Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field

The time-frequency properties of high-order harmonic generation in the presence of a static electric field are investigated. It is found that the quantum paths contributing to the harmonics can be controlled by adding a static electric field. The highest photon energies of harmonics emitted in the adjacent half-cycles of the laser field are modulated by the static electric field, and then an attosecond pulse train with one burst per optical cycle can be extracted. For the ratio between the laser and the static field of 0.39, the harmonic spectrum is extended to I-p + 9.1U(p), and the harmonics above I-p + 0.7U(p) are emitted almost in phase. The phase-locked harmonics covered by a broad bandwidth are produced, and then a regular attosecond pulse train with a pulse duration of 80 as is generated.