Topological Floquet edge states in periodically curved waveguides

Abstract

We study the Floquet edge states in arrays of periodically curved optical waveguides described by the modulated Su-Schrieffer-Heeger model. Beyond the bulk-edge correspondence, our study explores the interplay between band topology and periodic modulations. By analysing the quasi-energy spectra and Zak phase, we reveal that, although topological and non-topological edge states can exist for the same parameters, \emph{they can not appear in the same spectral gap}. In the high-frequency limit, we find analytically all boundaries between the different phases and study the coexistence of topological and non-topological edge states. In contrast to unmodulated systems, the edge states appear due to either band topology or modulation-induced defects. This means that periodic modulations may not only tune the parametric regions with nontrivial topology, but may also support novel edge states.

arXiv comment11 pages, 5 figures

References in corpus (28)

• Topological Photonics
• Photonic Floquet Topological Insulators
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Imaging topological edge states in silicon photonics
• Scheme to Achieve Silicon Topological Photonics
• Analogs of quantum Hall effect edge states in photonic crystals
• Topological States and Adiabatic Pumping in Quasicrystals
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Observation of photonic anomalous Floquet Topological Insulators
• Observation of the topological soliton state in the Su-Schrieffer-Heeger model
• Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
• Floquet-Bloch theory and topology in periodically driven lattices
• Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
• Optical Resonator Analog of a Two-Dimensional Topological Insulator
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Artificial Gauge Field for Photons in Coupled Cavity Arrays
• Measurement of topological invariants in a 2D photonic system
• Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators
• Topological Phase Transitions and Thouless Pumping of Light in Photonic Waveguide Arrays
• Network Models of Photonic Floquet Topological Insulators
• Measurement of a topological edge invariant in a microwave network
• Observing Topological Invariants Using Quantum Walk in Superconducting Circuits
• Measuring topological invariants in photonic systems
• Defect-free surface states in modulated photonic lattices

Cited by in corpus (12)

• Topological Photonics
• Non-linear second-order topological insulators
• Observation of anomalous π modes in photonic Floquet engineering
• Bulk-edge correspondence in the trimer Su-Schrieffer-Heeger model
• Gauge-induced Floquet topological states in photonic waveguides
• Probing topological phases in waveguide superlattices
• Robust edge states induced by electron-phonon interaction in graphene nanoribbons
• Floquet edge solitons in modulated trimer waveguide arrays
• Floquet-surface bound states in the continuum in a resonantly driven 1D tilted defect-free lattice
• Modulation-induced long-range magnon bound states in one-dimensional optical lattices
• Topological and nontopological edge states induced by qubit-assisted coupling potentials
• Floquet defect solitons