Divergence Control of High-Harmonic Generation

We show that the divergence of extreme ultraviolet pulses from high-harmonic generation, which is directly linked to the shape and size of the refocused beam, can be controlled by the relative delay between the fundamental and its intense orthogonally polarized second harmonic in two-color high-harmonic generation. We find that the divergence is minimized close to the delays where the number of emitted photons is maximized. These findings are rationalized as the suppression and enhancement of long and short electron trajectories as a function of the phase of the two-color laser field, respectively. The orthogonally polarized second harmonic introduces a lateral-momentum component that can select one trajectory, whereas it deflects the other. At the same time, the second harmonic profoundly modifies the tunnel-ionization process that initiates high-harmonic generation, which provides another trajectory gate. Our scheme for controlling the divergence facilitates imaging and metrology of embedded structures through the associated reduction of the focus size. In addition, the reduction of the focus size is beneficial for extreme ultraviolet nonlinear optics and spectroscopy.