Polaritonic states trapped by topological defects

Recent advances in symmetry engineering of electromagnetic modes in metamaterials enable tailoring of optical properties and generation of photonic pseudo-spin, allowing helicity-dependent trapping and guiding of structured light along topological interfaces. Crystalline symmetries have been used to realize higher-order topological phases and new classes of topological defects, enabling zero-dimensional (0D) photonic cavities. Topological boundary modes have underpinned applications from nonlinear optics and lasers to light–matter interactions. However, the detailed structure of optical fields on nano-structured polaritonic chips remains insufficiently understood, particularly for higher-order and defect modes, limiting control over light–matter selection rules. Here, the authors introduce a hybrid polaritonic cavity based on a 0D topological defect in a Kekulé-patterned planar metasurface integrated with hBN, designed to trap higher-order topological (HOT) polariton states and to reveal their chiral structure and selective coupling to spin-polarized edge modes.

The study builds on topological photonics leveraging spatial and crystalline symmetries to generate pseudo-spin and higher-order topological phases (e.g., Kekulé patterns, band inversions between dipolar and quadrupolar modes). Prior works demonstrated topological boundary modes across frequency domains and dimensions, with applications in nonlinear optics, lasers, and light–matter interactions. Chiral light–matter interactions have been reported in systems integrating van der Waals materials for guided topological edge modes, but systematic studies of higher-order and topological defect modes in hybrid polaritonic platforms were lacking. The work also relates to topological polaritons and strong light–matter coupling in van der Waals materials (e.g., hBN phonon polaritons), leveraging known dipolar/quadrupolar mode behavior and Dirac-type photonic metasurfaces.

• Device design: A hybrid topological metasurface comprising a silicon (Si) photonic crystal slab patterned with hexamers of triangular holes (Kekulé-deformed honeycomb lattice), covered by a thin hBN layer. Three off-set sectors (λ=1,2,3) of shrunken hexamers stitched at a core create a point defect, with accompanying line defects along sector boundaries; zig-zag domain walls between shrunken and expanded regions provide conventional 1D interfaces.
• Theoretical modeling: An effective Dirac-like Hamiltonian for coupled photonic (dipolar p and quadrupolar d modes, doubly degenerate at Γ) and phononic (two in-plane TO modes of hBN) degrees of freedom was derived in a 2D approximation. The mass term arises from Kekulé deformation with a sector-dependent phase Θ(λ), producing domain-dependent Dirac mass winding. Coupling to phonons is included via coupling strengths g1 (to dipolar) and g2≈0 (quadrupolar neglected due to detuning). The continuum model is solved for bulk, line-defect, and point-defect states; Susskind discretization is used for numerical dispersion of hybrid edge polaritons. Analytical expressions include: edge-state dispersion ω_es(kx)=ω0±√(Δ^2+4ω0^2 kx^2) (photonic limit), gap opening with phonon coupling, and closed-form 0D HOT mode frequency ω_a=(ω_p+ω0)/2 + ½√((ω_p−ω0)^2+2 g1^2) and photonic/phononic amplitude ratio u_b/p_{1,2}=g1/(√2(ω_a−ω0)). HOT mode localization and sublattice polarization are dictated by angular variation of λ(θ).
• Numerical simulations: Full-wave 3D finite-element simulations (COMSOL Multiphysics) with Floquet-periodic supercells to compute band structures and interface dispersions; parameter fitting to the effective model. Material parameters: ε_Si=11.69, ε_sapphire=2.05; hBN thickness 15 nm. Supercells: interfaces along x, 8 unit cells along y and 2 along x, with PML surroundings; spectra obtained by scanning frequencies and Floquet wave numbers and mapping interface energy density.
• Fabrication: Silicon-on-sapphire (SOS) substrate (1 μm Si/500 μm sapphire) patterned by electron-beam lithography (ZEP520A-7 resist; anti-charging layer; Elionix ELS-G100), developed in n-amyl acetate, followed by inductively coupled plasma etching (C4F8/SF6; ~2.5 nm/s at 5 °C) through 1 μm Si; resist removal in heated NMP. hBN flakes (15 nm) exfoliated and dry-transferred via PDMS to cover regions with line and point defects; thickness verified by AFM.
• Optical characterization: Custom mid-IR setup for real-space and back focal plane (Fourier-space) imaging in reflection, using a QCL (Daylight MIRcat-QT, 6.5–7.6 μm, 5-nm resolution), 0.56 NA objective, and microbolometer camera. Iso-frequency contours acquired to reconstruct 3D Fourier maps. Cross-polarized detection, polarization control via half-wave plate; circular polarization via quarter-wave plate for selective excitation; Stokes polarimetry (six intensity measurements) to reconstruct polarization textures.

