Stabilization of three-wave vortex beams in the waveguide

Arnaldo Gammal, Boris A. Malomed

Research output: Contribution to journalArticlepeer-review


We consider two-dimensional (2D) localized vortical modes in the three-wave system with the quadratic (?(2)) nonlinearity, alias nondegenerate second-harmonic (SH)-generating system, guided by the isotropic harmonic-oscillator (alias parabolic) confining potential. In addition to the straightforward realization in optics, the system models mixed atomic-molecular Bose Einstein condensates. The main issue is stability of the vortex modes, which is investigated through computation of instability growth rates for eigenmodes of small perturbations, and by means of direct simulations. The threshold of parametric instability for single-color beams, represented solely by the SH with zero vorticity, is found in an analytical form with the help of the variational approximation. Trapped states with vorticities (+1, ?1, 0) in the two fundamentalfrequency components and the SH one (the so-called hidden-vorticity modes) are completely unstable. Also unstable are semi-vortices, with component vorticities (1, 0, 1). However, full vortices, with charges (1, 1, 2), have a well-defined stability region.

Original languageEnglish
Article number045503
JournalJournal of Optics (United Kingdom)
Issue number4
StatePublished - 1 Apr 2015


  • azimutal instability
  • parametric instability
  • quadratic nonlinearity
  • second-harmonic-generation
  • vortex


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