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Discrete vector solitons in two-dimensional nonlinear waveguide arrays: solutions, stability, and dynamics.

J Hudock1, P G Kevrekidis, B A Malomed

  • 1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 6, 2003
PubMed
Summary

We discovered two-dimensional discrete vector solitons, which are self-induced channels in nonlinear optical waveguide arrays. These findings are applicable to Bose-Einstein condensates in optical lattices.

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Area of Science:

  • Nonlinear Optics
  • Condensed Matter Physics

Background:

  • Nonlinear optical waveguides support self-localized light states.
  • Discrete solitons exist in periodic structures like waveguide arrays.

Purpose of the Study:

  • To identify and investigate bimodal (vector) solitons in square-lattice nonlinear optical waveguide arrays.
  • To explore the possibility of two-dimensional discrete vector solitons.

Main Methods:

  • Newton relaxation methods were used to find stationary vector-soliton solutions.
  • Linearized eigenvalue computations were performed to assess stability.

Main Results:

  • Bimodal vector solitons were identified as self-induced channels in a nonlinear photonic-crystal matrix.

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  • Conditions for supporting these solitons in waveguide arrays were estimated.
  • Stationary solutions were obtained and their stability analyzed.

    • Conclusions:

    • Two-dimensional discrete vector solitons are feasible in specific waveguide array configurations.
    • The findings have potential applications in Bose-Einstein condensates trapped in optical lattices.