Interferometry of Attosecond Pulse Trains in the Extreme Ultraviolet Wavelength Region

The temporal coherence of an attosecond optical field in the extreme ultraviolet wavelength region can be defined in terms of the extent of interference in time domain. We successfully measured this phenomenon both with and without spectral decomposition. We also report the results of using this approach to directly observe both symmetry and symmetry breaking of interference fringes in an attosecond pulse train.

Figure 1

Schematic figure of the experimental setup. We show the modeled beam profile on each principal plane.

Figure 2

(a) Left-hand side: interference trace of each harmonic field generated from Ar gas. The harmonic fields range from the 15th (H15) to the 33rd (H33) orders. Right-hand side: enlarged view of the traces. Cross markers correspond to the sampling points of the scanned delay. They exhibit the interference fringes. The visibility of the fringes for each trace is typically 0.75–0.9. (b) Magnitude of the Fourier transform of each interferometric trace. The spectrum obtained from the Fourier transform (shaded area) is compared with that directly measured using an XUV spectrograph (dotted curve). The intensities are arbitrarily normalized.

Figure 3

(a) Interference trace of the APT generated from Ar gas (top row) and a magnified view (bottom row). Cross markers correspond to the sampling points of scanned delay. (b) Magnitude of the Fourier transform of the APT interferometric trace. Each HH spectrum observed with the XUV spectrograph is shown as dotted curve. The intensity is arbitrarily normalized. The observed intensity distribution in the XUV spectrograph is shown in the inset.

Figure 4

Interference trace of the APT generated from a Kr gas medium under the “high” intensity condition of the driving laser field (upper part), and a magnified view compared with that generated under the “optimal” conditions for maximum HH yield (lower part). We estimate the coherence time of the central pulse envelope with the FWHM to be 262 attoseconds.

Figure 5

Magnitude of the Fourier transform of interferometric trace of the APT depicted as blue lines and cross markers in Fig. 4 (blue curve with shaded area) and that depicted as brown lines and circles in Fig. 4 (brown curve). The scales of the magnitudes are arbitrarily adjusted. The distinct peaks on both curves corresponds to the spectra of HH fields ranging from the 13th order to 25th order. The shift of each peak frequency on the blue curve relative to that on the brown curve is shown as dark blue lines and solid circles in the inset. The reciprocal intensity at each harmonic order, calculated via the saddle point analysis of the dipole phase based on SFA, is also shown as green lines and solid squares in the same inset.