An In-Situ Method for the Reconstruction of Ultrashort and Ultrabroadband Synthesized Light Transients

We present a novel method for the reconstruction of ultrashort and ultrabroadband synthesized light transients generated by a parametric waveform synthesizer [1]. Our method relies on the measurement of the third-order nonlinear response ( $S_{NL}$ ) of a noble gas target normally used for high-harmonic generation (1 mm length at 0.1-1 bar) while scanning the relative delay $\tau$ between the two constituent ultrabroadband pulses $(E_{1}(t)$ and $E_{2}(t))$ that are synthesized (c.f. Fig. 1(d)). The recorded spectrogram can be described by $S_{NL}(f,\tau)\propto T(f)\vert FT[(E_{1}(t)+E_{2}(t+\tau))^{3}]\vert^{2}$ , where $T(f)$ describes a spectral transfer function and $FT$ denotes the Fourier transform.