Anisotropic coherence induced nonuniform amplification in N +2

The continuous progress in N ⁺₂ lasing recently stimulates a great deal of interest in nonlinear and quantum optics of molecular ions, while a complete description of the ionic polarization is still lacking to date. In this work, we are dedicated to constructing the fundamental ionic polarization theory where several ubiquitous strong-field processes including ionization, electronic couplings and molecular alignment jointly determine the spatial arrangement of ions. With the model, the elusive polarization of N ⁺₂ lasing can be well interpreted. Our results show that the different electronic transition rules for strong-field ionization and resonant couplings result in peculiar population distributions of various electronic states of N ⁺₂ in space. Meanwhile, the spatial nonuniformity of population distribution can be aggravated or mitigated during field-free evolutions of coherent molecular rotational wave packets. Furthermore, when a follow-up resonant seed pulse interacts with the prepared ionic system, the anisotropic quantum coherence determining the polarization of subsequent N ⁺₂ lasing can be established. The qualitative agreement between experiments and simulations confirms the validity of the proposed model. The findings provide critical insights into the polarization and radiation mechanisms of molecular ions constructed via ultrafast laser pulses.