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From solitons to rogue waves in nonlinear left-handed metamaterials

Yannan Shen1, P. G. Kevrekidis2, G. P. Veldes3,4, D. J. Frantzeskakis3, D. DiMarzio5, X. Lan5, and V. Radisic5

  • 1Department of Mathematics and Statistics, California State University, Northridge, California 91330, USA
  • 2Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
  • 3Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece
  • 4Department of Electronics Engineering, Technological Educational Institute of Central Greece, Lamia 35100, Greece
  • 5NG Next, Northrop Grumman Corporation, One Space Park, Redondo Beach, California 90278, USA

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Phys. Rev. E 95, 032223 – Published 27 March, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.032223

Abstract

In the present work, we explore soliton and roguelike wave solutions in the transmission line analog of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltage-dependent, symmetric capacitance motivated by recently developed ferroelectric barium strontium titanate thin-film capacitor designs. We develop both the corresponding nonlinear dynamical lattice and its reduction via a multiple scales expansion to a nonlinear Schrödinger (NLS) model for the envelope of a given carrier wave. The reduced model can feature either a focusing or a defocusing nonlinearity depending on the frequency (wave number) of the carrier. We then consider the robustness of different types of solitary waves of the reduced model within the original nonlinear left-handed medium. We find that both bright and dark solitons persist in a suitable parametric regime, where the reduction to the NLS model is valid. Additionally, for suitable initial conditions, we observe a rogue wave type of behavior that differs significantly from the classic Peregrine rogue wave evolution, including most notably the breakup of a single Peregrine-like pattern into solutions with multiple wave peaks. Finally, we touch upon the behavior of generalized members of the family of the Peregrine solitons, namely, Akhmediev breathers and Kuznetsov-Ma solitons, and explore how these evolve in the left-handed transmission line.

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Phys. Rev. E 95, 032223– Published 27 March, 2017
  • Received 1 December 2016
Article part of CHORUS

©2017 American Physical Society

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