Tight-binding methods for general longitudinally driven photonic lattices -- edge states and solitons

Abstract

A systematic approach for deriving tight-binding approximations in general longitudinally driven lattices is presented. As prototypes, honeycomb and staggered square lattices are considered. Time-reversal symmetry is broken by varying/rotating the waveguides, longitudinally, along the direction of propagation. Different sublattice rotation and structure are allowed. Linear Floquet bands are constructed for intricate sublattice rotation patterns such as counter rotation, phase offset rotation, as well as different lattice sizes and frequencies. An asymptotic analysis of the edge modes, valid in a rapid-spiraling regime, reveals linear and nonlinear envelopes which are governed by linear and nonlinear Schrodinger equations, respectively. Nonlinear states, referred to as topologically protected edge solitons are unidirectional edge modes. Direct numerical simulations for both the linear and nonlinear edge states agree with the asymptotic theory. Topologically protected modes are found; they possess unidirectionality and do not scatter at lattice defect boundaries.

17 pages, 15 figures

References in corpus (13)

• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Photonic Floquet Topological Insulators
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Imaging topological edge states in silicon photonics
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Topological Acoustics
• Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide
• Observation of Dirac plasmons in a topological insulator
• Edge Solitons in Nonlinear Photonic Topological Insulators
• Experimental observation of optical Weyl points
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators

Cited by in corpus (38)

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• Amplitude-dependent topological edge states in nonlinear phononic lattices
• Observation of edge solitons in topological trimer arrays
• Edge Solitons in Lieb Topological Floquet Insulators
• Observation of nonlinear disclination states
• Topological dipole Floquet solitons
• Topological insulators in longitudinally driven waveguides: Lieb and Kagome lattices
• Observation of $\pi$ solitons in oscillating waveguide arrays
• Observation of nonlinear fractal higher-order topological insulator
• Bragg solitons in topological Floquet insulators
• Nonlinear optical waveguide lattices: Asymptotic analysis, solitons, and topological insulators
• Dark topological valley Hall edge solitons
• Liquid-crystal-based topological photonics
• Hinge solitons in three-dimensional second-order topological insulators
• Nonlinear photonic disclination states
• Valley Hall edge solitons in a photonic graphene
• Observation of nonlinearity-controlled switching of topological edge states
• Floquet Edge Multicolor Solitons
• Whitham modulation theory for (2+1)-dimensional equations of Kadomtsev-Petviashvili type
• Vector valley Hall edge solitons in superhoneycomb lattices
• Light bullets in Su-Schrieffer-Heeger photonic topological insulators
• Peierls-Nabarro barrier effect in nonlinear Floquet topological insulators
• Observation of nonlinear topological corner states originating from different spectral charges
• Topological gap solitons in Rabi Su-Schrieffer-Heeger lattices
• Linear and nonlinear electromagnetic waves in modulated honeycomb media
• Topological edge states in photonic Floquet insulator with unpaired Dirac cones
• Discrete Approximation of Topologically Protected Modes in Magneto-Optical Media
• Floquet topological insulators with hybrid edges
• Vortex Pairs in the Discrete Nonlinear Schrödinger Equation
• Four-wave mixing Floquet topological soliton
• Floquet valley Hall edge solitons
• Floquet defect solitons
• Rotating topological edge solitons
• Data-driven model reconstruction for nonlinear wave dynamics
• Quantitative measure of topological protection in Floquet systems through the spectral localizer
• Self-Accelerating Topological Edge States