Rovibrational Wave-Packet Dispersion during Femtosecond Laser Filamentation in Air

An impulsive, femtosecond filament-based Raman technique producing high quality Raman spectra over a broad spectral range (1554.7--4155 cm) is presented. The filamentation dynamics of a loosely focused high-energy femtosecond pulse in air shortens the pulse, leading to impulsive excitation of all vibrational and rotational Raman-active modes present in the filament channel. For particular Raman modes, impulsive excitation requires pulse duration on the order of the characteristic oscillation periods of the mode, thus revealing the degree of pulse-shortening. The temperature of gas-phase molecules can be recovered by measuring the dispersion of the impulsively excited vibrational wave-packets using a delayed narrow-band pulse. This technique reveals that the initial rovibrational temperature in the filament is 300 K for both N$_{2}$ and O$_{2}$. The temperature-dependent wave-packet dynamics are interpreted using an analytic anharmonic oscillator model. The wave-packets reveal a 1/e dispersion time of 3.9 ps for N$_{2}$ and 2.8 ps for O$_{2}$. Pulse self-shortening up to 8 fs temporal features within the filament is directly measured by impulsive vibrational excitation of H$_{2}$.