Optical Skyrmions: Topology, Methods, Applications

• Optical skyrmions are two-dimensional topological textures of light formed by mapping a three-component optical field onto a unit sphere, yielding a quantized skyrmion number.
• They are realized via diverse methods including evanescent plasmonic fields, free-space superpositions of vector beams, and integrated metasurfaces, each employing electric field, spin, or normalized Stokes vector formulations.
• Their inherent topological robustness enables practical applications in remote super-resolution imaging, photonic computing, and reliable optical communications.

Optical skyrmions are two-dimensional, topologically nontrivial textures of light in which a three-component optical vector field maps a transverse domain onto a unit sphere. Depending on the construction, the mapped field can be the real electric field, the spin-angular-momentum vector, or the normalized Stokes vector, but in each case the defining property is a nonzero skyrmion number,

$$Q=\frac{1}{4\pi}\int \mathbf n\cdot(\partial_x\mathbf n\times\partial_y\mathbf n)\,dx\,dy,$$

which counts how many times the field wraps the sphere (Shen et al., 2022). In photonics, this has led to a family of localized or lattice-like quasiparticles of light, including Néel-type skyrmions, Bloch-type skyrmions, anti-skyrmions, merons, bimerons, and higher-order textures, realized in evanescent fields, free-space beams, fiber-integrated metasurfaces, waveguides, and integrated emitters (Shen et al., 2022).

1. Topological definition and mathematical structure

The common mathematical structure is a smooth map from a two-dimensional optical domain to $S^2$. In paraxial polarization-based formulations, the local state is represented by the normalized Stokes vector $S(x,y)=(S_1,S_2,S_3)^T$, equivalently written as $n(x,y)=S(x,y)$, with $|S|=1$ (McWilliam et al., 2022). In electric-field or spin-based formulations, one instead uses $n(x,y)=E(x,y)/|E(x,y)|$ or the unit helicity or spin vector (Tsesses et al., 2018). The skyrmion number is then the degree of this map, provided the boundary is constant or otherwise compactifiable (Wang et al., 2024).

A standard parameterization writes

$$\mathbf n(r,\phi)=\bigl(\cos\alpha(\phi)\sin\beta(r),\ \sin\alpha(\phi)\sin\beta(r),\ \cos\beta(r)\bigr),$$

with $\alpha(\phi)=m\phi+\gamma$, where $m$ is the vorticity and $\gamma$ the helicity; the resulting skyrmion number is $S^2$0, where $S^2$1 is the polarity (Shen et al., 2022). This directly encodes the canonical taxonomy. Néel-type skyrmions correspond to radial in-plane vectors, Bloch-type skyrmions to azimuthal in-plane circulation, anti-skyrmions to opposite winding, and higher-order skyrmions to $S^2$2 (Shen et al., 2022). Bimerons are the linear-polarization analogue of a skyrmion texture, with two merons separated by linear-polarization lines, while merons carry $S^2$3 over their domain (McWilliam et al., 2022).

A recurring point in the literature is that the topological invariant is not merely a geometric picture but a homotopy class. The rigorous statement is that the skyrmion number is preserved under smooth deformations that leave the relevant boundary behavior unchanged (Wang et al., 2024). This is central to both the experimental characterization of optical skyrmions and to proposals that treat them as digitally readable, perturbation-resilient carriers of information (Wang et al., 2024).

2. Field choices and skyrmion taxonomies in optics

Optical skyrmions are not tied to a single physical observable. The review literature explicitly distinguishes electric-field skyrmions, spin skyrmions, and Stokes skyrmions, depending on which three-component vector is normalized and mapped to the sphere (Yao et al., 2024). This distinction matters because different platforms naturally realize different order parameters.

In evanescent-field work, the real electric field can play the role of the order parameter because guided or evanescent electromagnetic modes permit a globally real three-component unit vector field with nonzero skyrmion number, unlike free-space propagating electromagnetic waves in that specific formulation (Tsesses et al., 2018). This led to the first experimentally observed optical skyrmion lattices through interference of surface plasmon polaritons. In paraxial free-space optics, by contrast, the normalized Stokes vector is the more common order parameter, yielding polarization skyrmions or Poincaré skyrmions (Zhu et al., 2021).

