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We numerically simulate the propagation of high-intensity laser pulses in helium to investigate the role of nonlinear effects in gas-cell high-harmonics experiments. An aperture located before the focusing lens is also included in the simulation. Numerical results for the radial fluence profile as a function of axial position, as well as for the spectral shift and ionization levels, agree with experimental observations. The simulations confirm that a significant Kerr effect is not required to generate the observed double focus in the fluence. The beam simulation also permits an investigation of high-harmonic phase matching. Most of the harmonic energy is seen to come from the forward portion of the laser pulse, whereas the latter portion gives rise to the incidental double laser focusing. Good phase matching for the harmonics arises in large measure from a balance between the linear phase delay of the neutral atoms and the Gouy shift, which is elongated and nearly linearized when the aperture is partially closed on the beam.

Simulated laser-pulse evolution for high-order harmonic generation in a semi-infinite gas cell