High-order-harmonic generation in gas with a flat-top laser beam

We present experimental and numerical results on high-order-harmonic generation with a flat-top laser beam. We show that a simple binary tunable phase plate, made of two concentric glass plates, can produce a flat-top profile at the focus of a Gaussian infrared beam. Both experiments and numerical calculations show that there is a scaling law between the harmonic generation efficiency and the increase of the generation volume.

Figure 1

Experimental setup.

Figure 2

(a) Simulated intensity and (b) phase distribution of a flat-top beam around focus.

Figure 3

Measured infrared laser beam profile and lineout (black line) at focus using the small plate [(a) and (d): $\Phi =0$ and (b) and (e): $\Phi =0.8\pi$ rad] and the intermediate plate [(c) and (f): $\Phi =0.8\pi$ rad]. The dashed black line and the gray line in (d), (e), and (f) represent, respectively, the calculated intensity and phase.

Figure 4

Evolution of the harmonic signal (H13) with the dephasing. The black lines correspond to low laser energy (2 mJ) and the dashed red ones to high laser energy (6.5 mJ). The data from the simulations (lines) have been scaled to match the experimental values (open symbols).

Figure 5

Evolution of the harmonic signal with the focus position with respect to the jet for a Gaussian beam (squares) and a shaped beam (circles). The open symbols correspond to simulations (right vertical axis) and the filled ones to experimental data (left vertical axis). For all cases, the laser energy is 11 mJ. The shaped profile is flat top for $z_{\text{jet}}-z_{\text{lens}}=0$.

Figure 6

Comparison between HHG with a Gaussian beam (squares) and a flat-top beam (circles) for different laser energies. (a) Waist of the laser profile in the middle of the generation jet, from the simulations. (b) Laser intensity in the middle of the generation jet, from the simulations. (c) Optimal measured harmonic signal (right) and calculated number of photons per laser pulse (left). The filled circles and squared correspond to measurements, the empty ones to calculations. See text for details.