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

Optics Express
G BaruchSemyon Tsynkov

Abstract

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.

References

Jan 15, 1987·Physical Review. B, Condensed Matter·W Chen, D L Mills
Jun 3, 1996·Physical Review Letters·G Fibich

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Citations

Jul 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D D Estelle Temgoua, T C Kofane

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