Strong transmission and reflection of edge modes in bounded photonic graphene

Abstract

The propagation of linear and nonlinear edge modes in bounded photonic honeycomb lattices formed by an array of rapidly varying helical waveguides is studied. These edge modes are found to exhibit strong transmission (reflection) around sharp corners when the dispersion relation is topologically nontrivial (trivial), and can also remain stationary. An asymptotic theory is developed that establishes the presence (absence) of edge states on all four sides, including in particular armchair edge states, in the topologically nontrivial (trivial) case. In the presence of topological protection, nonlinear edge solitons can persist over very long distances.

5 pages, 4 figures. Minor updates on the presentation and interpretation of results. The movies showing transmission and reflection of linear edge modes are available at https://www.youtube.com/watch?v=XhaZZlkMadQ and https://www.youtube.com/watch?v=R8NOw0NvRu0

References in corpus (6)

• Photonic Floquet Topological Insulators
• The Magnus expansion and some of its applications
• Observation of novel edge states in photonic graphene
• Unveiling pseudospin and angular momentum in photonic graphene
• Zero modes and the edge states of the honeycomb lattice
• Localized electron states near the armchair edge of graphene

Cited by in corpus (15)

• Topological Photonics
• Topological Photonics
• Demonstrating an in-situ topological band transition in cylindrical granular chains
• Topological dipole Floquet solitons
• Dark topological valley Hall edge solitons
• Hinge solitons in three-dimensional second-order topological insulators
• 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
• Conical Wave Propagation and Diffraction in 2D Hexagonally Packed Granular Lattices
• Fate of Topological Edge States in Disordered Periodically-driven Nonlinear Systems
• Floquet topological insulators with hybrid edges
• Nonlinear edge modes in a honeycomb electrical lattice near the Dirac points
• Damped photonic modes in helical graphene
• Edge Solitons in a Nonlinear Mechanical Topological Insulator