Attosecond soft X-ray high harmonic generation

Abstract

High harmonic generation (HHG) of an intense laser pulse is a highly nonlinear optical phenomenon that provides the only proven source of tabletop attosecond pulses, and it is the key technology in attosecond science. Recent developments in high-intensity infrared lasers have extended HHG beyond its traditional domain of the XUV spectral range (10-150 eV) into the soft X-ray regime (150 eV to 3 keV), allowing the compactness, stability and sub-femtosecond duration of HHG to be combined with the atomic site specificity and electronic/structural sensitivity of X-ray spectroscopy. HHG in the soft X-ray spectral region has significant differences from HHG in the XUV, which necessitate new approaches to generating and characterizing attosecond pulses. Here, we examine the challenges and opportunities of soft X-ray HHG, and we use simulations to examine the optimal generating conditions for the development of high-flux, attosecond-duration pulses in the soft X-ray spectral range. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Keywords: attosecond pulses; high harmonic generation; soft X-ray generation.

Figure 1.

Micro- and macroscopic aspects of HHG. (a) Energy-time structure of classical trajectories in HHG. Birth times and corresponding recollision are in blue, recollision times and energies are in red. Arrows link the corresponding birth and return times for the short and long trajectories. (b) Experimental SXR HHG spectrum as a function of He backing pressure, showing spectral shaping as macroscopic parameters are changed. (Online version in colour.)

Figure 2.

Laser field intensity on axis at the centre of the harmonic target for a pulse of 550 μJ and CEP = 0 focused 1.4 mm after the target, which is filled with 2 bar of helium. Fits to three different half-cycles are also shown (coloured dashed lines), where the half-cycle used for the fit is indicated by the coloured arrow. The three half-cycles correspond to timings of −9 fs, 0 fs and 9 fs at the entrance of the medium. Plasma-induced blue-shifts cause deviation between the fits and the underlying driving field at times after the fitted peak; for looser focusing or driving pulse energies, the quality of the fit over larger time spans improves. (Online version in colour.)

Figure 3.

(a) Peak intensity and (b) short-trajectory phasematching maps for the three most important half-cycles (columns) for 350 eV photon emission from 4 bar of helium when a pulse of 550 μJ and CEP = 0.3π is focused 1.4 mm after the target. The corresponding times of the half-cycles relative to the driving field envelope before the target are indicated above, and the dashed blue lines indicate the extent of the gas target. (Online version in colour.)

Figure 4.

Peak intensity (a) and phasematching maps for the short (b) and long (c) trajectories for harmonic emission at 350 eV from the half-cycle cut-off at −3 fs, under identical conditions as in figure 3. (Online version in colour.)