Edge states in dynamical superlattices

Abstract

We address edge states and rich localization regimes available in the one-dimensional (1D) dynamically modulated superlattices, both theoretically and numerically. In contrast to conventional lattices with straight waveguides, the quasi-energy band of infinite modulated superlattice is periodic not only in the transverse Bloch momentum, but it also changes periodically with increase of the coupling strength between waveguides. Due to collapse of quasi-energy bands dynamical superlattices admit known dynamical localization effect. If, however, such a lattice is truncated, periodic longitudinal modulation leads to appearance of specific edge states that exist within certain periodically spaced intervals of coupling constants. We discuss unusual transport properties of such truncated superlattices and illustrate different excitation regimes and enhanced robustness of edge states in them, that is associated with topology of the quasi-energy band.

arXiv comment9 pages, 6 figures

References in corpus (35)

• Photonic Floquet Topological Insulators
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Photovoltaic Hall effect in graphene
• Topological characterization of periodically-driven quantum systems
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Observation of a localized flat-band state in a photonic Lieb lattice
• Observation of bound states in Lieb photonic lattices
• Observation of topologically protected bound states in a one dimensional photonic system
• Two-particle bosonic-fermionic quantum walk via 3D integrated photonics
• Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide
• Observation of photonic anomalous Floquet Topological Insulators
• Light propagation and localization in modulated photonic lattices and waveguides
• Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
• Floquet-Bloch theory and topology in periodically driven lattices
• Discrete single-photon quantum walks with tunable decoherence
• Observation of novel edge states in photonic graphene
• Observation of dynamic localization in periodically-curved waveguide arrays
• Edge Solitons in Nonlinear Photonic Topological Insulators
• Optical Resonator Analog of a Two-Dimensional Topological Insulator
• PT-symmetry in honeycomb photonic lattices
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
• Floquet topological transitions in a driven one-dimensional topological insulator
• Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators
• Inhibition of light tunneling in waveguide arrays
• Towards large-Chern-number topological phases by periodic quenching
• Transport in Sawtooth photonic lattices
• Spectral and transport properties of time-periodic PT-symmetric tight-binding lattices
• Photonic Floquet Topological Insulator in an Atomic Ensemble
• Edge-state enhanced transport in a 2-dimensional quantum walk
• Defect-free surface states in modulated photonic lattices
• Light tunneling inhibition and anisotropic diffraction engineering in two-dimensional waveguide arrays
• Diffraction control in PT-symmetric photonic lattices: from beam rectification to dynamic localization
• Rectification of light refraction in curved waveguide arrays

Cited by in corpus (9)

• Observation of $\pi$ solitons in oscillating waveguide arrays
• Quantum decay in a topological continuum
• Probing topological phases in waveguide superlattices
• Floquet edge solitons in modulated trimer waveguide arrays
• $\pi$ mode lasing in the non-Hermitian Floquet topological system
• Floquet topological insulators with hybrid edges
• $\pi$-solitons on a ring of waveguides
• Floquet valley Hall edge solitons
• Floquet defect solitons