The field taxonomy has expanded beyond the early Néel and Bloch cases. Free-space superpositions of orthogonally polarized Bessel modes or Laguerre–Gaussian modes realize variable-order skyrmions, with the skyrmion number controlled by the orbital-angular-momentum difference between the components (Zhu et al., 2021). Plasmonic and phonon-polaritonic systems further support bubble-type textures, meron lattices, skyrmion lattices, and continuous transformations among these states under symmetry or dispersion control (Shen et al., 2024). More recent work adds hybrid optical skyrmions in which electric-field skyrmions, spin skyrmions, and Stokes skyrmions coexist in the same diffracted light field (Yao et al., 2024).

The literature also includes generalized constructions. The computing framework treats any continuous polarization field with constant boundary as carrying an integer degree $S^2$4, and further proposes generalized skyrmion tuples $S^2$5 obtained by counting connected Poincaré components carved out by the boundary curve (Wang et al., 2024). In waveguides, a generalized skyrmion number $S^2$6 can remain protected even when the usual skyrmion number fails (Wang et al., 10 May 2025). This suggests that the topic is better understood as a hierarchy of topological encodings rather than a single canonical texture.

3. Physical platforms and generation mechanisms

The first major experimental platform was the evanescent electromagnetic field. Optical skyrmion lattices were generated by interfering six transverse-magnetic guided waves, implemented experimentally with surface plasmon polaritons on a patterned gold film (Tsesses et al., 2018). In the simplest lattice construction, the out-of-plane field is a superposition of three standing waves at $S^2$7, $S^2$8, and $S^2$9, and the in-plane components follow from the TM condition and $S(x,y)=(S_1,S_2,S_3)^T$0, producing a Néel-type skyrmion pattern in each unit cell (Tsesses et al., 2018). A closely related theoretical result showed that any TM-polarized evanescent electromagnetic field with perfect rotational symmetry is a Néel-type optical skyrmion of the electric field vectors, independent of the operation frequency and medium (Tian et al., 2023).

Free-space realizations followed by using controlled mode superpositions. A representative construction uses two orthogonally polarized Laguerre–Gaussian modes,

$S(x,y)=(S_1,S_2,S_3)^T$1

so that the Poincaré vector acquires a hedgehog-like structure and the skyrmion number becomes $S(x,y)=(S_1,S_2,S_3)^T$2 (Zhu et al., 2021). An experimentally distinct route uses two orthogonal Bessel modes with matched cone-angle spectra; because the two constituent Bessel beams share the same $S(x,y)=(S_1,S_2,S_3)^T$3 and $S(x,y)=(S_1,S_2,S_3)^T$4, the normalized Stokes map becomes propagation invariant, yielding non-diffracting and self-healing optical skyrmions (Rao, 2024). Another free-space mechanism does not rely on vector-beam superposition at all: a focused scalar optical vortex naturally acquires a longitudinal field through Gauss’s law, and the resulting transverse–axial polarization around the singularity forms a Gauss–Stokes skyrmion with $S(x,y)=(S_1,S_2,S_3)^T$5 (Mata-Cervera et al., 28 Jan 2025).

Integrated and near-field architectures have become increasingly prominent. A metafiber platform splices a polarization-maintaining single-mode fiber to an expanding multimode section and terminates it with a single-layer dielectric metasurface; the metasurface imprints a zero-order Bessel axicon phase on one polarization and a first-order vortex-Bessel phase on the orthogonal polarization, so that their vectorial interference near the fiber facet generates a tunable skyrmion texture (He et al., 2024). A related integrated proposal uses a silicon microring-resonator optical phased array with optimized inner- and outer-grating microring emitters to synthesize free-space skyrmions with programmable type and skyrmion number (Cai et al., 11 May 2026).

