Time- and frequency-resolved coherent anti-Stokes Raman scattering spectroscopy with sub-$25fs$ laser pulses

In general, many different diagrams can contribute to the signal measured in broadband four-wave mixing experiments. Care must therefore be taken when designing an experiment to be sensitive to only the desired diagram by taking advantage of phase matching, pulse timing, sequence, and the wavelengths employed. We use sub-$25fs$ pulses to create and monitor vibrational wavepackets in gaseous iodine, bromine, and iodine bromide through time- and frequency-resolved femtosecond coherent anti-Stokes Raman scattering (CARS) spectroscopy. We experimentally illustrate this using iodine, where the broad bandwidths of our pulses, and Boltzmann population in the lower three vibrational levels conspire to make a single diagram dominant in one spectral region of the signal spectrum. In another spectral region, however, the signal is the sum of two almost equally contributing diagrams, making it difficult to directly extract information about the molecular dynamics. We derive simple analytical expressions for the time- and frequency-resolved CARS signal to study the interplay of different diagrams. Expressions are given for all five diagrams which can contribute to the CARS signal in our case.