as the first experimental storage and retrieval of optical skyrmions with their topological characteristics preserved (Wang et al., 23 Dec 2025).

Applications follow directly from the field observable chosen. Plasmonic Néel skyrmions have been proposed for all-optical magnetization switching, magnetic recording, and spin-wave excitation because they generate a stationary optomagnetic field in metal films (Karakhanyan et al., 2024). Accelerating skyrmion lattices have been proposed as carriers for topologically robust information distribution and for particle sorting and manipulation (Wu et al., 9 Jan 2025). Integrated and fiber-based sources are positioned toward ultra-dense optical communications, matter manipulation, remote super-resolution microscopy, and super-robust information transfer (Lin et al., 2024, He et al., 2024). More broadly, the unified optical-skyrmion perspective places these textures within spin optics, imaging and metrology, optical forces, structured light, and topological and quantum technologies, while leaving open the still unresolved questions of full propagation protection, nonlinear optical skyrmion dynamics, and the extension to higher-order, higher-dimensional, and more strongly interacting topological quasiparticles (Shen et al., 2022).