Understanding molecular harmonic emission at relatively long intense laser pulses: Beyond the Born-Oppenheimer approximation

The underlying physics behind the molecular harmonic emission in relatively long sin$^2$-like laser pulses is investigated. We numerically solved the full-dimensional electronic time-dependent Schr\"{o}dinger equation beyond the Born-Oppenheimer approximation for simple molecular ion H$_2^+$. The occurrence and the effect of electron localization, non-adiabatic redshift and spatially asymmetric emission are evaluated to understand better complex patterns appearing in the high-order harmonic generation (HHG) spectrum. Results show that the complex patterns in the HHG spectrum originate mainly from a non-adiabatic response of the molecule to the rapidly changing laser field and also from a spatially asymmetric emission along the polarization direction. The effect of electron localization on the HHG spectrum was not observed as opposed to what is reported in the literature.