Xiaoqin Bai | Searcharxiv

arXiv2026

High-energy topological edge states and strain-induced multiple flat bands in a honeycomb lattice

We propose a novel anti-twig edge in the honeycomb lattice (HCL) that supports two symmetric high-energy edge states. It is different from the twig edge supporting the zero-energy flat band. Moreover, multiple flat bands are produced by applying a strain to the HCL with a twig edge or an anti-twig edge, and the suppression or enhancement of the high-energy edge state is observed. Under the edge-parallel stretch strain, the high-energy edge state band merges into the bulk band, suppressing the high-energy edge state, while the zero-energy edge state becomes delocalized. On the other hand, under the action of the edge-parallel compression strain, both the high-energy and zero-energy edge states exhibit strong localization. Pseudo-topological protection of the high-energy edge state is explored too. Finally, by reconstructing the anti-twig edge in the HCL, degenerate flat bands and strain-induced multiple flat bands are produced, and topologically protected vacated anti-twig edge states are demonstrated.

physics.optics↗

arXiv2024

Spectrum conversion and pattern preservation of Airy beams in fractional systems with a dynamical harmonic-oscillator potential

We investigate the dynamics of optical Airy beams in the one-dimensional fractional Schrödinger equation with a harmonic-oscillator (HO) potential subjected to modulation along the propagation distance. Deriving general solutions for propagating beams and particular solutions for Airy waves with/without chirp, we study analytically the spectrum conversion and pattern preservation for the chirp-free and chirped Airy beams in the fractional system including the HO potential with moiré-lattice, hyperbolic-secant, and delta-functional modulation formats. For the HO-moiré-lattice potential, it is found that the chirp-free Airy beam experiences multiple spectrum conversions between the Airy and Gaussian patterns in the momentum space, preserving the Airy pattern in the coordinate space. The chirp magnitude of the chirped Airy beam determines whether the spectrum conversion occurs in the momentum space, and the splitting and evolution direction of the beam in the coordinate space. For the HO-hyperbolic-secant potential, the chirp-free Airy beam undergoes spectrum conversion and tunneling, with the positions of the spectrum conversion and tunneling significantly depending on parameters of the hyperbolic-secant potential; however, the spectrum conversion and pattern preservation of the chirped Airy beam occurs only under a certain relation of the chirp and parameters of the potential. In the case of the HO-delta-functional potential, the chirp-free Airy beam experiences abrupt spectrum conversion and a two-step spectrum shift; however, for the chirped Airy beam, the spectrum conversion is affected by the relation between the chirp and height of the potential. Effects of the fractional Lévy index on the spectrum conversion and pattern preservation of the Airy beams under the action of the three modulation patterns considered here are also explored in detail.

physics.optics↗