Tunable spectral shift of high-order harmonic generation in atoms using a sinusoidally phase-modulated pulse

High-order harmonic generation (HHG) from an atom illuminated by a sinusoidally phase-modulated pulse is investigated by solving the time-dependent Schrödinger equation. The spectral shift that occurs in atomic HHG can be achieved easily using our laser pulse. It is shown that the photon energy of the generated harmonics is controllable within the range of 1 eV. The shift of the frequency peak position is rooted in the asymmetry of the rising and falling parts of the laser pulse. We also show that by varying the phase parameters in the frequency domain of the laser one can adjust and control the shift in atomic harmonic spectra.