A one-way state inside the continuum
The most striking result is a prediction that light can travel one way along the edge of a patterned crystal even when the mode's quasi-energy sits among the crystal's bulk bands. In the simulations, edge states in the continuum, or EICs, remained localized on zigzag edges and propagated unidirectionally. A triangular-lattice example at β = 0.99 cm−1 placed the EIC in the bulk band continuum rather than in a gap.
That result came from a parameter regime the study describes as topologically trivial. The calculated Chern, valley Chern and winding numbers all vanished. The authors therefore describe the EIC's robustness as decoupled from those three quantities.
The helical ingredient
The study asked whether robust unidirectional EICs could exist in a topologically trivial Floquet photonic crystal modeled as a honeycomb lattice of helical waveguides. Its main-text simulations used lattices containing 64, 2025 and 3200 sites across the illustrated geometries.
The proposed explanation is tied to the shape of the waveguides. The authors say their helicity creates a z-periodic Floquet artificial gauge field geometrically locked to the helical trajectory. In their interpretation, that field is associated with both one-way propagation and resilience to the tested disturbances.
A comparison at zero helix radius reinforced that interpretation. At R = 0, no Floquet artificial gauge field was present, and the authors reported complete loss of EIC robustness.
What the model survived
Without disorder, a Gaussian EIC pulse traveled along a zigzag edge through corners of 120° with no observable backscattering or mode splitting.
The on-site noise tests gave a defined but limited margin. With on-site potential noise at ξ = 3%, the EIC retained unidirectional propagation and its pulse envelope. When the count was restricted to blue edge sites with occupation probability above 98%, it dropped to zero for ξ ≳ 6%.
Hopping-phase noise showed a different threshold. At ζ = 5%, the EIC retained stable unidirectional propagation and its pulse envelope, while the count of high-occupation EICs vanished for ζ ≳ 27%.
Applying the two disturbances together produced a harsher result than either alone. When on-site and hopping-phase perturbations were applied at identical strengths, with ξ = ζ, the EIC-loss threshold was lower than in either single-disorder case. The authors labeled this effect cooperative disruption.
A result tied to its design
The calculations used a Shirley–Floquet representation truncated at the ninth order, with the two centralmost quasi-energies and their eigenstates retained for later analysis. Chern numbers were computed by Berry-flux integration, cross-checked with an effective Floquet Hamiltonian, while finite-lattice Chern numbers were evaluated with the Kitaev formula.
The effect was also selective about boundary shape. EICs propagated along zigzag interfaces but could not be sustained on armchair edges in the reported configuration. By contrast, valley edge states were supported on armchair interfaces when a valley domain wall was present.
A supplemental propagation check reported continued EIC robustness when G = 0, reproducing the main simulations under that setting.
Taken together, the paper offers a bounded numerical result: a particular helical-waveguide Floquet design produced one-way EIC behavior, passed the specified corner and disorder tests, and did so while the reported topological invariants vanished. The findings do not establish the same behavior for every edge or every form of disorder; the armchair comparison and the finite noise thresholds tie the claim to the tested setup.
The work is an arXiv version 1 preprint dated 26 Aug 2026.
Paper data and sources
Original title: Robust Unidirectional Edge States in the Continuum in non-Topological Floquet Photonic Crystals
Authors: Hairong Huo, Yongyou Zhang, Bingsuo Zou
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text