Strong-field-assisted x-ray second harmonic generation

We theoretically demonstrate x-ray second harmonic generation (SHG) with strong-field-driven high harmonic generation (HHG) from core electrons in gas-phase atoms, highlighting its potential as a powerful spectroscopic tool for studying atomic and molecular systems. Our simulations confirm the generation of HHG with x-ray SHG (HHG-XSHG) from atomic core electrons through the rescattering of electrons from x-ray two-photon excitation and subsequent tunneling ionization in an optical laser field. The resulting HHG-XSHG spectrum features a broadband multipeak structure and a distinct spectral cutoff in the x-ray regime. These findings indicate that HHG-XSHG is a valuable technique for probing core-electron dynamics, generating attosecond x-ray pulses, and exploring nonlinear interactions, effectively merging laser-driven attosecond technology with nonlinear x-ray methodologies provided by x-ray free-electron lasers.