Plasmonic and polaritonic platforms provide additional control knobs. Focused structured light on a silver film generates isolated plasmonic Néel-type skyrmions, meron lattices, and skyrmion lattices, with continuous transformation among them through aperture-engineered symmetries and input phase control (Shen et al., 2024). In thin SiC membranes, six chromium nanoridges launch interfering surface phonon-polaritons whose strong sub-linear dispersion allows continuous tuning between bubble-type and Néel-type optical skyrmions by changing the excitation wavelength by only $S(x,y)=(S_1,S_2,S_3)^T$6 (Mangold et al., 23 Mar 2026). Moiré plasmonic nanostructures extend this further by nesting multiple elementary skyrmions into large supercells with $S(x,y)=(S_1,S_2,S_3)^T$7 or $S(x,y)=(S_1,S_2,S_3)^T$8 (Zhang et al., 2024).

Platform	Mapped field	Representative result
Interfering SPPs on gold (Tsesses et al., 2018)	Real electric field	Optical skyrmion lattices with $S(x,y)=(S_1,S_2,S_3)^T$9 in a 37-site lattice
Orthogonally polarized LG modes (Zhu et al., 2021)	Normalized Stokes vector	Free-space skyrmionic optical structures with $n(x,y)=S(x,y)$0
Metafiber-integrated metasurface (He et al., 2024)	Stokes vector	$n(x,y)=S(x,y)$1 up to $n(x,y)=S(x,y)$2 at $n(x,y)=S(x,y)$3
Conducting cylindrical waveguide (Wang et al., 10 May 2025)	Stokes vector	Preservation of $n(x,y)=S(x,y)$4 determined by topologically stabilizing modes
Silicon microring OPA (Cai et al., 11 May 2026)	Normalized Stokes vector	Dynamic tuning across $n(x,y)=S(x,y)$5 to $n(x,y)=S(x,y)$6

These mechanisms are physically diverse, but the underlying design principle is the same: engineer a three-component optical vector field whose center, edge, and intermediate region enforce a full or fractional wrapping of the target sphere.

4. Measurement, reconstruction, and robustness

Experimental characterization has developed along two complementary routes: full-field reconstruction and discrete topological extraction. In free-space polarization skyrmions, standard Stokes tomography records six intensity images in mutually unbiased polarization bases and reconstructs $n(x,y)=S(x,y)$7 point by point (McWilliam et al., 2022). In metafibers, a two-path interferometric field-recovery setup reconstructs the complex amplitudes $n(x,y)=S(x,y)$8 and $n(x,y)=S(x,y)$9, from which the Stokes vector and the skyrmion number are computed (He et al., 2024). Near-field plasmonic and phonon-polaritonic platforms rely on scattering-type near-field scanning optical microscopy with pseudo-heterodyne interferometry to recover amplitude and phase of $|S|=1$0, then reconstruct in-plane components through known Maxwell relations (Tsesses et al., 2018).

A major methodological advance is the topological characterization of skyrmions via their polarization singularities. Using Stokes’s theorem and the vector potential $|S|=1$1, McWilliam et al. derived the discrete formula

$|S|=1$2

where the contribution comes only from singularities and the periphery, not from derivatives of noisy data (McWilliam et al., 2022). For $|S|=1$3 skyrmions and bimerons, this topological method achieves errors below $|S|=1$4 when choosing the optimal basis, versus several percent for the surface integral, and under added background noise the topological method in an orthogonal basis remains virtually exact (McWilliam et al., 2022). This is a technical clarification of an important point: the skyrmion number is often easier to measure from the topology of singularities than from direct numerical differentiation.

Robustness claims in optical skyrmion research are now grounded in explicit theorems rather than heuristic analogy alone. The general proof of topological protection shows that the skyrmion number is preserved under any smooth, compactifiable perturbation, and that the necessary and sufficient condition is that the perturbation respect the compactifiability boundary conditions of the unperturbed skyrmion (Wang et al., 2024). Experimentally, paraxial skyrmion beams of target degrees $|S|=1$5 were passed through cascades of polarization aberrators, including spatially varying retarders, diattenuators, and weak depolarizers; across all degrees $|S|=1$6 and all aberration combinations, the absolute error $|S|=1$7 remained below $|S|=1$8, with typical errors $|S|=1$9 (Wang et al., 2024).

