Control of a spectral minimum in high-order harmonic generation by adjusting the phase-matching conditions in a gas medium

A spectral minimum in the high-order harmonic generation (HHG) is of great interest, usually generated by specific atoms or molecules. Here we show through detailed simulations that the minimum in the HHG spectrum can be created and tuned by varying the phase-matching conditions when a gas medium is located at the focus of a long-wavelength laser. We reveal that the minimum can be shifted spatially depending on the quantum orbit due to its sensitivity to the phase-matching condition. We provide a formula to relate the position of the minimum to the coherence length of HHG. We also show that the position(s) and the number of (multiple) minimum(s) can be changed by varying the beam waist and the intensity of the driving laser. In addition, we establish the scaling relations with the laser wavelength to maintain the spectral position of the minimum. We expect that this method can be effectively implemented to shape the attosecond pulse in the extreme ultraviolet and soft x rays.