Fig. 1: Schematic diagram of basic principle for SC generation.

Following injection of ions through ionization of neutral molecules, the dynamic Stark shift driven by an intense mid-infrared laser forces various vibrational energy levels of \({B}^{2}{\Sigma }_{{{{{{\rm{u}}}}}}}^{+}\) and \({X}^{2}{\Sigma }_{{{{{{\rm{g}}}}}}}^{+}\) states of \({{{{{{\rm{N}}}}}}}_{2}^{+}\) to shift towards contrary directions. These instantaneously varying energy levels are indicated with shaded regions. The continual variation of transition energies with the driver laser envelope triggers dynamic five-photon resonances in multiple ionic transitions. The five-photon resonances for two special cases (i.e., without field and maximum field) are indicated with red arrows. Multi-channel five-photon resonances cause dipole oscillations and enhancement of nonlinear polarization of \({{{{{{\rm{N}}}}}}}_{2}^{+}\). The coherent polarization leads to the laser-assisted continuum emission (LACE) due to continuously changing transition energies within the laser pulse as well as some narrowband \({{{{{{\rm{N}}}}}}}_{2}^{+}\) characteristic radiations due to the free-induction decay (FID) of dipole oscillations after the laser pulse. These signals contribute to SC radiation together with five harmonic generation (FHG). The typical SC spectrum is shown on the right, in which the relative sizes of transition dipole moments are denoted with colored lines. (See Supplementary Movie 1 for more details).