Simulations of the Nonlinear Helmholtz Equation: Arrest of Beam Collapse, Nonparaxial Solitons, and Counter-Propagating Beams

Details Simulations of the Nonlinear Helmholtz Equation: Arrest of Beam Collapse, Nonparaxial Solitons, and Counter-Propagating Beams Simulations of the Nonlinear Helmholtz Equation: Arrest of Beam Collapse, Nonparaxial Solitons, and Counter-Propagating Beams

2008-02-24

arxiv.org/abs/0802.3506v4

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

Physics

Optics

6 pages, 6 figures, Letter

Scientific paper

10.1364/OE.16.013323

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.

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