Tunable high-harmonic generation by chromatic focusing of few-cycle laser pulses

In this work we study the impact of chromatic focusing of few-cycle laser pulses on high-order-harmonic generation (HHG) through analysis of the emitted extreme ultraviolet (XUV) radiation. Chromatic focusing is usually avoided in the few-cycle regime, as the pulse spatiotemporal structure may be highly distorted by the spatiotemporal aberrations. Here, however, we demonstrate it as an additional control parameter to modify the generated XUV radiation. We present experiments where few-cycle pulses are focused by a singlet lens in a Kr gas jet. The chromatic distribution of focal lengths allows us to tune HHG spectra by changing the relative singlet-target distance. Interestingly, we also show that the degree of chromatic aberration needed for this control does not degrade substantially the harmonic conversion efficiency, still allowing for the generation of supercontinua with the chirped-pulse scheme, demonstrated previously for achromatic focusing. We back up our experiments with theoretical simulations reproducing the experimental HHG results depending on diverse parameters (input pulse spectral phase, pulse duration, and focus position) and proving that, under the considered parameters, the attosecond pulse train remains very similar to the achromatic case, even showing cases of isolated attosecond pulse generation for near-single-cycle driving pulses.

Figure 1

HHG $z$ scans for chromatic and achromatic cases. HHG in Kr depending on focusing system-target distance $z$ ($z=0$ mm stands for focus on the gas jet, $z<0$ for focus before the gas jet, and $z>0$ for focus after the gas jet) for three different driving pulses (shown in Fig. 2): (a), (d) 5.2-fs FWHM pulse (Fourier limit, 3.35 fs) with residual third-order dispersion; (b), (e) 5.3-fs FWHM pulse (Fourier limit, 4.9 fs); and (c), (f) 3.3-fs FWHM pulse (Fourier limit, 2.9 fs). The top row (a)–(c) corresponds to focusing with a silver spherical mirror ($f=50$ cm), and the bottom row (d)–(f) corresponds to focusing with a BK7 singlet ($f=30$ cm).

Figure 2

Characterization of the driving pulses. Left column: Spectra (thick solid blue line) and spectral phase (thin dashed green line); right column: time-dependent electric field amplitude (thin dashed red line) and envelope (thick solid blue line) of the three pulses used for the HHG $z$ scan shown in Fig. 1. Top row shows a pulse with higher dispersion order, and corresponds to Figs. 1 and 1. Middle row displays a pulse closer to its Fourier-limit duration, where the spectral phase is flatter than in the previous case, and corresponds to Figs. 1 and 1. Bottom row presents a shorter pulse, lasting less than 1.5 cycles, which corresponds to Figs. 1 and 1. Specified pulse durations correspond to the FWHM in intensity.

Figure 3

CEP dependence of the chromatic HHG $z$ scan. HHG $z$ scan in Kr (backing pressure of 6 bar) as a function of singlet-target distance in the few-cycle pulse regime (pulse energy of 56 $\mu \mathrm{J}$; pulse duration, 3.6 fs FWHM; Fourier limit, 2.9 fs FWHM) for different values of CEP: (a) ${\varphi }_0$, (b) ${\varphi }_0+\pi /4$, (c) ${\varphi }_0+\pi /2$, and (d) ${\varphi }_0+3\pi /4$.

Figure 4

HHG dispersion scans with chromatic focusing. HHG performed in krypton in three different cases: (a) pulse duration of 5.3 fs and energy of 80 $\mu \mathrm{J}$, (b) pulse duration of 4 fs and 50 $\mu \mathrm{J}$, and (c) pulse duration of 3.3 fs and 50 $\mu \mathrm{J}$. Focus is placed 2 mm after the gas jet in (a) and (b), while it is placed at the gas jet position in (c). Pulse durations are measured at 0 $\mu \mathrm{m}$ of BK7 insertion. Color axis is normalized to the maximum signal measured in each scan.

Figure 5

Numerical simulation of HHG with chromatic focusing. Dispersion scan of far field on-axis HHG for Fourier limited pulse of 4.8 fs FWHM focused with an $f=40$ cm singlet lens. Single-atom response and collective response including propagation effects are considered.

Figure 6

HHG dispersion-scan impact of focusing scheme and pulse structure. Dispersion scan of far field on-axis HHG for Fig. 2 pulse focusing with (a) an $f=40$ cm singlet at 2 mm before the gas jet, (b) the same pulse focused with a spherical mirror ($f=40$ cm) at 2 mm after the gas jet, and (c) a 2.9-fs FWHM Fourier limit pulse focusing with a $f=40$ cm singlet at 2 mm before the gas jet. Maximum peak intensities are estimated to be (a) $2.5\times {10}^{14} \mathrm{W}/{\mathrm{cm}}^2$ for chromatic focusing and (b) $3.5\times {10}^{14} \mathrm{W}/{\mathrm{cm}}^2$ for the achromatic case.

Figure 7

Attosecond pulse emission along the HHG dispersion scan. Attosecond pulse emission corresponding to (a) Fig. 6, (b) Fig. 6, and (c) Fig. 6 HHG dispersion scans. The temporal profile in each case is obtained by means of Fourier transforming the simulated spectrum after simulating the propagation through the aluminum filter.