Solitons in PT-symmetric ladders of optical waveguides

N. V. Alexeeva, I. V. Barashenkov, Yuri S. Kivshar

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16 Citations (SciVal)


Weconsider a PT-symmetric ladder-shaped optical array consisting of a chain of waveguides with gain coupled to a parallel chain of waveguides with loss. All waveguides have the focusing Kerr nonlinearity. The array supports two co-existing solitons, an in-phase and an antiphase one, and each of these can be centred either on a lattice site or midway between two neighbouring sites.Weshow that both bond-centred (i.e. intersite) solitons are unstable regardless of their amplitudes and parameters of the chain. The site-centred in-phase soliton is stable when its amplitude lies below a threshold that depends on the coupling and gainloss coefficient. The threshold is lowest when the gain-to-gain and loss-to-loss coupling constant in each chain is close to the interchain gain-to-loss coupling coefficient. The antiphase site-centred soliton in the strongly-coupled chain or in a chain close to the PT -symmetry breaking point, is stable when its amplitude lies above a critical value and unstable otherwise. The instability growth rate of solitons with small amplitude is exponentially small in this parameter regime; hence the small-amplitude solitons, though unstable, have exponentially long lifetimes. On the other hand, the antiphase soliton in the weakly or moderately coupled chain and away from the PT -symmetry breaking point, is unstable when its amplitude falls in one or two finite bands. All amplitudes outside those bands are stable.

Original languageEnglish
Article number113032
JournalNew Journal of Physics
Issue number11
Publication statusPublished - 22 Nov 2017


  • discrete nonlinear Schroedinger equation
  • gain and loss
  • optical waveguides
  • parity-time symmetry
  • solitons
  • stability

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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