Tunable polaritonic topologies generated by non-local photonic modes

Topology provides a foundational framework for understanding a wide range of natural phenomena^1,2,3. Among its key manifestations are topological defects, which cannot be removed or transformed without fundamentally altering the system’s configuration, intrinsically preventing their decay. The skyrmion⁴ is a prime example, consisting of a three-dimensional (3D) vector field mapped onto a two-dimensional (2D) plane. It is typically described as a vector field encoding distinct mappings on a 3D unit sphere in order-parameter space, capturing the winding and twisting of the field. A skyrmion is characterized by fully covering the unit sphere such that all possible orientations of the vector field are represented. In condensed matter and solid-state physics, skyrmions appear in systems ranging from magnetic materials^5,6 to superconductors^7,8, superfluids⁹ and liquid crystals^10,11,12.

Recently, topological defects have been extended to photonics, where skyrmions were observed via controlled interference of free-space waves^13,14,15,16 and surface plasmon polaritons^17,18,19. These photonic skyrmions exhibit deeply subwavelength features²⁰ and inherent topological robustness against material defects and environmental perturbations^21,22,23, highlighting their potential for optical computing, metrology and twistronics²⁴. They also possess non-trivial features such as topological domain walls, tunable via the ratio of in-plane to out-of-plane momentum. This enables transitions from bubble-type skyrmions with sharp domain walls to Néel-type skyrmions with smeared domain walls^17,25. Following their initial realization in plasmonics, recent demonstrations include free-space skyrmions^13,26, skyrmion bags²⁴ and various polaritonic topologies, such as optical meron lattices²⁷, and deeply subwavelength optical vortices carrying orbital angular momentum. The latter were achieved by interfering surface phonon polaritons in isotropic polar materials²⁸ (ε_xx = ε_yy = ε_zz) or hyperbolic phonon polaritons (HPhPs) in anisotropic polar materials^29,30 (ε_xx = ε_yy ≠ ε_zz), with applications in structured thermal emission³¹.

However, existing approaches for generating polaritonic field skyrmions^14,25,32 rely on non-reconfigurable, wavelength-dependent structures such as gratings or phase-correcting offsets, or on structured light such as radial polarization to launch and interfere surface waves (Fig. 1a, left). These constraints limit same-structure topological tunability, hindering integration into optical computing platforms requiring broadband reconfigurability. This contrasts with free-space skyrmions, where tunability has been demonstrated¹³. In addition, excitation typically requires circular or radial polarization³³, necessitating extra optical elements such as waveplates and increasing experimental complexity.

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a, A comparison between polaritonic topologies generated via conventionally used wavelength-dependent coupling structures^17,24 (left) and our topology-generating metasurface (right). While previous platforms relied on circularly polarized incident light and polariton wavelength-dependent offsets to compensate for the phase mismatch at each edge, our approach enables the generation of HPhPs in regular polygons. b, An illustration of the topology-generating metasurface introduced in this work, consisting of hexagonal amorphous silicon resonators on a CaF₂ substrate that supports the non-local qBIC resonance. c, The simulated real part Re(E_z) (left) and phase φ_z (right) of the out-of-plane electric field at the qBIC resonance. The optical phase on the surface of each resonator is uniform and does not contain any singularities. d, A schematic of a dielectric resonator covered by hBN and illuminated with linearly polarized light. The excitation launches HPhPs at the edges of the resonator. e, The real part of the in-plane permittivity of hBN (orange curve) ε_r,|| and reflectance spectra (blue curves) of the qBIC metasurface simulated for various resonator sizes, from smaller (light blue) to larger (dark blue). For the modelling of the permittivity of hBN and the calculated dispersion, see Supplementary Notes 1 and 2 and Supplementary Fig. 3, respectively. f, The qBIC resonances lie spectrally within the in-plane RS-band of hBN to excite HPhPs (grey shaded area in e), allowing for the in-phase generation of HPhPs at each resonator edge, resulting in photonic skyrmion lattices. g–i, Our approach contrasts with the use of local modes, such as a dipolar resonance in single resonators (g), which do not generate uniform field distributions (h) and therefore no notable topological configurations can be observed (i). Simulations of the out-of-plane electric fields were conducted at ω = 1,560 cm⁻¹, within the RS-band of hBN.