Other experiments reinforce this picture with platform-specific metrics. In the metafiber generator, the skyrmion number reached $n(x,y)=E(x,y)/|E(x,y)|$0 experimentally and $n(x,y)=E(x,y)/|E(x,y)|$1 in simulation at $n(x,y)=E(x,y)/|E(x,y)|$2, high-quality skyrmions persisted for $n(x,y)=E(x,y)/|E(x,y)|$3, and the inversion width was $n(x,y)=E(x,y)/|E(x,y)|$4 for skyrmions and $n(x,y)=E(x,y)/|E(x,y)|$5 for bimerons, both well below the diffraction limit $n(x,y)=E(x,y)/|E(x,y)|$6 (He et al., 2024). In the photonic-computing experiments, measured operations $n(x,y)=E(x,y)/|E(x,y)|$7 and $n(x,y)=E(x,y)/|E(x,y)|$8 all returned the correct integer outputs, the particular sample exhibited large fabrication asymmetry yet $n(x,y)=E(x,y)/|E(x,y)|$9 was always correct, and zero observed mis-assignments of integer result occurred across dozens of trials (Wang et al., 2024). These results support a narrower and more accurate statement than generalized “immunity”: robustness holds against smooth perturbations and noise so long as the relevant topological and boundary constraints are maintained.

5. Functional operations and applications

Applications divide broadly into information processing, imaging and metrology, and light–matter interaction. The compact metafiber skyrmion generator was proposed for remote super-resolution microscopy, robust information transfer, and topological light–matter interactions (He et al., 2024). Its deep-subwavelength polarization singularities can enhance imaging contrast beyond the diffraction limit, while fiber delivery enables endoscopic or in situ use; the same platform suggests broad bandwidth $$\mathbf n(r,\phi)=\bigl(\cos\alpha(\phi)\sin\beta(r),\ \sin\alpha(\phi)\sin\beta(r),\ \cos\beta(r)\bigr),$$0 and fiber compatibility for high-capacity, error-resilient channels (He et al., 2024).

In photonic computing, the central idea is digitization by topological number assignment. Any continuous polarization field with constant boundary maps topologically to $$\mathbf n(r,\phi)=\bigl(\cos\alpha(\phi)\sin\beta(r),\ \sin\alpha(\phi)\sin\beta(r),\ \cos\beta(r)\bigr),$$1 and therefore has an integer degree $$\mathbf n(r,\phi)=\bigl(\cos\alpha(\phi)\sin\beta(r),\ \sin\alpha(\phi)\sin\beta(r),\ \cos\beta(r)\bigr),$$2, providing a digital read-out robust against field noise (Wang et al., 2024). The same work gives a transformation law $$\mathbf n(r,\phi)=\bigl(\cos\alpha(\phi)\sin\beta(r),\ \sin\alpha(\phi)\sin\beta(r),\ \cos\beta(r)\bigr),$$3 and realizes passive integer arithmetic with a structured retarder designed so that a skyrmion of degree $$\mathbf n(r,\phi)=\bigl(\cos\alpha(\phi)\sin\beta(r),\ \sin\alpha(\phi)\sin\beta(r),\ \cos\beta(r)\bigr),$$4 is transformed according to $$\mathbf n(r,\phi)=\bigl(\cos\alpha(\phi)\sin\beta(r),\ \sin\alpha(\phi)\sin\beta(r),\ \cos\beta(r)\bigr),$$5 depending on beam direction (Wang et al., 2024). This is presented as the first direct achievement of discrete mathematical operations using optical skyrmions without external energy input (Wang et al., 2024).

Communications research has begun to exploit the same topological observables. A silicon microring optical phased array integrates spin-selective emission and programmable phase control to actively switch between Néel-type and Bloch-type skyrmions while dynamically tuning the skyrmion number across $$\mathbf n(r,\phi)=\bigl(\cos\alpha(\phi)\sin\beta(r),\ \sin\alpha(\phi)\sin\beta(r),\ \cos\beta(r)\bigr),$$6 to $$\mathbf n(r,\phi)=\bigl(\cos\alpha(\phi)\sin\beta(r),\ \sin\alpha(\phi)\sin\beta(r),\ \cos\beta(r)\bigr),$$7 (Cai et al., 11 May 2026). Using these programmable states, a 4-symbol free-space communication link was compared with ideal LG-OAM encoding under Kolmogorov turbulence, and the skyrmion-encoded link maintained a lower symbol error rate over a broader turbulence range (Cai et al., 11 May 2026). A plausible implication is that topological observables can be operationally more robust than scalar OAM observables in turbulence-limited links.

