Extension of high-order harmonic cutoff frequency by synthesizing waveform of laser field via optimization of classical electron trajectory in laser field

We theoretically investigate the high-order harmonic generation by employing the strong-field approximation (SFA) and present a new approach to the extension of the high-order harmonic cutoff frequency via an exploration of the dependence of high-order harmonic generation on the waveform of laser fields. The dependence is investigated via a detailed analysis of the classical trajectories of the ionized electron moving in the continuum in the velocity-position plane. The classical trajectory consists of three sections (Acceleration Away, Deceleration Away, and Acceleration Back), and their relationship with the electron recollision energy is investigated. The analysis of classical trajectories indicates that, besides the final (Acceleration Back) section the electron recollision energy also relies on the previous two sections. We simultaneously optimize the waveform in all the three sections to increase the electron recollision energy, and an extension of the cutoff frequency up to I_p+20.26U_p is presented with a theoretically synthesized waveform of the laser field.