Extension of the cut-off in high-harmonic generation using two delayed pulses of the same colour

We demonstrate a novel technique for an extension of the cut-off frequency in high-harmonic generation using a shaped field, consisting of two delayed pulses, identical in all parameters except a carrier envelope phase shift of π. We obtain high harmonics up to an energy of 5.5Up + Ip, surpassing the conventional limit of 3.17Up + Ip. For high intensities approaching the threshold for barrier suppression ionization, beyond which no harmonics are generated, this mechanism acquires practical importance as a means to overcome the limit imposed by saturation. We analyse the underlying mechanism using both classical and quantum approaches, and highlight the role of the shaped field in modifying the electron trajectories in the continuum to enhance the collection of kinetic energy from the driving field. Of greatest importance are the trajectories describing electrons ionized across the first peak of the laser field which receive the enhanced kinetic energies responsible for the cut-off extension above the conventional limit. Interestingly, the most energetic trajectories do not contribute to the harmonic cut-off in the single pulse case. We conclude with a discussion of the sub-cycle structure of the emitted harmonic radiation and possible applications of the technique.