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We study the effect of Coulomb potential on high-order harmonic generation(HHG) numerically and analytically. We focus on the influence of Coulombpotential on emission times of HHG associated with specific electrontrajectories. By using a numerical procedure based on numerical solution oftime-dependent Schr\"{o}dinger equation (TDSE) in three dimensions, we extractthe HHG emission times both for long and short electron trajectories. Wecompare TDSE predictions with those of a Coulomb-modified model arising fromstrong-field approximation (SFA). We show that the Coulomb effect inducesearlier HHG emission times than those predicted by the general SFA modelwithout considering the Coulomb potential. In particular, this effectinfluences differently on long and short electron trajectories and is moreremarkable for low-energy harmonics than high ones. It also changes the HHGamplitudes for long and short electron trajectories. We validate ourdiscussions with diverse laser parameters and forms of Coulomb potential. Ourresults strongly support a four-step model of HHG.

Coulomb Effects on time-trajectory-resolved high-order harmonic generation