Light–matter interaction provides a distinct application axis. In plasmonic optomagnetism, a focused radially-polarized vortex beam excites a plasmonic Néel skyrmion that maximizes optically induced drift currents in a thin gold film, generating a quasi-static magnetic field through the inverse Faraday effect (Karakhanyan et al., 2024). The paper explicitly connects this to all-optical magnetization switching, magnetic recording, and the excitation of spin waves (Karakhanyan et al., 2024). Other works point to selective manipulation of nano-objects or quantum emitters through sub-$$\mathbf n(r,\phi)=\bigl(\cos\alpha(\phi)\sin\beta(r),\ \sin\alpha(\phi)\sin\beta(r),\ \cos\beta(r)\bigr),$$8 spin textures (He et al., 2024).

Storage is now included in the experimental landscape. A dual-path electromagnetically induced transparency memory in cold $$\mathbf n(r,\phi)=\bigl(\cos\alpha(\phi)\sin\beta(r),\ \sin\alpha(\phi)\sin\beta(r),\ \cos\beta(r)\bigr),$$9 vapor stored and retrieved optical skyrmions while preserving the skyrmion number for storage times up to several microseconds, even under imbalanced loss between the two paths and substantial perturbations in control beam power (Wang et al., 23 Dec 2025). For $\alpha(\phi)=m\phi+\gamma$0, the retrieved values remained within experimental uncertainty of the input values, establishing the survival of a non-trivial topological invariant in a quantum memory (Wang et al., 23 Dec 2025).

6. Limits, controversies, and emerging directions

A recurring misconception is that any structured polarization field is automatically a skyrmion. The rigorous literature does not support that. The degree is quantized only when the field is defined as a continuous $\alpha(\phi)=m\phi+\gamma$1-valued map with suitable boundary conditions or compactifiability (Wang et al., 2024). This is why several papers emphasize constant boundary polarization, fixed boundary circularity, or compactification at infinity (Wang et al., 2024). It also clarifies why some free-space constructions are described as quasi-skyrmions or why the review literature notes that paraxial beams can lack the confinement boundary needed for a rigorously quantized $\alpha(\phi)=m\phi+\gamma$2 in certain formulations (Rao, 2024).

Another point of clarification concerns “topological protection.” In optics, topological protection does not imply unconditional invariance under arbitrary propagation or arbitrary perturbation. In waveguides, preservation of the skyrmion number during propagation depends on the presence of topologically stabilizing modes, specifically sufficiently large $\alpha(\phi)=m\phi+\gamma$3 TE or TM content that keeps the transverse field nonzero across the cross-section (Wang et al., 10 May 2025). If singularities are born or annihilated, or if boundary polarizations shift so that compactifiability fails, the usual skyrmion number can change (Wang et al., 10 May 2025). The generalized skyrmion number was introduced precisely to recover protected topological data in such cases (Wang et al., 10 May 2025).

Platform choice also remains an active issue. Plasmonic implementations enabled the earliest deep-subwavelength demonstrations but are limited by loss; the SiC phonon-polariton platform was explicitly proposed as a route beyond the loss-limited tunability of plasmonic approaches, with lower intrinsic damping and strong dispersion enabling bubble-to-Néel tuning (Mangold et al., 23 Mar 2026). Fiber-integrated approaches address compactness and alignment; free-space systems offer flexibility and direct manipulability; waveguides and silicon OPAs address integration and communications; quantum memories address coherent storage (He et al., 2024).

The field is also expanding in topological complexity. Current directions include generalized skyrmion adders and rational arithmetic (Wang et al., 2024), multi-degree-of-freedom hybrid skyrmions in a single light field (Yao et al., 2024), moiré plasmonic skyrmion clusters with $\alpha(\phi)=m\phi+\gamma$4 and quasicrystalline order (Zhang et al., 2024), and customized intensity distributions and trajectories for isolated skyrmions and skyrmion arrays (Tian et al., 13 Aug 2025). This suggests that “optical skyrmion” is no longer a single construction but a broad photonic framework for encoding topology into field, spin, and polarization textures across free-space, near-field, and integrated platforms.