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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 17 — Aug. 18, 2008
  • pp: 13323–13329

Simulations of the nonlinear Helmholtz equation: arrest of beam collapse, nonparaxial solitons and counter-propagating beams

G. Baruch, G. Fibich, and Semyon Tsynkov  »View Author Affiliations

Optics Express, Vol. 16, Issue 17, pp. 13323-13329 (2008)

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We solve the (2+1)D nonlinear Helmholtz equation (NLH) for input beams that collapse in the simpler NLS model. Thereby, we provide the first ever numerical evidence that nonparaxiality and backscattering can arrest the collapse. We also solve the (1+1)D NLH and show that solitons with radius of only half the wavelength can propagate over forty diffraction lengths with no distortions. In both cases we calculate the backscattered field, which has not been done previously. Finally, we compute the dynamics of counter-propagating solitons using the NLH model, which is more comprehensive than the previously used coupled NLS model.

© 2008 Optical Society of America

OCIS Codes
(190.3270) Nonlinear optics : Kerr effect
(190.5940) Nonlinear optics : Self-action effects
(190.6135) Nonlinear optics : Spatial solitons

ToC Category:
Nonlinear Optics

Original Manuscript: April 15, 2008
Revised Manuscript: June 23, 2008
Manuscript Accepted: July 25, 2008
Published: August 14, 2008

G. Baruch, G. Fibich, and Semyon Tsynkov, "Simulations of the nonlinear Helmholtz equation: arrest of beam collapse, nonparaxial solitons and counter-propagating beams," Opt. Express 16, 13323-13329 (2008)

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