The most efficient thickness of Si nano film for high-harmonic generation

We performed first-principles calculations of high-harmonic generation (HHG) in reflected and transmitted waves from a Si nano film exposed to an intense light pulse. We develop and utilize first-principles methods coupling Maxwell and time-dependent Kohn-Sham equations with and without course-graining approximation. For a film of thickness less than or equal to a few nm, we may treat the film as 2D materials and employ a microscopic scheme without course-graining. For thicker films, propagation effects become significant and we employ a macroscopic scheme with course-graining. We studied the thickness dependence of HHG taking into account the effects of light propagation and surface electronic structure. Calculations are performed for Si films of thickness up to 200 nm, and reveal a peak structure in the thickness dependence of HHG. The HHG shows the strongest signal at the thickness around 2 to 15 nm for both of reflection and transmission HHG. We found that the most efficient thickness of the Si film for HHG is roughly determined by the dielectric function of bulk Si and the thickness dependence of HHG is correlated with the transmittance of the film.