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We solve the (2+1)D nonlinear Helmholtz equation (NLH) for input beams thatcollapse in the simpler NLS model. Thereby, we provide the first ever numericalevidence that nonparaxiality and backscattering can arrest the collapse. Wealso solve the (1+1)D NLH and show that solitons with radius of only half thewavelength can propagate over forty diffraction lengths with no distortions. Inboth cases we calculate the backscattered field, which has not been donepreviously. Finally, we compute the dynamics of counter-propagating solitonsusing the NLH model, which is more comprehensive than the previously usedcoupled NLS model.

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