Time-dependent density functional theory for strong electromagnetic fields in crystalline solids

We apply the coupled dynamics of time-dependent density functional theory and Maxwell equations to the interaction of intense laser pulses with crystalline silicon. As a function of electromagnetic field intensity, we see several regions in the response. At the lowest intensities, the pulse is reflected and transmitted in accord with the dielectric response, and the characteristics of the energy deposition are consistent with two-photon absorption. The absorption process begins to deviate from that at laser intensities of $\sim$ ${10}^{13}$ W/cm${}^2$, where the energy deposited is of the order of 1 eV per atom. Changes in the reflectivity are seen as a function of intensity. When it passes a threshold of about $3\times {10}^{12}$ W/cm${}^2$, there is a small decrease. At higher intensities, above $2\times {10}^{13}$ W/cm${}^2$, the reflectivity increases strongly. This behavior can be understood qualitatively in a model treating the excited electron-hole pairs as a plasma.