Semi-classical description of electron dynamics in extended systems under intense laser fields

We propose a semi-classical approach based on the Vlasov equation to describe the time-dependent electronic dynamics in a bulk simple metal under an ultrashort intense laser pulse. We include in the effective potential not only the ionic Coulomb potential and mean-field electronic Coulomb potential from the one-body electron distribution but also the exchange-correlation potential within the local density approximation (LDA). The initial ground state is obtained by the Thomas-Fermi model. To numerically solve the Vlasov equation, we extend the pseudo-particle method, previously used for nuclei and atomic clusters, to solids, taking the periodic boundary condition into account. We apply the present implementation to a bulk aluminum (FCC) conventional unit cell irradiated with a short laser pulse. The optical conductivity, refractive index, extinction coefficient, and reflectivity as well as energy absorption calculated with the Vlasov-LDA method are in excellent agreement with the results by the time-dependent density functional theory and experimental references.