Abstract
We propose a novel method to determine the complex amplitude of each eigenfunction composing a vibrational wavepacket of / molecular ions evolving with a ~10 fs time scale. We find that the two-dimensional spectrogram of the kinetic energy release (KER) of H(+)/D(+) fragments plotted against the time delay of the probe pulse is equivalent to the spectrogram used in the frequency-resolved optical gating (FROG) technique to retrieve the complex amplitude of an ultrashort optical pulse. By adapting the FROG algorithm to the delay-KER spectrogram of the vibrational wavepacket, we have successfully reconstructed the complex amplitude. The deterioration in retrieval accuracy caused by the bandpass filter required to process actual experimental data is also discussed.