Spectrogram representation of pulse self compression by filamentation

We report on numerical simulations and experiments of pulse self-compression by filamentation. Spectral and temporal evolution during ultrashort-pulse laser filamentation can be intuitively represented using spectrograms, which display spectra at different time delays of a gate pulse. This representation makes evident the features of self-compression by filamentation, namely spectral broadening and pulse shortening. In addition, it allows for an analysis of the spectral phase during the nonlinear propagation. In our simulations we observe occurrence of negative chirp over a few cm before the shortest pulse is obtained during filamentation; this provides an important basis for the understanding of the mechanisms leading to self-compressed filaments. We attribute the negative chirp to spatio-temporal reshaping due to the competition between self-phase modulation and group velocity dispersion. We show that the plasma induced dispersion plays a minor role in establishing the negative chirp.