• Demonstration of strong coupling between Si metasurface photonic modes and hBN TO phonons, yielding upper and lower polariton branches (absent in the photonic-only structure), confirmed by experimental band diagrams.
• Existence of tightly confined defect modes: 1D line-defect modes and a 0D HOT point-defect polaritonic mode spectrally located inside the line-defect gap, consistent with Dirac physics and higher-order topology.
• The line-defect edge-state spectrum exhibits a sizable gap due to phonon coupling; this gap is about five times larger than that of conventional armchair domain walls, favoring emergence of well-localized 0D HOT modes within it.
• Numerical prediction and experimental observation of a high-Q in-gap point-defect mode around λ≈6.93–6.95 μm (simulated 6.93 μm; observed 6.95 μm). Fig. 1 shows line-defect imaging at 6.80 μm and point-defect imaging at 6.95 μm.
• The 0D HOT mode shows chiral far-field radiation with a three-lobe directivity pattern featuring a singularity at normal emission. Beam divergence ~15°, with lobe angles below ~10°, in agreement between simulations and experiments.
• Spiral polarization texture in the far field, captured by Stokes polarimetry and matching theoretical predictions from both full-wave and Dirac/TBM models. Shrunken versus expanded lattices exhibit opposite chiralities of the three-lobe pattern.
• Analytical model provides the 0D mode frequency and photonic/phononic composition, showing tunability of the photon–phonon fraction by detuning midgap relative to the phonon resonance.
• Selective excitation in heterogeneous networks: Spin-polarized (helicity-selective) 1D edge waves launched at zig-zag domain walls propagate unidirectionally to corner junctions and, at resonance, selectively excite HOT point-defect modes localized at vertices. Off-resonance excitation yields only edge transport without defect excitation.

The findings confirm that Kekulé-engineered topological defects in a hybrid Si–hBN metasurface can host 0D HOT phonon-polaritonic states. The effective Dirac model with sector-dependent mass winding explains both the emergence and properties of these localized modes and the gapped hybrid edge dispersions. Embedding hBN introduces strong photon–phonon coupling that not only reshapes the band structure into polariton branches but also enlarges interface gaps, enabling robust 0D trapping within a topological network. The observed chiral far-field emission with a singularity and spiral polarization directly evidences the topological origin and structured nature of these polaritons, while helicity-selective coupling between 1D edge modes and 0D defects demonstrates controlled interconversion across dimensionalities. Together, these results address the challenge of controlling the field structure of light–matter excitations on polaritonic chips, offering a route to deterministic selection rules and robust manipulation of hybrid states for mid-IR photonics and phononics.

The work introduces and validates a hybrid topological metasurface platform that traps higher-order topological phonon-polaritonic states at 0D defects formed by stitched Kekulé domains. It establishes mutual transformation between pseudo-spin-locked 1D edge modes and 0D HOT defect states, and demonstrates chiral radiation with spiral polarization and selective edge-to-defect excitation. The approach enables engineering of topological networks or super-crystals that manipulate half-light, half-matter excitations for guiding, resonant trapping, and structured emission in the mid-IR. Future directions include tuning light–matter interaction strength to induce topological phase transitions, designing extended topological polaritonic super-crystals, and realizing selective excitation of structured vibrational modes using mid-IR Gaussian vortex beams for advanced control of phononic degrees of freedom.

• The demonstrations are confined to mid-IR frequencies (6.5–7.6 μm) and rely on hBN TO phonons; extension to other spectral ranges/materials is not shown.
• Strong coupling and losses depend on hBN thickness, with optimal operation reported for 10–25 nm (15 nm used), indicating a trade-off between coupling strength and dissipation.
• The selective excitation experiments use specific geometries (zig-zag domain walls, trapezoid networks) and polarization-controlled sources; generality to arbitrary layouts is not established here.
• The zig-zag domain wall exhibits a very small gap (effectively linear crossing in the continuum limit), which may limit certain trapping schemes compared to the larger-gapped line defects.
• Spectral resolution of the QCL (5 nm) and far-field collection NA constrain quantitative assessment of Q-factors and radiation profiles.