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The high-order harmonic generation (HHG) has attracted much attention due to its wide application in attosecond science in last decades. The selection rules have also been broadly studied in experiments and theories since they play an important role in HHG. In this review, we give an overview of recent developments on selection rules of HHG from atoms to molecules. For targets with rotational symmetries, if the rotational symmetries of targets and laser pulses are the M-fold (the projective symmetry on the laser polarization plane) and L-fold, the selection rules are Nk ± 1, where N is the the greatest common divisor of M and L. However, for asymmetric molecules in non-Born-Oppenheimer approximation, the situation is more complicated, where the nuclear dipole acceleration can produce even harmonics, but it is three orders lower than that of the electron. Hence, the HHG is mainly relied on the electronic dipole acceleration. In this case, the broken degree of system-symmetry dominates the generation of even-order harmonics.
}, issn = {2079-7346}, doi = {https://doi.org/10.4208/jams.042017.061517a}, url = {http://global-sci.org/intro/article_detail/jams/10430.html} }The high-order harmonic generation (HHG) has attracted much attention due to its wide application in attosecond science in last decades. The selection rules have also been broadly studied in experiments and theories since they play an important role in HHG. In this review, we give an overview of recent developments on selection rules of HHG from atoms to molecules. For targets with rotational symmetries, if the rotational symmetries of targets and laser pulses are the M-fold (the projective symmetry on the laser polarization plane) and L-fold, the selection rules are Nk ± 1, where N is the the greatest common divisor of M and L. However, for asymmetric molecules in non-Born-Oppenheimer approximation, the situation is more complicated, where the nuclear dipole acceleration can produce even harmonics, but it is three orders lower than that of the electron. Hence, the HHG is mainly relied on the electronic dipole acceleration. In this case, the broken degree of system-symmetry dominates the generation of even-order harmonics.