In this work, we introduce structured polaritonic topologies generated through non-local photonic resonances^34,35, enabling skyrmion formation without phase-correcting offsets and using linearly polarized light (Fig. 1a, right). We realize this by using arrays of high refractive-index dielectric hexagonal resonators (Fig. 1b) on a transparent CaF₂ substrate supporting quasi-bound states in the continuum (qBICs)^36,37 under linear polarization. These resonances arise from engineered in-plane asymmetry within each unit cell, allowing control over their linewidths³⁶. Crucially, symmetry-protected qBICs require extended periodic arrays rather than isolated resonators^38,39. This allows multiple resonators to be driven simultaneously by the same excitation, with topology governed by resonator geometry. As a result, optical skyrmions can be scaled from single structures to photonic chips, enabling large-area metasurfaces with multiple encoded skyrmion lattices.

On the basis of this principle, we experimentally demonstrate the generation and reconfigurability of qBIC-driven polaritonic topologies via interference of HPhPs in hexagonal boron nitride (hBN) thin films. Using scattering-type scanning near-field optical microscopy (s-SNOM), we resolve amplitude and phase of deeply subwavelength photonic skyrmion lattices induced by the non-local qBIC. By tuning the excitation frequency within the Reststrahlen (RS) band of hBN, we dynamically control the diameter D_hex of individual skyrmions without modifying the metasurface geometry. Our platform provides a route towards frequency-encoded topological states as reconfigurable building blocks for next-generation quantum photonic platforms.

Non-local mode formation for the generation of polaritonic skyrmions

The non-local photonic mode that emerges from our structure relies on strong mutual field interactions between individual resonators³⁴ that generate out-of-plane electric fields E_z (Fig. 1c). Importantly, these fields are highly uniform across the resonator surface in both amplitude and phase, in contrast to, for example, those emerging from a dipolar resonance (Fig. 1g–i). By covering each resonator with hBN (Fig. 1d) and tailoring the resonance to lie within the in-plane RS band of hBN (Fig. 1e) (where ε_r,|| < 0), our approach enables in-phase generation of HPhPs⁴⁰ on individual resonators. These modes arise in thin hBN films due to long-range coulomb interactions and the macroscopic polarization field that leads to a spectral splitting between longitudinal and transverse optical phonons, together with the intrinsic anisotropy of hBN. This anisotropy originates from strong in-plane covalent bonding and weaker out-of-plane van der Waals interactions, leading to strong polariton confinement.

A key advantage of our platform is that HPhPs are generated with identical intensity and phase at each resonator edge (Supplementary Fig. 1), unlike traditional approaches using single resonant structures^41,42,43. We simulate the out-of-plane electric field E_z of the hBN-covered metasurface and observe constructive interference of HPhPs at the resonator centre, forming a lattice of photonic skyrmions (Fig. 1f). This contrasts with local dipolar resonances in single dielectric resonators (Fig. 1g), which produce non-uniform E_z distributions and polarization-dependent intensity (Fig. 1h and Supplementary Fig. 2). Thus, local resonances such as dipolar modes are fundamentally incapable of generating the relevant topologies (Fig. 1i).

We started our experimental investigation by imaging the all-dielectric metasurface, schematically shown in Fig. 1b. Our design consists of hexagonal amorphous silicon (a-Si) pillars, with each pair laterally offset from one another. A scanning electron microscopy (SEM) image of the fabricated metasurface is shown in Fig. 2a, and atomic force microscopy (AFM) measurements of single unit cells with hexagonal, circular, and square resonators are shown in Fig. 2b–d. To spectrally tune the metasurface resonance, we vary the in-plane scaling factor S, which linearly modifies all unit cell dimensions except the height of the a-Si pillars. For all experiments, the pitch was set to P_x = 5,250 nm, P_y = 4,725 nm for a scaling factor S = 1 and the height of the resonators to h_Si = 1,450 nm. For a periodic array of resonators with C₄ symmetry (that is, no lateral offset), the qBIC manifests as a dark mode without radiative loss channels (infinite Q-factor) and cannot be observed in the far field. To access this photonic mode experimentally, the in-plane symmetry within each unit cell is broken, opening a radiative loss channel and resulting in an observable resonance (Supplementary Fig. 4) with finite radiative Q-factor Q_rad, which can be tuned by offsetting alternating resonator pairs by a distance D_x (Fig. 2b).

