We present a S-matrix description of the process of high order harmonic generation during the interaction of atoms with strong electromagnetic fields. In contrast with the state-of-the-art approaches, our model does not employ the stationary phase approximation and accounts as well for the continuum-continuum transitions. Therefore we are able to reproduce quantitatively the higher frequency part of the spectrum for arbitrary pulse shapes, and for intensities corresponding to multiphoton, tunnel and soft over-the barrier ionization regimes. In addition this model can be implemented very efficiently in a Personal Computer to calculate the harmonic generation for the atom interacting with an eight-cycle pulse at λ =800 nm in, roughly, ten minutes (a reduction of two orders of magnitude from the typical time requirements of the exact integration).
©2007 Optical Society of America
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