Adiabatic dynamics of edge waves in photonic graphene. (13th April 2015)

• Record Type: Journal Article
• Authors: Ablowitz, Mark J; Curtis, Christopher W; Ma, Yi-Ping
• Is Part Of: 2D materials. Volume 2:Number 2(2015)
• Publication Date: 2015-04-13
• Subjects: photonic graphene -- edge waves -- topological insulators; 42.70.Qs -- 42.65.Tg -- 05.45.Yv; Graphene -- Periodicals; Materials science -- Periodicals; Nanostructured materials -- Periodicals; 620.115
• DOI: 10.1088/2053-1583/2/2/024003
• Languages: English
• ISSNs: 2053-1583

Abstract

Abstract: The propagation of localized edge modes in photonic honeycomb lattices, formed from an array of adiabatically varying periodic helical waveguides, is considered. Asymptotic analysis leads to an explicit description of the underlying dynamics. Depending on parameters, edge states can exist over an entire period or only part of a period; in the latter case an edge mode can effectively disintegrate and scatter into the bulk. In the presence of nonlinearity, a 'time'-dependent one-dimensional nonlinear Schrödinger (NLS) equation describes the envelope dynamics of edge modes. When the average of the 'time varying' coefficients yields a focusing NLS equation, soliton propagation is exhibited. For both linear and nonlinear systems, certain long lived traveling modes with minimal backscattering are found; they exhibit properties of topologically protected states.