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a, An SEM image of the fabricated metasurface. b, An AFM measurement showing the geometry of a single hexagon resonator unit cell with pitches P_x and P_y, scaling factor S and distances between each resonator pair D − D_x and D + D_x, where D_x determines the radiative loss γ_rad. c,d, AFM measurements of a single unit cell with discs (c) and squares (d) as resonators. e, A sketch of a metallic s-SNOM tip on top of a dielectric resonator that scatters the local near-field in transmission mode. See the Methods for more information. f–h, The experimental out-of-plane optical near-field phase φ_z measured on the a-Si metasurface for hexagonal (f), disc (g) and square (h) resonators, showing similar uniform out-of-plane electric field distributions regardless of the resonator shape. The observed phase patterns for all structures agree well with simulations shown in Fig. 1 and Supplementary Fig. 4.

To quantify this asymmetry, we define the asymmetry parameter α as follows:

For all samples fabricated in this work, we choose α = 0.045, as it provides relatively high Q_rad of around 50–100 (Supplementary Fig. 4) while maintaining sufficiently broad resonances to experimentally reconfigure the HPhP wavelength, as the linewidth of the qBIC resonance corresponds to the tuning range of our approach. Such tunability arises from the strong sublinear dispersion of hBN (Supplementary Fig. 4), which enables large changes in polariton wavelength with small changes in excitation frequency^28,42. To ensure that the uniform out-of-plane electric fields can be accessed over a broad range of HPhP momenta, the metasurface is purposefully designed to support resonances with modest Q-factors.

The local near-fields of the photonic qBIC mode are imaged using transmission-mode s-SNOM with a sharp metallic tip (radius ≈ 50 nm) as a local scatterer (Fig. 2e). The full setup is shown in Supplementary Fig. 5. As the tip is polarized along the shaft, it primarily scatters out-of-plane electric fields E_z. By focusing a single-wavelength mid-IR beam onto the metasurface at normal incidence and scanning across individual resonators, both the local out-of-plane amplitude |E_z| and phase φ_z are extracted via pseudo-heterodyne (PsHet) detection⁴³. The measured φ_z for hexagonal resonators is shown in Fig. 2f and agrees well with simulations (Fig. 1c and Supplementary Fig. 4), exhibiting uniform out-of-plane electric fields across each resonator surface. In addition, edge scans on the metasurface (Supplementary Fig. 6) show that the non-local mode forms after approximately 6–7 resonators (3–4 unit cells), indicating that only a few unit cells are required to generate the qBIC mode in the near field, consistent with previous studies^38,39.

We demonstrate the versatility and generality of our concept by measuring the φ_z of unit cells with modified resonator shapes, namely discs (Fig. 2g) and squares (Fig. 2h), in addition to the hexagonal structures. The results show high uniformity of E_z across all geometries, indicating that the approach is generally applicable to different resonator shapes, provided sufficient mode volume is available for proper formation of the photonic mode. Further details are given in the Methods, and a fabrication sketch is shown in Supplementary Fig. 7. For this study, transmission-mode s-SNOM is preferred over reflection mode, as it enables excitation of the qBIC mode at normal incidence while suppressing tip-launched polaritons⁴⁴. This allows the tip to act as a passive scatterer, detecting near-fields generated by the photonic mode without perturbing the polaritonic topologies.

To generate qBIC-driven photonic skyrmion lattices localized on individual resonators, we fabricated dielectric metasurfaces covered with hBN flakes of thickness h_hBN = 50–70 nm. A SiO₂ layer (h_SiO2 = 50 nm) is inserted between a-Si and hBN to enhance adhesion and increase polariton lifetimes owing to its lower refractive index⁴⁵. For all samples, hBN flakes of size 50 × 50 to 100 × 100 μm², covering 10–20 unit cells, were used. To maximize spatial mode density, we employed a spectral gradient metasurface^46,47 by continuously varying the in-plane scaling factor S along one axis, spatially encoding a range of resonance wavelengths within a single array (Supplementary Fig. 8) and reducing the footprint⁴⁶. The spatial encoding was verified via large-area near-field scans (Supplementary Fig. 9).

