To date, classical trajectory and Monte-Carlo techniques have been used to model ultraintense field electron dynamics1. Some salient points, such as the electron energy gain2 enhancement when the electrons are introduced at the right phase of the field 3 and the non-planar electron dynamics in a real laser focus4, have been established by these methods. Fully quantum calculations using the Dirac or Klein-Gordon equation are difficult but have also been used to gain insight into electron-ion scattering 5 and the properties of the continuum wave functions6. Interactions at the atomic level are quantum mechanical, and incorporation of the quantum nature into model is essential for an accurate representation of many phenomena. Keeping this in mind, we present the results from a semi-classical, wavelet model of the continuum that incorporates the quantum mechanical tunnel ionization. In this approach a classical relativistic trajectory is generated for each time interval. Every trajectory has a corresponding ionization probability associated with it and is called a wavelet. When all these wavelets are projected onto position or momentum spaces they create, albeit semi-classically, a dynamical view of the atomic response of a bound electron to the ultra-intense field during the whole laser pulse. The wavelet approach allows us to model the spatially distributed electron probability in the continuum, calculate a probability distribution of continuum momentum states, and capture (as shown in Fig. 1) a clear change in the continuum dynamics from 1017W/cm2 to 1020W/cm2. The momentum states of the semiclassical electron probability are used to interpret the dynamics at ultrahigh intensities and model, e.g., the bremsstrahlung radiation spectrum. Normalized to give the total energy radiated by a single electron, i.e. one ionization event, the bremsstrahlung radiation is shown in Fig. 2. The spectrum is relatively flat out to the cutoff energy, which scales linearly with intensity. This material is based upon work supported by Research Corporation and the National Science Foundation under Grant No. 0140331.

© 2004 Optical Society of America

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