Topologically-Controlled Photonic Flatbands

• Topologically-controlled photonic flatbands are nearly dispersionless energy bands engineered via symmetry and topological charge splitting, enabling slow light and nonlinear optical effects.
• Metasurface design using anisotropic ReS₂ and precise nanofabrication techniques allows tunable qBIC modes with split polarization and controlled radiative lifetimes.
• Hybridization with excitonic resonances in ReS₂ forms robust exciton-polaritons with large Rabi splittings, paving the way for advanced quantum photonic applications.

Topologically-controlled photonic flatbands are photonic band structures in which the energy dispersion is rendered nearly flat (i.e., vanishing group velocity) via mechanisms rooted in the topology and symmetry of the underlying system. Recent advances combine metasurface engineering, intrinsic material anisotropy, and exciton-polariton physics to create, manipulate, and hybridize flatbands in platforms that exhibit robust topological protection and tunable light-matter interaction. This domain leverages the topological manipulation of photonic quasi-bound states in the continuum (qBICs) and their interaction with anisotropic excitons, enabling new functional regimes for slow light, nonlinear optics, and quantum polaritonic devices (Heimig et al., 1 Sep 2025).

1. Anisotropy in van der Waals Metasurfaces

The archetypal system for this class of phenomena is a metasurface fabricated from rhenium disulfide (ReS$_2$), a van der Waals (vdW) material characterized by strong in-plane optical anisotropy and a direct-gap excitonic spectrum. In-plane birefringence of ReS$_2$ leads to pronounced direction-dependent refractive index variation, which directly influences both symmetry and dispersion of supported photonic modes. Unlike isotropic media, this anisotropic response fundamentally alters photonic band topology by lifting degeneracies and modifying the polarization and spatial profile of resonant states.

This anisotropy is pivotal when patterning the material into a metasurface, as it splits symmetry-protected qBICs into orthogonally polarized resonances distinct along principal axes of the optical tensor.

2. Metasurface Design and Photonic Mode Structure

ReS$_2$ metasurfaces are engineered as C$_4$-symmetric arrays of nanocuboids etched directly from the crystal. The fourfold symmetry is maintained by careful geometric control, with the ability to introduce a controlled asymmetry parameter to fine-tune the modal field overlap and mode frequencies.

In isotropic scenarios, the metasurface supports a double-degenerate qBIC at the T-point in reciprocal space. The in-plane anisotropy inherent to ReS$_2$ splits this doublet into two nondegenerate, linearly polarized qBIC modes. Each mode is associated with a different optical axis, and the overall photonic band structure reflects this splitting with distinct, nearly dispersionless branches (flatbands) along high-symmetry lines of the Brillouin zone.

The fabrication proceeds through electron-beam lithography and reactive-ion etching, preserving the C$_4$ symmetry necessary for targeted topological features and controlled radiative lifetimes.

3. Topological Transformations: Charge Splitting and Flatband Formation

In the photonic band structure of the metasurface, the initial integer topological charge (typically $q=-1$) of the qBIC at the T-point (momentum center) splits into two fractional, half-integer singularities ($q=-\frac{1}{2}$ each) due to the dielectric anisotropy. These singularities manifest as polarization vortex points in the polarization-resolved k-space photonic maps.

The splitting of integer charge into two half-integer singularities is directly responsible for flattening the photonic band, as it enforces a condition where the eigenfrequencies become nearly independent of momentum along one direction—a flatband. This transformation is mathematically captured by the perturbed eigenfrequency expression: $$\omega_\pm \approx \omega_0 \left[1 \pm x\Delta\epsilon\right]$$ where $\omega_0$ is the unperturbed frequency, $\Delta\epsilon$ measures the anisotropy, and $x$ reflects the modal field overlap.

This topological effect results in flatbands that are robust over a wide k-range, limited primarily by onset of diffraction from the periodic structure. The geometry ensures that along one direction of k-space, the group velocity of photonic states is quenched, resulting in a far-field accessible flatband.

4. Flatband–Exciton Hybridization: Exciton-Polaritons

ReS$_2$ supports two prominent excitonic resonances, each linearly polarized along a different in-plane crystallographic direction due to its intrinsic anisotropy. By tuning the metasurface parameters (such as the nanocuboid size and lattice scaling factor $S$), the photonic flatbands (reshaped qBIC modes) are brought into resonance with these excitons.

This enables the formation of exciton–polaritons: mixed light–matter quasiparticles resulting from the strong coupling regime. The hybridization manifests as clear anticrossing in the spectra, with large Rabi splittings ($\approx 102$–$109$ meV) measured via angle-resolved reflectivity and confirmed by temporal coupled-mode theory (TCMT) plus electromagnetic simulations.

The two polariton branches arising from the hybridized qBICs selectively inherit the flat dispersion along their polarization axis, resulting in two distinct polaritonic flatbands—each directionally hybridized with a different excitonic transition.

5. Topological and Dispersion Properties of Photonic Flatbands

Topologically-controlled photonic flatbands in this context are characterized by:

• Flat (dispersionless) energy bands along specific momentum directions, leading to vanishing group velocity.
• Fractional (half-integer) topological charge singularities in the polarization vortex structure of the far-field.
• Dirac-like crossings between the split modes, with local density of states enhanced near flatband regimes.
• Robustness of the mode flattening against moderate variations in device parameters, attributed to the underlying topological origin of the charge splitting.

The flatband photonic dispersion can be approximated near the flat direction by a constant frequency $\omega_0$, while along the orthogonal direction, it remains weakly parabolic (i.e., $\omega(k) \simeq \omega_0 (1 - \beta k^2)$).

6. Applications and Future Directions

The topological control of polaritonic flatbands in anisotropic metasurfaces enables multiple application frontiers:

Application Domain	Enabled Property	Rationale
Polarization-resolved emitters	Directionally selective emission	Orthogonally polarized qBICs
Nonlinear optics	Flatband-enhanced $\chi^{(2)}$ effects	High DOS, slow light
Low-threshold polariton lasing	Room-temperature condensation potential	Flatband polaritons, low mass
Quantum photonics	Robust, topological quantum logic modes	Topological charge singularities
Reconfigurable photonic devices	Dispersion engineered by geometry/tuning	Adjustable metasurface structure

Robust flatbands and their polaritonic derivatives are expected to underpin future optoelectronic and quantum devices, including ultra-low power switches, directionally controlled quantum emitters, and polarization multiplexing platforms. Furthermore, Dirac cone–flatband coexistence offers an avenue for realizing robust topological edge or interface states with slow light and enhanced nonlinearity (Heimig et al., 1 Sep 2025).

A natural extension includes integrating such topologically-controlled flatband metasurfaces with advanced quantum materials or further hybrid photonic platforms, leveraging the unique combination of polarization control, band topology, and strong light-matter interaction.