  We theoretically investigate high harmonic generation (HHG) from silicon thin
films with thicknesses from a few atomic layers to a few hundreds of
nanometers, to determine the most efficient thickness for producing intense HHG
in the reflected and transmitted pulses. For this purpose, we employ a few
theoretical and computational methods. The most sophisticated method is the ab
initio time-dependent density functional theory coupled with the Maxwell
equations in a common spatial resolution. This enables us to explore such
effects as the surface electronic structure and light propagation, as well as
electronic motion in the energy band in a unified manner. We also utilize a
multiscale method that is applicable to thicker films. Two-dimensional
approximation is introduced to obtain an intuitive understanding of the
thickness dependence of HHG. From these ab initio calculations, we find that
the HHG signals are the strongest in films with thicknesses of 2-15 nm, which
is determined by the bulk conductivity of silicon. We also find that the HHG
signals in the reflected and transmitted pulses are identical in such thin
films. In films whose thicknesses are comparable to the wavelength in the
medium, the intensity of HHG signals in the reflected (transmitted) pulse is
found to correlate with the magnitude of the electric field at the front (back)
surface of the thin film.
