Nonlinear propagation effects in high harmonic generation in reflection and transmission from gallium arsenide.

High harmonic spectroscopy in solids is emerging as a new tool to investigate ultrafast electron dynamics in the presence of strong optical fields. However, the observed high harmonic spectra do not usually reflect the microscopic origin of high harmonic generation (HHG) because of nonlinear and/or linear propagation effects. Here, we systematically investigate the HHG in reflection and transmission from gallium arsenide exposed to intense mid-infrared optical pulses. In transmission geometry, we find that the properties of high harmonics are drastically changed by nonlinear effects during the propagation of even tens of micrometers. Especially, the nonlinear absorption and/or nonlinearly induced ellipticity of the drive pulses as well as a cascade nonlinear mixing significantly alter the high harmonic signals in the case of the transmission geometry, making an extraction of the microscopic electron dynamics of gallium arsenide difficult. On the contrary, in reflection geometry, we obtain HHG spectra that are free from propagation effects, opening a general approach for high harmonic spectroscopy.