## 3 Results and Discussion  
A series of spectra measured at different time delays between the two pump pulses with total energy of 2 mJ, is shown in Figure 2. The spectra were measured with time delay steps of 0.333 ps. The two strong pump beams are not shown on this figure. The lowest frequency line shown is the first anti-Stokes order. The spectral intensity is color coded, such that the lowest intensities are light blue and the most intense is dark red. The spectra shown in Figure 2 display a number of interesting features. First the total number of Raman orders is maximized when a positive time delay of 667 fs is applied. With a delay of two thirds of the pulse duration, the intensity in the pulse overlap region is greatly reduced and yet the nonlinear MRG process has been increased. With a positive delay, the instantaneous frequency separation of the two pumps is less than the Raman frequency. This result of increased orders for a slight red detuning of the pump beams agrees with the results obtained by [PERSON] and coworkers, which were taken in the adiabatic regime [10]. It is surprising that pulse durations of just 1 ps would display the same behavior as the adiabatic case. With the time delay increased beyond 1 ps, the number of orders decreases most likely because the intensity of the pulses in the temporal overlap region has further decreased, but it could also indicate that there is an optimum red-detuning. Again as in the adiabatic case, there is no increase in orders for pump frequency separation greater than the Raman transition, which is given in our case for the negative time delays. The decrease in number of orders at increased time delay is more pronounced for negative time delays, indicating that for blue detuning, there is no resonant enhancement to counter the reduced nonlinearity due to the lower overlap intensity. Secondly, if the red-shifted shoulders were due to non-resonant four-wave mixing, we would expect a plot of MRG spectra as a function of time delay to show the Raman orders as vertical lines and the peaks from non-resonant four-wave mixing would be sloped lines, where the slope would be given by the chirp rate. This is not what we observe. When the time delay is negative, only the vertical lines appear. The spectral orders remain narrow peaks separated by the Raman frequency until zero time delay. At a positive time delay of 667 fs, not only is the number of orders maximized, but also the orders themselves are maximally broadened. The broadening is not linearly dependent on the time delay as would be expected with non-resonant four-wave mixing. The spectral orders do not simply broaden but appear to become double peaked, with a narrow line remaining at the Raman transition and then a broader peak to the red side. The frequency of the red-shifted spectral peak does not vary linearly with pulse delay. We need to look at how a two-photon Rabi frequency shift caused by linearly chirped Gaussian pulses would change with time delay between the two pulses. The Rabi  
Figure 2: The multi-frequency Raman generation (MRG) spectra are shown for two positively chirped pump pulses with total energy of 2 mJ as a function of time delay between the two pulses. frequency has two terms. The second term is the detuning, \(\Delta\), which has three terms: the single color Stark shift which is dependent on the term I, is independent of time delay as is the detuning between the peak frequencies, \(\delta\omega\), which in our case is set to zero leaving only the d0/dt term which increases linearly in magnitude with time delay. The first term in the Rabi frequency is given by the overlap of the amplitudes V\({}_{\mathrm{j}}\)V*\({}_{\mathrm{j-1}}\) which decreases in magnitude with time delay. The decrease is not linear with delay but certainly has the opposite trend to the detuning and so somewhat balances the time dependence of the detuning term.