Extreme Ultraviolet Interferometer Using High-Order Harmonic Generation from Successive Sources

We present a new interferometer technique whereby multiple extreme ultraviolet light pulses are generated at different positions within a single laser focus (i.e., from successive sources) with a highly controllable time delay. The interferometer technique is tested with two generating media to create two extreme ultraviolet light pulses with a time delay between them. The delay is found to be a consequence of the Gouy phase shift. Ultimately the apparatus is capable of accessing unprecedented time scales by allowing stable and repeatable delays as small as 100 zs.

Figure 1

(a) A schematic depicting the principle of operation of the HHG interferometer. Two gas jets are placed perpendicular to one another in the focus of few-cycle infrared laser. (b) Measured beam spot size (circles) and fit to Gaussian beam propagation theory (line). (c) Estimated Gouy phase from the fit of panel (b). Positioning the two gas jets at different distances along the focus causes the carrier-envelope phase of the driving laser to be shifted between interacting with gas jet 1 (d) and gas jet 2 (e). This results in the electron ionization and return time shifting with the Gouy phase. The small delay time $\Delta t$ between the electrons recombining gives a phase shift between the two successively generated XUV photons.

Figure 2

(a) A reference spectrum showing five of the harmonics captured (21st to the 29th) when only gas jet 2 was producing harmonics. (b) The degree of coherence of the spectrum as the gas jet separation is increased. Each harmonic undergoes destructive and then constructive interference as represented by the degree of coherence approaching 0 and then 1, respectively. (c) The degree of coherence at the white dotted line of (b); error bars are measured data points including their uncertainty while the line is included as a guide to the eye.

Figure 3

The position at which the HHG radiation was found to constructively interfere (called the revival distance, here) was determined from the experimental data. Plotted here are the inverse of these positions versus the harmonic order of interest (blue error bars are data). The green-dashed line represents the theoretical prediction of the inverse revival distance if only the Gouy phase is considered. The red-solid line is a curve fit to the data using Eq. (7) with the derivative of the Gouy and action phases as fitting parameters.

Figure 4

The Allan deviation of timing resolution for the Gouy phase interferometer. The timing stability is better than 100 zs for averaging times between 8 and 30 s.