Coherence control in high-order harmonic generation with Laguerre-Gaussian beams

We investigate phase matching for high-order harmonic generation with linearly polarized Laguerre-Gaussian (LG) beams with nonzero orbital angular momentum (OAM). We compare the conditions for efficient phase matching for LG beams with those of Gaussian beams. In particular, we show how the OAM of the incident beams affects the phase-matching conditions for the short and long trajectories that arise from the saddle-point approximation of the dipole moment. Thereby we illustrate that the coherence length for the short trajectories decreases for LG beams near the focus compared to Gaussian beams, whereas efficient phase matching can be achieved before and behind the focus. Furthermore, we demonstrate that the coherence length for the long trajectory behind the focus plane can be controlled by the OAM. This paper provides a route for the experiment in order to have good coherence control to enhance the conversion efficiency for high-order harmonic generation with beams carrying OAM.