Bulk and surface contributions to high-harmonic generation in solids

While the generation of high-harmonics (HH) from gaseous atoms is well understood [1], HH generation from solids is discussed theoretically for decades [2], still debated [3, 4], and scrutinized experimentally only recently [3]. We investigated the field-strength and carrier-envelope-phase dependence of HH generation by the interaction of intense mid-infrared few-cycle laser pulses with Au, SiO$_{\mathrm{2}}$, and ZnO, for which experimental data exists [3]. We numerically solved the time-dependent Schr\"{o}dinger equation in one spatial dimension to analyze bulk and surface effects within a basis-set-expansion approach that allows us to (i) perform many steps of the calculation analytically and (ii) tune band-structure parameters of the solid to the valence-electronic structure of the solids. [1] A.-T. Le, \textit{et al.}, Phys. Rev. A \textbf{80}, 013401 (2009). [2] L. Plaja and L. Roso-Franco, \textit{Phys. Rev. B} \textbf{45}, 8334 (1992). [3] S. Ghimire \textit{et al}., \textit{Nat. Phys,} \textbf{7}, 138 (2011); M. Wu, \textit{et al.,} Phys. Rev. A \textbf{91}, 043839 (2015) [4] G. Vampa, \textit{et al}. \textit{Phys. Rev. Lett,} \textbf{113}, 073901 (2014).