Spectral redshift of high-order harmonics by adding a weak pulse in the falling part of the trapezoidal laser pulse

We investigate the spectral redshift of high-order harmonics of the H₂⁺ (D₂⁺) molecule by numerically solving the non-Born-Oppenheimer time-dependent Schrödinger equation (TDSE). The results show that the spectral redshift of high-order harmonics can be observed by adding a weak pulse in the falling part of the trapezoidal laser pulses. Comparing with the H₂⁺ molecule, the shift of high-order harmonic generation (HHG) spectrum for the D₂⁺ molecule is more obvious. We employ the spatial distribution in HHG and time-frequency analysis to illustrate the physical mechanism of the spectral redshift of high-order harmonics.