We investigate the dynamics of femtosecond laser pulses propagating in a hollow fiber filled with argon, through a full numerical solution of the nonlinear Schrödinger equation. The simulation results show that, if the intensity is low and no ionization takes place, the spatial profile of the beam does not change very much so that its propagation model may be simplified to a one-dimensional model. If the intensity is high and ionization takes place, the spatial dynamics as well as temporal dynamics become very complicated because of self-focusing and defocusing. It is found that, for the same value of the B integral, self-focusing inside a hollow fiber can be substantially suspended by a differential gas pressure technique, where the gas pressure is set to be a minimum at the entrance and then increased with the propagation distance. Numerical simulations show that using such a technique, the energy transmitted during propagation inside hollow fiber is significantly enhanced, and the spatial phase is also improved.
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