Effect of spin-orbit coupling on high-order harmonic generation in atoms.

We present an ab initio investigation of the influence of spin-orbit coupling (SOC) on high-order harmonic generation (HHG) in hydrogen atoms by numerically solving the time-dependent Schrödinger equation including the SOC term (TDSE-SOC). We find that the SOC does not affect the HHG spectra produced by the initial ground state. However, for the excited state 2P, and its spin-split 2P_3/2 and 2P_1/2 states which are superpositions of m_l = 0 and m_l = 1 wave functions, the harmonic yields generated from the above three states vary significantly. We developed a modified strong-field approximation theory incorporating the spin-split states to analyze the SOC effect on HHG spectra. Considering the depletion of bound states, the simulation results are qualitatively consistent with the TDSE calculations. Analysis indicates that the m_l = 0 component in the spin-split 2P states predominantly contributes to harmonic yields, and the m_l = 1 component has a non-negligible influence on lower-energy harmonics in a linearly polarized laser field.