Robust control of the minima of high-order harmonics by fine-tuning the alignment of CO2 molecules for shaping attosecond pulses and probing molecular alignment

In a recent paper [C. Jin, S.-J. Wang, X. Zhao, S.-F. Zhao, and C. D. Lin, Phys. Rev. A 101, 013429 (2020)], we reported that the position and depth of the minima in the harmonic spectra of ${\mathrm{CO}}_{2}$ molecules can be dramatically manipulated by a slight change of the degree of alignment, thus providing a convenient method of shaping attosecond pulses which could lead to the splitting of a typical single attosecond burst into two. Here, we demonstrate that harmonic minima can also be dramatically controlled by changing the pump-probe angles to shape attosecond pulses. In the meanwhile, since the pump-probe angle-dependent harmonic spectra are very sensitive to the degree of alignment, harmonic spectra can also be used to calibrate the alignment distribution of molecules. We identify such robust control of harmonic generation is due to the optical property of ${\mathrm{CO}}_{2}$ and the coherent harmonic emission from the oriented molecules. The photoionization transition dipoles (PITDs) of ${\mathrm{CO}}_{2}$ exhibit deep minima that change rapidly with molecular orientations accompanied by large phase changes of $\ensuremath{\pi}$ in PITDs, thus leading to strong interference when the dipoles are added up coherently.