Existence, Stability and Dynamics of Discrete Solitary Waves in a Binary Waveguide Array

Abstract

Recent work has explored binary waveguide arrays in the long-wavelength, near-continuum limit, here we examine the opposite limit, namely the vicinity of the so-called anti-continuum limit. We provide a systematic discussion of states involving one, two and three excited waveguides, and provide comparisons that illustrate how the stability of these states differ from the monoatomic limit of a single type of waveguide. We do so by developing a general theory which systematically tracks down the key eigenvalues of the linearized system. When we find the states to be unstable, we explore their dynamical evolution through direct numerical simulations. The latter typically illustrate, for the parameter values considered herein, the persistence of localized dynamics and the emergence for the duration of our simulations of robust quasi-periodic states for two excited sites. As the number of excited nodes increase, the unstable dynamics feature less regular oscillations of the solution's amplitude.

References in corpus (4)

• Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays
• Dark Solitons in Discrete Lattices: Saturable versus Cubic Nonlinearities
• Optical simulation of neutrino oscillations in binary waveguide arrays
• Dark lattice solitons in one-dimensional waveguide arrays with defocusing saturable nonlinearities and alternating couplings

Cited by in corpus (2)

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