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We theoretically investigate high-order harmonic generation (HHG) in crystals induced by linearly polarized laser fields. We obtain the HHG spectra by solving the semiconductor Bloch equations and analyze the radiation process by different models. Here we propose a multiple collision model, in which the electrons and holes are produced at different times and places. It is found that the multiple collision trajectories can help us comprehensively and better explain the results of the quantum calculation. Moreover, we find that the harmonic suppression occurs due to the overlap of multiple collision trajectories.

We present a systematic investigation of the depolarization properties of a supercontinuum accompanied with femtosecond laser filamentation in barium fluoride (BaF2) crystal. It is found that the depolarization of the supercontinuum depends strongly on the crystal orientations with respect to the incident laser polarization. At most crystal orientations, the depolarization of the supercontinuum rises with the increase of the input laser energies and finally saturates. While at 45°, the depolarization of the supercontinuum is not changed and keeps nearly negligible with the increase of the input laser energies. These peculiar depolarization properties of the supercontinuum can be ascribed to the orientation dependence of the cross-polarized wave (XPW) generation and ionization-induced plasma scattering in the BaF2 crystal.