Owing to the high tunability of HPhPs with small shifts in excitation frequency in hBN thin films^42,48, the broad range of resonances covered by our metasurface (Fig. 3a) generates HPhPs with drastically different wavelengths along the gradient (Fig. 3b–d), resulting in photonic skyrmion diameters ranging from D_hex = 451 nm down to 271 nm. Note that by definition, D_hex = λ_HPhP. Individual photonic skyrmions are visible in both the measured phase φ_z and amplitude |E_z|, with decreasing size and increasing number per resonator at higher excitation wavenumbers and smaller scaling factor S. Our qBIC-driven skyrmions are deeply subwavelength (~λ/25) and are about twice as small as plasmonic skyrmions reported previously¹⁷. This strong confinement arises from the polariton dispersion, which yields large in-plane momenta, leading to an imaginary out-of-plane wavevector and evanescent decay normal to the surface⁴⁹. The HPhP wavelength can be further reduced by increasing the excitation wavenumber or using thinner hBN, potentially combined with sharper tips to resolve smaller features. Note that the volumetric HPhPs, which are typically observed in hBN slabs (>10 nm), would shift towards purely surface modes when approaching the single atomic layer limit⁵⁰. In principle, this enables an arbitrary number of photonic skyrmions on a single resonator, allowing localized and optically reprogrammable topological charges (Supplementary Fig. 10). While hBN supports multiple hyperbolic modes at a given excitation wavelength, the dominant mode (m = 0; Supplementary Fig. 3) is primarily detected with s-SNOM²⁹. Although we use α = 0.045 for all fabricated structures, simulations show that the topology is generated regardless of the resonance Q-factor (Supplementary Fig. 11).

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a, The measured far-field reflectance spectra of fabricated metasurface for varying S, exhibiting a shift towards larger wavenumbers when decreasing the unit cell size. b–d, Experimental near-field out-of-plane optical phase φ_z (left) and amplitude |E_z| (right) images measured in unit cells of S varying between 1.1 and 1.0, resulting in HPhP wavelengths of λ_HPhP = 451 nm (b), 370 nm (c) and 271 nm (d). Below each image is a 2D cross section of the electric field vector extracted from the dashed white line marked in the experimental phase images. All measurements were taken on hBN flakes with a thicknesses h_hBN between 50 and 70 nm and excitation wavenumbers of 1,517 cm⁻¹ (b), 1,532 cm⁻¹ (c) and 1,560 cm⁻¹ (d). Images were filtered using the fast Fourier transform (FFT) procedure described in Supplementary Fig. 12 and Supplementary Note 3, and unfiltered images are shown in Supplementary Fig. 13.

Topological reconfigurability of qBIC-driven polaritonic skyrmions

To characterize the topological properties of qBIC-driven photonic skyrmions, we calculated the skyrmion number density (SND), which describes the spatial distribution of the field’s topological characteristics, and topological winding number S_T, which describes how many times the vector field in a given area σ wraps around the unit sphere. These quantities can be written as

where \(\hat{\mathbf{e}} = (E_{x}, E_{y}, E_{z}) / \sqrt{|E_{x}|^2 + |E_{y}|^2 + |E_{z}|^2}\) is the normalized electric field vector. Hereby, the winding number denotes the number of skyrmions within any given area σ on the surface of a resonator. The in-plane electric field components can be directly obtained from the out-of-plane electric field measured with s-SNOM through Maxwell’s equations, as shown in Supplementary Note 4 and in previous works^17,32.

We study the SND and S_T for the measurement shown in Fig. 3d (D_hex = 271 nm). Each resonator is labelled with a notation of (↑, n) or (↓, n), where ↑ or ↓ denotes the field direction of E_z for the central skyrmion and \(n\) distinguishes two resonators of the same polarity. The calculated SND (Fig. 4a) shows a typical Néel-type skyrmion pattern with domain walls that are smeared-out¹⁷, owing to the deeply subwavelength nature of the HPhPs generated in our structure (λ_HPhP ≈ λ₀/25). In general, Néel-type photonic skyrmions with smeared domain walls are more readily accessible in materials that support phonon polaritons, as surface plasmon polaritons with long propagation lengths generally exhibit only a moderate reduction in wavelength compared with the incident light⁴⁴. Calculated SNDs for the measurements in Fig. 3b,c are shown in Supplementary Fig. 14.

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a, The SND calculated from the measurements shown in Fig. 3d. Each resonator is marked with a notation showing the out-of-plane electric field direction (↑ or ↓) of the centre skyrmion and a number to distinguish opposing pairs (1 or 2). The resonators (↑, 1) and (↓, 1) are further analysed in the right panels, which show the calculated topological charge within each lattice site being close to the theoretical value of 1. The total topological charges of seven adjacent lattice sites are found to be \({S}_\text{T}^{(\uparrow ,1)}=6.95\) and \({S}_\text{T}^{(\downarrow ,1)}=-6.99\), close to the theoretical values of 7 and −7, respectively. b,c, The measured topological charge stability of the central lattice site for (↑, 1) (red circles) and (↑, 2) (red triangles) (b) and (↓, 1) (blue circles) and (↓, 2) (blue triangles) (c), proving the robustness of our photonic skyrmions under continuous tuning of the optical phase φ_z. The insets show the respective 2D cross sections through the central lattice site of the measured electric field vector. d, The experimental reconfigurability shown by scanning a single resonator repeatedly with different excitation wavenumbers. Inset images show the measured optical amplitude |E_z| for each excitation frequency. The topological charge S_T of the central lattice sites consistently stays at the theoretical value of +1 despite sizeable tuning of the skyrmion diameter D_hex. The inset in the lower left shows a sketch of the qBIC resonance and the excitation wavenumbers (dashed brown lines) used for imaging. Unfiltered images are shown in Supplementary Fig. 15.

