Frequency-resolved optical gating for complete reconstruction of attosecond bursts

We describe a method for the complete temporal characterization of attosecond extreme ultraviolet (xuv) fields. An electron wave packet is generated in the continuum by photoionizing atoms with the attosecond field, and a low-frequency dressing laser pulse is used as a phase gate for frequency-resolved-optical-gating-like measurements on this wave packet. This method is valid for xuv fields of an arbitrary temporal structure, e.g., trains of nonidentical attosecond pulses. It establishes a direct connection between the main attosecond characterization techniques demonstrated experimentally so far, and considerably extends their scope, thus providing a general perspective on attosecond metrology.

Figure 1

(a) CRAB trace of a single 315 as pulse [full width at half maximum (FWHM) of intensity], having second- and third-order spectral phases (Fourier $\text{limit}=250$ as), gated by a Fourier-limited $6\text{−}\mathrm{fs}$ $800\mathrm{nm}$ laser pulse, of $0.5\mathrm{T}\mathrm{W}∕{\mathrm{cm}}^2$ peak intensity. The electrons are collected around $\theta =0$ with an acceptance angle of $\pm 30°$. (b), (c) A comparison of the exact as pulse and the laser-induced gate phase $\varphi \left(t\right)$ (full line) with the corresponding reconstructions (dots) obtained from the CRAB trace after 100 iterations of the PCGPA algorithm [20]. The gate modulus $\mid G\left(t\right)\mid$ is constant and equals to 1.

Figure 2

(a) CRAB trace at $\theta =0$ of a $12\text{−}\mathrm{fs}$-train of nonidentical as pulses, of period $T∕2=1.3\mathrm{fs}$, gated by a $30\text{−}\mathrm{fs}\text{−}800\mathrm{nm}\text{−}(T=2.6\mathrm{fs})$ laser pulse, of $0.05\mathrm{T}\mathrm{W}∕{\mathrm{cm}}^2$ peak intensity, assuming a spectrometer resolution of $100\mathrm{meV}$. The as pulses are shorter in the center of the train $(\approx 250\mathrm{as})$, than in the edges $(\approx 400\mathrm{as})$. The outer and inner sidebands are respectively labelled $S_o$ and $S_i$. (b) A comparison of the exact as train (red line) and the reconstruction (dotted blue line) obtained from the CRAB trace after 750 iterations of the PCGPA algorithm.

Figure 3

(a) CRAB trace at $\theta =0$ of a complex as field, whose spectrum (shaded curve) and spectral phase (red line) are shown in panel (b). The spectrum consists of discrete peaks spaced by $\approx 3\mathrm{eV}$ in its lower part, and a continuous component in its upper part. In (c) and (d), the exact intensity profile of the as field and the laser electric field (full lines) are compared to the ones retrieved from this trace (dots) after 300 iterations of PCGPA.