  Theoretical investigation is conducted of high-order harmonic generation
(HHG) in silicon thin films to elucidate the effect of light propagation in
reflected and transmitted waves. The first-principles simulations are performed
of the process in which an intense pulsed light irradiates silicon thin films
up to 3 $\mu$m thickness. Our simulations are carried within the time-dependent
density functional theory (TDDFT) with the account of coupled dynamics of the
electromagnetic fields and the electronic motion. It was found that the
intensity of transmission HHG gradually decreases with the thickness, while the
reflection HHG becomes constant from a certain thickness. Detailed analyses
show that transmission HHG have two origins: the HHG generated near the front
edge and propagating to the back surface, and that generated near the back edge
and emitted directly. The dominating mechanism of the transmission HHG is found
to depend on the thickness of the thin film and the frequency of the HHG. At
the film thickness of 1 $\mu$m, the transmission HHG with the frequency below
20 eV is generated near the back edge, while that with the frequency above 20
eV is generated near the front edge and propagates from there to the back
surface.