Within a cluster of seven adjacent hexagonal cells of the skyrmion lattice (each with diameter D_hex), the winding number S_T is close to the theoretical value of ±1 within each area (Fig. 4a, right), with the sign depending on the direction of E_z. Owing to opposing field directions in each resonator pair emerging from the non-local qBIC resonance, both S_T values of +1 and −1 are recovered within each lattice site. This contrasts with photonic skyrmions in non-resonant isolated structures, where S_T is solely determined by the phase of the incident light. Summing all winding numbers for the resonators (↑, 1) and (↓, 1) across the seven hexagonal cells yields values of 6.95 and −6.99, respectively, in good agreement with the theoretical value S_T = ±7, demonstrating the topological robustness of qBIC-driven photonic skyrmion lattices. This stability is further illustrated by smoothly varying the optical phase φ_z (Fig. 4b,c) and calculating the S_T for each value, where for (↑, 1) (↑, 2) and (↓, 1) (↓, 2), S_T abruptly switches from +1 to −1 and back to +1, consistent with theoretical modelling.

As illustrated in Fig. 1a, our platform circumvents geometrically wavelength-specific offsets for phase compensation, relying instead on engineered qBIC resonances mediated by long-range coupling between resonators. We demonstrate optical reconfigurability by consecutively imaging the same resonator while tuning the excitation frequency in small steps (∆ω = cm⁻¹), which changes λ_HPhP substantially owing to the strong dispersion within the hBN in-plane RS-band. Our measurements (Fig. 4d) show continuous tuning of D_hex within the same resonator from 448 nm to 342 nm, while the winding numbers S_T around each central skyrmion remain close to the theoretical value of 1. This tunability window can, in principle, be made arbitrarily large by broadening the qBIC resonance via increasing the asymmetry parameter α, enabling the photonic mode to form over a wider wavelength range.

Generation of arbitrarily structured topologies

Our platform offers a straightforward route to generate arbitrarily structured optical topologies through variation of the resonator shape. As shown in Supplementary Fig. 4, the uniform out-of-plane electric fields of the non-local qBIC metasurface are preserved when moving from hexagonal resonators to discs or squares of comparable mode volume. As with the hexagonal design generating skyrmion lattices, disc and square resonators exhibit the same degree of E_z uniformity across each surface. We expect this behaviour to extend to more complex resonator shapes resembling a disc, such as twisted hexagons for the generation of skyrmion bags.

To demonstrate the generality of our platform, we experimentally probe polaritonic kπ-twist skyrmions, previously only observed in singular graphene discs⁵¹, as well as optical meron lattices, previously realized in patterned gold films²⁷ (Supplementary Fig. 16). The measured kπ-twist skyrmions are generated in disc resonators (Fig. 5a–d) and consist of concentric rings centred around a single skyrmion with alternating out-of-plane electric field directions. Square resonators instead generate optical meron lattices (Fig. 5e–h), with both simulated and measured S_T values shown in Supplementary Fig. 17. Note that merons are topologically less stable than skyrmions as they span only half a unit sphere, resulting in S_T values deviating further from the ideal ±0.5. For large-scale SEM images of the fabricated devices, see Supplementary Fig. 18. As shown previously for the tunable skyrmion lattices in hexagonal resonators, this approach removes the need for wavelength-specific geometries and enables same-structure reconfigurability.

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a–d, An SEM image (a), experimental optical amplitude (|E_z|) (b), optical phase (φ_z) (c) and SND (d) of an optical kπ-twist skyrmion, exhibiting characteristic concentric rings around the centre of the disc. e–h, An SEM image (e), experimental optical amplitude (|E_z|) (f), optical phase (φ_z) (g) and SND (h) of an optical meron lattice. Simulated and experimentally obtained S_T values for meron lattices are shown in Supplementary Fig. 17. Unfiltered images are shown in Supplementary Fig. 19.