Floquet Edge Multicolor Solitons

Abstract

Topological insulators are unique physical structures that are insulators in their bulk, but support currents at their edges which can be unidirectional and topologically protected from scattering on disorder and inhomogeneities. Photonic topological insulators can be crafted in materials that exhibit a strong nonlinear response, thus opening the door to the exploration of the interplay between nonlinearity and topological effects. Among the fascinating new phenomena arising from this interplay is the formation of topological edge solitons -- hybrid asymmetric states localized across and along the interface due to different physical mechanisms. Such solitons have so far been studied only in materials with Kerr-type, or cubic, nonlinearity. Here the first example of the topological edge soliton supported by parametric interactions in ${\chi }^{(2)}$ nonlinear media is presented. Such solitons exist in Floquet topological insulators realized in arrays of helical waveguides made of a phase-matchable ${\chi }^{(2)}$ material. Floquet edge solitons bifurcate from topological edge states in the spectrum of the fundamental frequency wave and remain localized over propagation distances drastically exceeding the helix period, while travelling along the edge of the structure. A theory of such states is developed. It is shown that multicolor solitons in a Floquet system exists in the vicinity of (formally infinite) set of linear resonances determined by the Floquet phase matching conditions. Away from resonance, soliton envelopes can be described by a period-averaged single nonlinear Schrödinger equation with an effective cubic nonlinear coefficient whose magnitude and sign depend on the overall phase-mismatch between the fundamental frequency and second harmonic waves.

References in corpus (50)

• Topological Insulators
• Topological insulators and superconductors
• Topological Photonics
• Topological Photonics
• 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
• Robust optical delay lines via topological protection
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Lasing in topological edge states of a 1D lattice
• Nonlinear topological photonics
• Exciton-polariton topological insulator
• Observation of photonic anomalous Floquet Topological Insulators
• Topologically protected acoustic helical edge states and interface states in strongly coupled metamaterial ring lattices
• Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
• Interacting topological insulators: a review
• Photonic Topological Anderson Insulators
• Edge Solitons in Nonlinear Photonic Topological Insulators
• Observation of Topological Band Gap Solitons
• Active topological photonics
• Polariton $\mathbb{Z}$ Topological Insulator
• Disorder-induced Floquet Topological Insulators
• Nonlinearity-induced photonic topological insulator
• Self-induced topological transitions and edge states supported by nonlinear staggered potentials
• Non-linear second-order topological insulators
• Direct imaging of topological edge states in cold-atom systems
• Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators
• Observation and control of nonlinear electromagnetic topological edge states
• Observation of Edge Solitons in Photonic Graphene
• Bistable topological insulator with exciton-polaritons
• Nontrivial coupling of light into a defect: the interplay of nonlinearity and topology
• Exploring nonlinear topological states of matter with exciton-polaritons: Edge solitons in kagome lattice
• Nonlinear one-way edge-mode interactions for frequency mixing in topological photonic crystals
• Topological Frequency Combs and Nested Temporal Solitons
• Topological edge states and gap solitons in the nonlinear Dirac model
• Amplitude-dependent topological edge states in nonlinear phononic lattices
• Lieb polariton topological insulators
• Tight-binding methods for general longitudinally driven photonic lattices -- edge states and solitons
• Vector Topological Edge Solitons in Floquet Insulators
• Weakly nonlinear topological gap solitons in Su-Schrieffer-Heeger photonic lattices
• Parametric localized modes in quadratic nonlinear photonic structures
• Edge Solitons in Lieb Topological Floquet Insulators
• Localized modes in ${\chi }^{(2)}$ media with $\PT$-symmetric localized potential
• Topological insulators in longitudinally driven waveguides: Lieb and Kagome lattices
• Mobility of Discrete Solitons in Quadratically Nonlinear Media
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric periodic systems with the quadratic nonlinearity
• Bragg solitons in topological Floquet insulators
• Multicolor vortex solitons in two-dimensional photonic lattices
• Hinge solitons in three-dimensional second-order topological insulators
• Topological Edge-State Manifestation of Interacting 2D Condensed Boson-Lattice Systems in a Harmonic Trap

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