Temporal characterization of attosecond wave forms in the sub-optical-cycle regime

We present a temporal characterization of sub-optical-cycle extreme ultraviolet radiation generated in a hollow-core waveguide. This generation scheme permits the use of relatively long $13\text{−}\mathrm{fs}$ driving laser pulses to generate sub-optical-cycle bursts of high-order harmonic light. Using two-color cross-correlation and phase retrieval techniques, we extract the extreme ultraviolet wave form and show that it consists of chirped $470\text{−}\mathrm{as}$ bursts, spaced by $\sim 1.3\mathrm{fs}$, within a $1.4\text{−}\mathrm{fs}$ intensity envelope. The radiation is spectrally narrow and energy tunable, making it a useful tool to investigate state-selective molecular and materials dynamics.

Figure 1

(Color online) (a) Experimental photoelectron spectrum as a function of time delay between the EUV and IR pulses, when these pulses are focused simultaneously into He gas. (b) FROGCRAB simulation of the data in (a) based on theory presented in [14]. (c) FROGCRAB trace obtained from a generalized projections (GP) algorithm. (d) EUV spectrum of the pulse that generated the photoelectron spectrum shown in (a). The energy tuning range is indicated.

Figure 2

(Color online) Simulated FROGCRAB data, when higher dispersion orders are artificially introduced into the EUV field: (a) second-order $D2$, (b) third-order $D3$, and (c) fourth-order $D4$ dispersion. Intuitively, the sideband shape shows the group delay of the EUV light, indicated by black lines.

Figure 3

(Color online) rms deviation between the FROGCRAB simulation and the experimental cross-correlation trace as the parameters of the simulated pulse are varied: (a) Varying the linear chirp $D2$, (b) varying the quadratic chirp $D3$, and (c) varying the EUV pulse envelope. (d) Experimental FROGCRAB data, (e) FROGCRAB data simulated using the optimized values of $D2$, $D3$ and EUV pulse envelope of $1.4\mathrm{fs}$. (d), (e) are zoom-ins of the centers of Figs. 1a, 1b. (f), (g) Simulated FROGCRAB data using the optimized values of $D2$ and $D3$, but when the EUV pulse envelope is changed from the optimized value of $1.4\mathrm{fs}\text{to}1\mathrm{fs}$ and $2.5\mathrm{fs}$, respectively. These traces do not match the experimental data.

Figure 4

(Color online) (a) Chirped EUV electric field envelope vs time: (Dashed green line) obtained from optimized fit shown in Fig. 1b, magnitude (solid blue line) and phase (solid blue line) retrieved from a GP algorithm, and (dotted red line) transform-limited pulse for comparison. (b) (Solid blue line, dashed green line) EUV intensities vs time corresponding to the chirped pulses shown in (a), (dash-dotted green line) intensity of a double pulse with the same envelope, and (dotted black line) intensity envelope of the extracted EUV field.