Exact and approximate solutions for optical solitary waves in nematic liquid crystals

J. Michael L. MacNeil, Noel F. Smyth*, Gaetano Assanto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The equations governing optical solitary waves in nonlinear nematic liquid crystals are investigated in both (1+1) and (2+1) dimensions. An isolated exact solitary wave solution is found in (1+1) dimensions and an isolated, exact, radially symmetric solitary wave solution is found in (2 + 1) dimensions. These exact solutions are used to elucidate what is meant by a nematic liquid crystal to have a nonlocal response and the full role of this nonlocal response in the stability of (2 + 1) dimensional solitary waves. General, approximate solitary wave solutions in (1+1) and (2+1) dimensions are found using variational methods and they are found to be in excellent agreement with the full numerical solutions. These variational solutions predict that a minimum optical power is required for a solitary wave to exist in (2 + 1) dimensions, as confirmed by a careful examination of the numerical scheme and its solutions. Finally, nematic liquid crystals subjected to two different external electric fields can support the same solitary wave, exhibiting a new type of bistability. (C) 2014 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalPhysica D: Nonlinear Phenomena
Volume284
DOIs
Publication statusPublished - 15 Sep 2014

Keywords

  • Soliton
  • Liquid crystals
  • Modulation theory
  • Nematicon
  • Self-focusing
  • SPATIAL SOLITONS
  • MODULATIONAL INSTABILITY
  • PULSE-PROPAGATION
  • NONLINEARITY
  • COMPUTATION
  • EQUATION
  • MEDIA
  • NONLOCALITY
  • TURBULENCE
  • STABILITY

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