Abstract
We present the results of a numerical simulation showing the harmonic spectra produced by the interaction of ultrashort laser pulses with helium, neon, and their ions. We calculate the harmonic spectrum for intensities close to and above saturation (${10}^{14}$-{m W/cm${\mathrm{}}}^{2}$ to ${10}^{17}$-{m W/cm${\mathrm{}}}^{2}$) using wavelengths in the region 248 nm to 527 nm. We find that, in order to observe harmonic production from ions, it is best to use a relatively short-wavelength laser, i.e., KrF. We also discuss the effects of the pulse shape on the harmonic generation, including a blueshifting of the single-atom response. Our results are mostly based on a numerical integration of the one-dimensional Schr\"odinger equation, but we include a comparison with results produced by a three-dimensional model for critical cases. We also include a discussion of various methods of calculating the harmonic spectrum in the strongly ionizing regime.
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